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xtended Kalman
Create constant-acceleration extended Kalman filter from detection report
Since R2021a
filter = initcaekf(detection) creates and initializes a constant-acceleration extended Kalman filter from information contained in a detection report. For more details, see Algorithms and trackingEKF
Initialize 3-D Constant-Acceleration Extended Kalman Filter
Create and initialize a 3-D constant-acceleration extended Kalman filter object from an initial detection report.
Create the detection report from an initial 3-D measurement, (-200;30;0) , of the object position. Assume uncorrelated measurement noise.
detection = objectDetection(0,[-200;-30;0],'MeasurementNoise',2.1*eye(3), ...
Create the new filter from the detection report and display its properties.
filter = initcaekf(detection)
filter =
trackingEKF with properties:
State: [9x1 double]
StateCovariance: [9x9 double]
StateTransitionFcn: @constacc
StateTransitionJacobianFcn: @constaccjac
ProcessNoise: [3x3 double]
HasAdditiveProcessNoise: 0
MeasurementFcn: @cameas
MeasurementJacobianFcn: @cameasjac
HasMeasurementWrapping: 1
MeasurementNoise: [3x3 double]
HasAdditiveMeasurementNoise: 1
MaxNumOOSMSteps: 0
EnableSmoothing: 0
Show the filter state.
ans = 9×1
Show the state covariance matrix.
ans = 9×9
2.1000 0 0 0 0 0 0 0 0
0 100.0000 0 0 0 0 0 0 0
0 0 100.0000 0 0 0 0 0 0
0 0 0 2.1000 0 0 0 0 0
0 0 0 0 100.0000 0 0 0 0
0 0 0 0 0 100.0000 0 0 0
0 0 0 0 0 0 2.1000 0 0
0 0 0 0 0 0 0 100.0000 0
0 0 0 0 0 0 0 0 100.0000
Create 3D Constant Acceleration EKF from Spherical Measurement
Initialize a 3D constant-acceleration extended Kalman filter from an initial detection report made from an initial measurement in spherical coordinates. If you want to use spherical coordinates, then
you must supply a measurement parameter structure as part of the detection report with the Frame field set to 'spherical'. Set the azimuth angle of the target to $4{5}^{\circ }$, the elevation to $2
{2}^{\circ }$, the range to 1000 meters, and the range rate to -4.0 m/s.
frame = 'spherical';
sensorpos = [25,-40,-10].';
sensorvel = [0;5;0];
laxes = eye(3);
Create the measurement parameters structure. Set 'HasVelocity' and 'HasElevation' to true. Then, the measurement vector consists of azimuth, elevation, range, and range rate.
measparms = struct('Frame',frame,'OriginPosition',sensorpos, ...
'OriginVelocity',sensorvel,'Orientation',laxes,'HasVelocity',true, ...
meas = [45;22;1000;-4];
measnoise = diag([3.0,2.5,2,1.0].^2);
detection = objectDetection(0,meas,'MeasurementNoise', ...
detection =
objectDetection with properties:
Time: 0
Measurement: [4x1 double]
MeasurementNoise: [4x4 double]
SensorIndex: 1
ObjectClassID: 0
ObjectClassParameters: []
MeasurementParameters: [1x1 struct]
ObjectAttributes: {}
filter = initcaekf(detection);
Display the state vector.
Input Arguments
detection — Detection report
objectDetection object
Detection report, specified as an objectDetection object.
Example: detection = objectDetection(0,[1;4.5;3],'MeasurementNoise', [1.0 0 0; 0 2.0 0; 0 0 1.5])
Output Arguments
filter — Extended Kalman filter
trackingEKF object
Extended Kalman filter, returned as a trackingEKF object.
• The function initializes a trackingEKF object with a constacc motion model and a cameas measurement model. The state of the filter is defined as [x; v[x]; a[x]; y; v[y]; a[y]; z; v[z]; a[z]], in
which x, y, z are the position coordinates, v[x], v[y], v[z] are the corresponding velocities, and a[x], a[y], a[z] are the corresponding accelerations.
• The detection input can be an objectDetection object of Cartesian or spherical measurement:
□ For a Cartesian measurement,
☆ By default, the function assumes the measurement is a 3-D position measurement ([x; y; z]). The function uses the position measurement to initialize the position state of the filter and
sets the velocity and acceleration components of the filter state as 0. For the state error covariance matrix of the filter, the function sets the position components same as those of the
measurement noise matrix and sets the velocity and acceleration components as 100 m^2/s^2 and 100 m^2/s^4, respectively. The function sets all the cross-components of the state error
covariance matrix as 0.
☆ You can also use a 6-D measurement ([x; y; z; v[x]; v[y]; v[z]]) by specifying the MeasurementParameters property of the objectDetection object. Specify the HasVelocity field of the
measurement parameter structure as true so that the initcaekf function can recognize the 6-D measurement. In this case, the position and velocity components of the state and the state
error covariance matrix are the same as the measurement and measurement noise matrix of the detection, respectively. The function sets the acceleration states as 0 and sets the
acceleration components of the state error covariance matrix as 100 m^2/s^4.
□ For a spherical measurement, you must specify the Frame field in the MeasurementParameters property of the objectDetection object as "Spherical". Also, use the MeasurementParameters property
to specify if the detection has azimuth, elevation, range, and range rate. A full spherical measurement has four elements [az, el, r, rr], representing azimuth in degrees, elevation in
degrees, range in meters, and range-rate in meters per second, respectively. Some of the four elements can be missing.
☆ If the detection has elevation, the function uses the elevation measurement and its covariance to construct the position components of the filter state and state error covariance after
performing coordinate transformation from the spherical frame to the Cartesian frame. Without elevation, the function sets the elevation as 0 and set its covariance as 180^2/12 deg^2
before performing the coordinate transformation.
☆ If the detection has range-rate, the function uses the range-rate measurement and its covariance to construct the velocity components of the filter sate and state error covariance. The
function also assumes the velocity covariance of the cross-range direction is 100 m^2/s^2. Without range-rate, the function sets the velocity states of the filter as 0 and its
corresponding covariances as 100 m^2/s^2.
□ The function sets the acceleration component of the filter state as 0 and set the acceleration components of the state error covariance matrix as 100 m^2/s^4. The function sets all the
cross-components (for example between position and velocity) of the state error covariance matrix as 0.
□ You can use other fields of the MeasurementParameters property of an objectDetection object, such as OriginPosition and OriginaVelocity, to further specify the measurement coordinates.
• The function models the process noise as non-additive and computes the process noise matrix assuming a unit acceleration increment per step following the Weiner-sequence acceleration model.
• The measurement noise matrix in the initialized filter is the same as that in the detection.
• You can use this function as the FilterInitializationFcn property of a radarTracker object.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced in R2021a
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Lesson Tutor : Algebra Lesson Grade 9 Order of Operations - Lesson Tutor
Basic Algebra – Lesson 4
by Elaine Ernst Schneider
Objective(s): By the end of this lesson the student will be able to:
apply the order of operations to solve math equations.
Pre Class Assignment: Completion of Algebra Lesson 3
Resources/Equipment/Time Required:
In the first lesson, you learned that numbers and variables form sentences, or algebraic “expressions.” When you take information from a sentence and turn it into a mathematical expression, it is
called “translating.” In another lesson, you learned that when you write algebraic expressions, use +, -, and = signs; and for division, use / , the same way you know that when you see a fraction, it
means to divide the top number by the bottom number. Then, for multiplication, we learned to write the expression with no symbol or sign between them (such as 3a), with an X , or using parentheses.
The parenthesis is especially useful in longer problems such as (3y)(4-2x).
But what if there are no parentheses or brackets? How do you know which to do first? Add, divide, multiply? Which one?
When there are no other indications as to which computation to do first, mathematicians follow The Order of Operations rule. Multiply, Divide, Add, Subtract.
A good way to remember the Order of Operations is to think about My Dear Aunt Sally. The M is for multiply, the D in Dear is for Divide, the A is for Add, and the S in Sally is for subtract.
HINT: If the problem has only multiplication and division, then work from left to right.
HINT: If the problem has only subtraction and addition, then work from left to right.
Let’s Get Started:
13 – 2 X 5
If I just do the math from left to right, I would say 13 – 2 = 11. Then 11 times 5 = 55.
But the Order of Operations tells me to multiply first! So, 2 X 5 = 10. Then, I subtract 10 from 13 and get 3.
You can see that which order you choose makes a BIG difference in the answer! That’s why it’s important to follow the Order of Operations.
Now it’s time for you to try a few.
Assignment(s) including Answer key:
1. 10 – 4 + 3
2. 10 + 4 X 2
3. (5 X 4) -15 + 2
4. 12 – 2(3 + 1)
5. 18 + 2(3)
6. (12 – 2)(3 + 4)
7. 4 X 3 + 5
8. 24 – 6 +2
9. 24 – 6 X 2
10. 36/9 – 2
For Answer Key, Click Here
Pre-Requisite To: Basic Algebra – Lesson 5
For more Articles by this Author, Click Here
For more Lesson Plans in the Subject: Algebra, Click Here
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Rules - AZWL.orgRules
Setting Up:
Place your washer boards 10 feet apart on a fairly level surface. Measure 10ft from each of the front corners so boards are parallel. Place scoreboard in middle to the side. Six washers are provided,
three per player/team.
Initial Play:
Players must stand on the board when throwing without touching the ground and throw all three washers. On 2 vs 2 your team member will be on the opposite board.
Who Goes first: The player/team that scored the most points in the previous throw “has control” or “has honors” and has won the right to throw first in the next round. Once a player reaches 16, 19,
or 20 and can win with one throw they throw first, so your opponent has a chance to cancel the wining game point throw.
If there is no precedent on who should throw first and need help determining who will go first flip a washer, the tails side has numbers stamped into it.
Two-Player Game (1-on-1):
Each player will throw all three of their washers from the same side toward the opposite board. The first player will throw their three washers; the second player will then throw their three washers
to complete one round. After all of the washers have been thrown scores are notated and players will then move to the opposite board to continue play. All points count.
Team Game (2-on-2):
Team members will throw from opposite boards. The first player from Team One will throw their three washers; the first player from Team Two will throw their three washers to the same board. Mark
scores, then opposing players pick up washers, and proceed to throw from their side back and again mark scores.
Keeping Score:
The hole closest to you is worth 1 point, the middle hole is 2 and the furthest from you is 5 points. To score points the washer must fall into the hole and stay. “in and out doesn’t count.” If a
washer is knocked into a hole by an opponent, the points go to the player who originally threw the washer.
You have two scoring clips use the one to keep track of last rounds score, one to score this rounds score. This allows others to check your math.
Winning the Game:
The first player or team to reach exactly twenty-one points wins the game!
OR the first person to Throw 125 wins!!
“The Bust”
If a throw adds points to a score that exceeds 21 you just went “Bust” or you “Busted” or “Linskied” and your score goes ALL THE WAY back to zero. If the player/team goes over 21 points again, they
automatically lose the game on the second bust.
“Game Point Cancellations”
Every point counts and cannot be canceled until Game Winning Point. If a player throws into the appropriate “hole” to score the points needed to reach 21 and win the game, the opposing player must
throw into the same “hole” to cancel. If the winning point is canceled and the first player still has a washer they haven’t thrown, they can throw again to win. Otherwise, the score shall be
neutralized and the next round will begin. That point was (aka, covered, canceled) Once a player/team can win with 1 throw at 16, 19, or 20 points they will throw first so that the opponent has a
chance to cancel.
If a single player, in a single round can throw one washer in each hole in any order at any time, that player/team WINS!!
Cancel a 125? If the opposing player/team has not thrown their washers, they have the opportunity to throw and cancel each hole. If they cover ALL 3 holes then the 125 shall be neutralized and the
next round will begin.
125 rules have evolved to increase the fun and pace of a washers game. We’ve played 135, and played where every throw cancels or played where you bust back to 13, however, we’ve settled on the above
rules to maximize entertainment. Throw 125!!
Rule Disputes
Washer disputed calls by the president of AZWL (aka Eric Craig)
1. I have 21, the opponent pushes in one of my other washers am I bust? Yes, your washer points count even if they are pushed in by your opponent.
2. I shot a 2 to get 21 for the win, the opponent has 16 and shot a 5 to reach 21 who wins? The first person to reach 21 wins!
3. I shot a 2 to get 21 with my last washer, my opponent covered/canceled my 2 and then shot a 1 and a 5. Did my opponent get a 125? Yes! 125 wins NO MATTER WHAT *(unless a person throws out of
4. I shot a 2 to get 21 for the win, the opponent has 16 and shot a 5 to reach 21 but then shot a 2 to cancel my winning score did my opponent win? No, your opponent can get a 125 but cannot score
points until AFTER they cancel your winning point or 2 in this example. If they hit the 5 after they cancel your 2 in this example then they win, or if they hit a 5 then cancel your 2 THEN hit a
1 for a 125, then they win!
5. I shot a 1 to reach 21 but have a hanger on the one. My opponent hit my hanger into the 1 busting me but at the same time his washer also went into the 1 hole, did I bust or win? Your opponents 1
cancels your 1 for the win but since he pushed in another washer of yours into the 1 hole you again win.
6. I had 19 but a washer hanging on the 2, my opponent has 16. My opponent threw their washer which hit mine knocking it in and my opponents’ washer went into the 5 giving him 21 too. Who won? If
your 2pt washer went in first you win, if the 5pt washer went in first they win. If you can’t tell, either cancel the throw or each team gets one washer to throw for the tiebreaker.
7. If I sink a washer in the 2pt hole to win and get 21 and my opponent sinks two 1pt shots does that cancel my 2pt shot. Nope, you must cover/cancel the same hole.
8. If I need a 1 to win but throw a 2 and bust but then throw a 5 and a 1 do I win? YES, any 125 is a win!
9. A player bounces a washer off the ground and it lands on the board. That washer is dead and must be removed from the washer board. If that washer bounces off the ground and goes into the hole
those points do not count.
10. I have 19 and my opponent has 16 who gets to throw first? The person closest to 21 if they can make it in one throw, so 19.
Please submit any other washer disputes to get an AZWL call to sa@throw125.com
Dojo Rules:
If your opponent throws out of turn you deserve CLEAR BOARD JUSTICE. Clear Boar Justice is where the washers that were thrown out of turn are removed from the board and do not count toward score and
cannot be rethrown. You get a clear board to throw on.
If the first throw has happened and the score is still Zero to Zero, there is no money on the line and it’s not a multiple game series, then the first person to take the board gets to throw first.
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Delta geometry
A 'delta' robot or printer is a robot where a platform is maintained by three pair of arms set in a triangle. The pairs of parallel arms maintain the horizontality of the platform and the movement of
these arms displace the platform in the three dimensions. Many solutions exists, but a few are used practically.
There are two principles to displace the arms pairs:
• Each arm pair is installed on a main articulated arm, the movement being generated be the rotation of this main arm. The geometry is the rotational delta or 'Clavel delta' from the name of its
inventor. The principle is widely used on 'pick and place' machine in a wide range of industries, from electronic to food. This system can be found in the Delta by Energetic or on the FirePick
Delta printers.
• Arm pairs are attached to carriage sliding along parallel rails. This geometry is called linear delta and is the most frequent type used in 3D printer world, the machines originating the movement
being the Rostock and the Kossel. The term 'parallel delta' shall not be used as all robots with parallel arms are called parallel robots.
There is another solution without rigid mechanics which is to suspend the platform to wires. There are a few examples and notably the Skydelta or this suspended delta
The linear delta kinematic calculation is simple because the carriage follow a straight line, so the horizontal movement of the platform is linked to the vertical movement of the carriage by
Pythagorean theorem (which states that the diagonal length squared, is equal to the sum of the triangles sides squared, the triangle must be a right angle triangle). Here the diagonal is the arm
length, constant, the vertical branch is the relative vertical position of the platform and carriage, the horizontal branch is the relative horizontal position of the platform and carriage.
The math is not difficult, but for a printer a lot of square roots must be done. Control boards based on 8 bit processors are struggling doing these calculations so a lot of fine software
optimization were done for the delta geometry for these processors. 32 bit controllers are becoming the controller boards of choice more commonly for delta printers as they have much faster
processors and do not struggle with the math at all. It shall be noted that the three sliders columns can be on positioned on a non-equilateral triangle and asymmetric dispositions were tested,
notably the 'Square' delta with angles of 90°,90° and 180°.
Geometry of a linear delta
The arm angle with effector at center is the result of the arms length, minimum angle and angles of the arms while at maximum diameter. For minimum angle of 20°, this angle is around 60° for maximum
diameter arm verticals, but if the minimum angle is increased, it may be higher. Minimum angles of 22° will gives an angle of 63° with vertical arms.
Arms may not be able to reach the vertical due to clearance problem, notably with the part cooling fans or effector accessories. In that case, for a given minimum angle, arm length may be reduced and
the angle while effector is at center will be lower.
On the other way, some printers have arms capable to go over vertical (e.g. Rostock Max).
The minimum arm angle, while effector is at maximum diameter, is one of the basic design parameters. It is important for effector stability, precision and carriage speed. A low angle induce high
carriage speed for a given effector horizontal speed. Low angle also decrease effector stability. Generally, 20° angle is considered as a practical minimum and induce a carriage speed 2.75 times
higher than effector horizontal speed. Some printers with theoretical minimum angle of 15° may experience lost steps at their maximum diameter.
│mini angle │speed multiplier │
│22.5° │2.41 │
│20° │2.75 │
│17.5° │3.17 │
│15° │3.73 │
│12.5° │4.51 │
Arm space does not influence movement calculation, but have an importance for the effector stability. Best stability is obtained for the minimum offset, with the maximum possible arm space for this
offset (minimising b dimension).
Reachable area
For a given minimum angle, the reachable area is a triangle with bulged sides, with the ends of the triangle oriented toward the columns, which cannot be accessed without impacting the column. Then,
for simplicity, the reachable area is generally considered circular. It might be interesting to evaluate the real reachable area when one want to inscribe a rectangle or square in the printing area.
The accessories (belts and fans) are critical for the real usable area.
• Green : the area which may be reachable without obstacle
• Orange : the practical area taking into account the clearance required between effector and columns.
Delta columns and axis names
View from top
Effector stability
What is effector stability ?
This is the fact that an effector resist to tilting moments. The tilt may displace the hotend nozzle and creates imprecision. It also have an effect on level measurement sensor while the sensors are
offset from the hotend. Two things have important effect on an effector stability:
• The geometry, as different geometries may induce higher or lower loads on arms and articulation, so higher or lower deformation. A geometry reducing the load will increase precision.
• The moment resistance induced by arm articulation, say a cardan will resist to torsion induced by the effector, while ball articulation will not.
The moment which will induce tilt will be created by :
• Inertia
• Load on the nozzle
• Friction in articulation, which may be significant for some types of articulations.
How to improve geometry
• A small offset will reduce the load on arms/articulation for a moment and shall be researched.
• For a given offset, the distance between the centers of articulation (noted 'b' on drawing) will modify the moment created by side loads. The lower this space, the better the stability. When
these articulation are merged, the geometric stability is very important, as there is no possible level difference in the merged articulations, hence, no possibility to have an 'articulated'
tilt. This solution is used by example on the Spiderbot delta.
Position of the hotend
What is also very important is the position of the hotend to minimize the effect of effector tilt. Experience show that a nozzle near the effector plane seems the best solution. However, care shall
be taken to limit the raise of the center of gravity, to avoid creating dynamic moments.
Quantifying the effects of the geometrical stability: TES coefficient
Understanding that there are other causes that the effector stability to nozzle movement imprecision, it is however interesting to quantify the displacement due to geometrical instability.
A coefficient could be defined, that we may called TES, for tilt effector stability, which will not quantify the effector instability, but its effect on the hotend, by combining the moment effect and
the displacement related to the distance between the virtual articulation and the nozzle location.
a being the lever due to arm space (see drawing) b being the space between balls (articulations)
• Tilt geometric load moment is related to a/b, a being proportional to arm space
• Tilt stiffness is proportional to arm space
TES = (Arm space)²/b, Dimension units shall be mm.
It is important to note that the TES does not depend from arm length, only effector geometry. Indeed, the arm stiffness in their axis is huge compared to other elements, notably articulation
stiffness, so the arm length have nearly no effect on tilting stability. This is why you could install the small Kossel mini effectors on large printers without problems. It shall be noted that for
merged articulations, this coefficient will be infinite.
This coefficient is calculated in the OpenScad delta simulator.
The practical improvements added by a good geometry is closely related to the quality of the mechanical implementation. By example, if you widen the arm space to improve stability, but the side
extensions on the carriage to reach the new width add excessive flexibility, you may have at the end reduced the real stability. It shall be noted that wider arm space does not raise or decrease the
moment and only help to fight play in articulation. If your problem is the rotation of the carriage, that is the carriage which shall be reinforced, no geometry can help.
Interactive web simulation
Linear deltas
Rotational deltas
• Parola Java based simulator, rotational delta with many options
Simulation on software
Delta calculators
Linear deltas
Rotational deltas
Math and research papers
Rotational delta are a quite common research topic, notably for university students.
Calculation links
Simulation without source/access
Some people have done Delta simulation on CAD/Math software, but not publicly release them.
In addition to site licence GFDL1.2, this page is also released under license CC BY-SA 4.0
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The examples in the toolbox are meant to be show how the the features of BBTools can be used in real-world situations. They may be complex, require large amounts of memory, and may need to run a long
In time it is intended to put more extensive examples on the web page.
Demos are given in the form of "playscripts", and are generally designed to be runnable for an average user (although, the average user of BBTools is expected to have a modern machine targeted for
number crunching).
These are a more appropiate place to start, but does not show the real strength of the toolbox. To start a demo, open the Demos pane in the Help browser and select under Toolboxes. You can also type
demo in the MATLAB prompt.
This example creates the function bbpca, which computes a Principal Component Analysis (PCA) of a data-matrix.
The datasets shipped with BBTools are released under the terms of the GPL. They are intended for used in both examples and demos, and is available for everyone who obeys the license.
The bird image was captured by Germ Wind, and graciously donated to this project. It was shot with a Sigma camera utilizing a Foveon image sensor. This has the important property that all pixels in
the image are significant, in contrast to other digital cameras that interpolate.
In order to compress the image shipped with this toolbox, colors were removed by adding the seperate components of the camera. This has the advantage that the intensity remains a count, and can
roughly be modelled as Poisson distributed. Pixels were summed in blocks of 4 for additional compression, retaining the discrete distribution.
The image shipped with the toolbox therefore represents raw counts. To display this properly, it is necessary to correct for the non-linearity of the display. Assuming exact display is overkill, this
can be done by raising each pixel to the power of 1/2.2 for any sRGB compliant monitor.
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Maximum permissible air pressure in the tank (Part(a)) is 777.8 psi
Maximum permissible air pressure in the tank (Part(b)) is 666.7 psi
Maximum permissible air pressure in the tank (Part(c)) is 671.3 psi
Maximum permissible air pressure in the tank (Part(d)) is 720.0 psi
Maximum permissible air pressure in the tank (Part(e)) is 666.7 psi
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Math (mental abuse to humans), also known as mathematics or maths is a satanic ritual and disease preformed by corrupted numbers. They find ways onto paper and glare at you until you do it. Most
people die when confronted with math. If you do math, you are very smart, and only teachers and Albert Einstein have figured out how to do this. Other smart people just don't do it. Teachers use it
to give children work to solve their problems. Many children DIE from math. Math is unlegal in some places, such as the United States. Purple Pi are very fond of math, and are attracted towards
anywhere or anyone with a high concentration of math. This is why Purple Pi can be found in teachers and are ubiquitous in schools. Math can also be sometimes spotted in the skies of the Mushroom
Types of Math[ ]
There are many types of math, each more deadlier then the last.
Addition [ ]
Adding more mass to the universe.
Subtraction [ ]
Able to cause black holes.
Multiplication [ ]
Allows you to clone stuff.
Division[ ]
Rips stuff in half
Rips stuff in NaN.
Exponentiation[ ]
Able to expand s*** faster and faster. This is what Expand Dong uses.
Number Theory[ ]
The theory of numbers.
Calculus[ ]
The most advanced form of math.
Use as Weapon[ ]
2 has allowed the numbers to use their math as a weapon against people. It is used in many wars like the Supernova War. Not all numbers like this use though and end up killing the user. Uses as a
weapon include:
• Sword
• Add mass to universe
• Black Hole creation
• Rip in half
• Child abuse
• Murder
• Airplane
• Laser
• Slow down time
• Speed up time
Math also has other uses than being a weapon though, as it keeps everything in the entire UnHyperverse in place, and without it, 1+1 could equal brown.
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In mathematics, a Hankel contour is a path in the complex plane which extends from (+∞,δ), around the origin counter clockwise and back to (+∞,−δ), where δ is an arbitrarily small positive number.
The contour thus remains arbitrarily close to the real axis but without crossing the real axis except for negative values of x. The Hankel contour can also be represented by a path that has mirror
images just above and below the real axis, connected to a circle of radius ε, centered at the origin, where ε is an arbitrarily small number. The two linear portions of the contour are said to be a
distance of δ from the real axis. Thus, the total distance between the linear portions of the contour is 2δ.^[1] The contour is traversed in the positively-oriented sense, meaning that the circle
around the origin is traversed counter-clockwise.
A Hankel contour path, traversed in the positive sense.
This is a version of the Hankel contour that consists of just a linear mirror image across the real axis.
Use of Hankel contours is one of the methods of contour integration. This type of path for contour integrals was first used by Hermann Hankel in his investigations of the Gamma function.
The Hankel contour is used to evaluate integrals such as the Gamma function, the Riemann zeta function, and other Hankel functions (which are Bessel functions of the third kind).^[1]^[2]
The Hankel contour and the Gamma function
The Hankel contour is helpful in expressing and solving the Gamma function in the complex t-plane. The Gamma function can be defined for any complex value in the plane if we evaluate the integral
along the Hankel contour. The Hankel contour is especially useful for expressing the Gamma function for any complex value because the end points of the contour vanish, and thus allows the fundamental
property of the Gamma function to be satisfied, which states ${\displaystyle \Gamma (z+1)=z\Gamma (z)}$ .^[2]
Derivation of the contour integral expression of the Gamma function
The Hankel contour can be used to help derive an expression for the Gamma function,^[2] based on the fundamental property ${\displaystyle \Gamma (z+1)=z\Gamma (z)}$ . Assume an ansatz of the form ${\
displaystyle \Gamma (z)=\int _{C}f(t)t^{z-1}dt}$ , where ${\displaystyle C}$ is the Hankel contour.
Inserting this ansatz into the fundamental property and integrating by parts on the right-hand side, one obtains ${\displaystyle \int _{C}f(t)t^{z}dt=[t^{z}f(t)]-\int _{C}t^{z}f'(t)dt.}$
Thus, assuming ${\displaystyle f(t)}$ decays sufficiently quickly such that ${\displaystyle t^{z}f(t)}$ vanishes at the endpoints of the Hankel contour, ${\displaystyle \int _{C}t^{z}(f(t)+f'(t))dt=0
\implies f(t)+f'(t)=0.}$
The solution to this differential equation is ${\displaystyle f(t)=Ae^{-t}.}$ While ${\displaystyle A}$ is a constant with respect to ${\displaystyle t}$ , ${\displaystyle A}$ may nonetheless be a
function of ${\displaystyle z}$ . Substituting ${\displaystyle f(t)}$ into the original integral then gives ${\displaystyle \Gamma (z)=A(z)\int _{C}e^{-t}(-t)^{z-1}dt,}$ where the minus sign in ${\
displaystyle (-t)^{z-1}}$ is accounted for by absorbing a factor ${\displaystyle (-1)^{z-1}}$ into the definition of ${\displaystyle A(z)}$ .
By integrating along the Hankel contour, the contour integral expression of the Gamma function becomes${\displaystyle \Gamma (z)={\frac {i}{2\sin {\pi z}}}\int _{C}e^{-t}(-t)^{z-1}dt}$ .^[2]
1. ^ ^a ^b Krantz, Steven G. (Steven George), 1951- (1999). Handbook of complex variables. Boston, Mass.: Birkhäuser. ISBN 0-8176-4011-8. OCLC 40964730.{{cite book}}: CS1 maint: multiple names:
authors list (link) CS1 maint: numeric names: authors list (link)
2. ^ ^a ^b ^c ^d Moretti, Gino (1964). Functions of a Complex Variable. Englewood Cliffs, N.J.: Prentice-Hall, Inc. pp. 179–184. LCCN 64012240.
Further reading
• Schmelzer, Thomas; Trefethen, Lloyd N. (2007-01). "Computing the Gamma Function Using Contour Integrals and Rational Approximations". SIAM Journal on Numerical Analysis. 45 (2): 558–571. doi
:10.1137/050646342. ISSN 0036-1429.
• Hugh L. Montgomery; Robert C. Vaughan (2007). Multiplicative number theory I. Classical theory. Cambridge tracts in advanced mathematics. 97. p. 515. ISBN 0-521-84903-9.
External links
• http://mathworld.wolfram.com/HankelContour.html
• NIST Digital Library of Mathematical Functions:Gamma Function:Integral Representation
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Select the correct answer. This graph represents a quadratic function. What is the value of a in this function’s equation? A)-1
All categories
Select the correct answer. This graph represents a quadratic function. What is the value of a in this function’s equation? A)-1
B)2 C)1 D)-2
2 answers:
Step-by-step explanation:
Step-by-step explanation:
We will use the work form of a quadratic to determine what a is...in fact we will write the equation for the whole thing in the process, because it's part of solving for a.
y = ±|a|(x - h)² + k
where x and y are from a coordinate point on the graph, h and k are the coordinates of the vertex, the absolute value of a indicates how steep or flat the graph is compared to the parent graph, and
the ± is because a positive parabola opens up and a negative one opens upside down.
The vertex is (0, 9) and the coordinate point I chose to use is (3, 0). Filling those in and solving for a:
0 = ±|a|(3 - 0)² + 9 and
0 = ±|a|(3)² + 9 and
-9 = ±|a|9 and
-1 = ±|a| so a = 1. Because this is an upside down parabola the negative is out front, but a is independent of it. The correct choice is C. The quadratic function is
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5/6 +5/6 = 10/6 = 1 2/3 glasses of juice
Step-by-step explanation:
He needs to put $10345 in the account today, in order to get 15000 in five years.
We know that,
A = future value of the investment with interest = 15000
P = principal investment amount
r = annual interest rate (decimal) = 7.5% = 0.075
n = number of times that interest is compounded per year = 4
t = the number of years the money is invested = 5
Putting the values,
Which one you need help on?
1/4 for both
Step-by-step explanation:
2/8 -- you divide 2 by 2 you get 1, 8 divided by 2 is 4 -- 1/4
3/12 -- you divide 3 by 3 you get 1, 12 divided by 3 is 4 -- 1/4
** tip: what you do to one half of the fraction you have to do to the other
hope this helps!
Step-by-step explanation:
Add answer
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what makes you happy
What makes me happy? Singing 'Jamaadeey, wax jacayl aan moodaa, intuu jilibka ii dhigay, i jibaaxay anigee. Jiribtiyo dhibkaan qabo, jini qabe shabeeliyo, Aar jimicsanayaa, Jenyaha i saaree....
The rest of life takes care of itself.
^^ Nice song.
What makes me happy? My beautiful girls and their smile. They are the world to me.
Waar horta runtaa fiicane ,,, bahalkan aad sheegayso markaan musqusha galo ee aan arko uun baan xasuustaa niyow
the little things are what make me happy.
I like the sky 15 mins before it rains
The smell of the sidewalk after a downpour
the first awakening gust of wind on a morning jog
Mercury Espresso's soy moccas with an organic choc chip cookie on my walk to school (they are the best)
having breakfast for dinner
and my monthly craft circle
these things make me smile like a broken jawed *****
Trying to observe my obligatory duties as a muslima, wife, mother, doughter, sister, freind and as a living being.
My moms voice
Giving help when most needed,
Reading quraan
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whenever i hear my husbands praise and love for me.
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knowing i don't have work or school
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being in the masjid and feeling so peaceful
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having money to go shopping
when i know i just bought new clothes
my parents being pleased with me
when the whole family is happy
havin someone u love n someone love u
building goals n dreams with someone u love
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Analog Computers: Looking to the Past for the Future of Computing - USC Viterbi School of Engineering
Computer Science Electrical Engineering Issue III Power Volume XXIII
Analog Computers: Looking to the Past for the Future of Computing
About the Author: Micah See
Micah is a junior studying Electrical and Computer Engineering. His major-related interests include mixed-signal circuit design and control systems. In his spare time he enjoys baking, weightlifting,
and language learning.
Although computers have made great jumps in efficiency and speed in the past several decades, recent developments in machine learning and artificial intelligence applications are increasingly
challenging the efficiency of powerful computers. The tremendous pressure in the computer hardware industry to significantly improve performance with each new generation of computer chips has
traditionally followed a pattern called Moore’s Law, which states that the complexity and performance of computer chips doubles every two years. Transistors, which are small electronic components
that make up computer chips, have shrunk in size with each new generation in order to keep up with Moore’s Law. However, we are now approaching a limit in which it is no longer physically possible
to make transistors any smaller [23]. In other words, we are approaching a dead end when it comes to improving the performance of traditional computers. Clearly, a new approach to building computers
is needed. This article proposes analog computers as a possible solution for creating new, more powerful computers in the future. It will describe how analog computers work and differ from
traditional computers, as well as the benefits of analog computers in solving very complex mathematical problems.
Figure 1: modern prototype of a manually configurable analog computer [12]
What is an Analog Computer?
These days, when most people think of a computer, they picture a desktop computer or a laptop. Both of these devices, along with Xboxes, smartphones, and even handheld calculators, actually belong to
one specific category of computers: digital electronic computers. In reality, the definition of a computer is much broader and encompasses many other categories of devices, including analog
According to Merriam-Webster Dictionary, a computer is “a programmable, usually electronic device that can store, retrieve, and process data” [1]. This definition highlights two important points
about computers. First, a computer does not necessarily have to be an electronic device, even though nearly all modern computers are. Second, for a device to be considered a computer, it must be
programmable and have the ability to process data.
All computers can be classified as either analog or digital. The primary difference between these two types of computers is the way in which data is represented. In a digital computer, all data is
represented using a limited set of numerical values [2, p. 2]. In modern digital computers, data is represented with binary, a number system which uses only 0’s and 1’s. The simplicity of binary is
both an advantage and limitation of digital computers. Long lists of binary digits are used to represent all types of data in digital computers, including text, images, and audio. However,
representing data in binary form often requires approximating the data and losing some of its detail. For example, audio stored on a digital computer loses some of the quality it had when it was
originally recorded [13].
Another distinct feature of digital computers is their ability to be reprogrammed to solve many different types of problems. Digital computers are configured to run an algorithm, which is essentially
a list of instructions for completing a task. Another way to think of an algorithm is to consider it as a recipe for the computer to follow [24]. All digital computers run various programming
languages, and these programming languages give users the flexibility to create an algorithm for any task they wish to complete.
Finally, digital computers can solve problems of virtually any level of complexity if they are given enough time to run. The more complex the problem, the longer a digital computer will take to solve
it [2, pp. 3-4]. For example, imagine a digital computer is asked to sort two lists of numbers, a list with 100 numbers and a list of 1000 numbers. Due to the way a digital computer operates, it can
take the computer up to 100 times longer to sort the list of 1000 numbers, even though the list is only ten times larger than the one with 100 items [20]. This inefficiency when solving certain types
of problems is a major downside of digital computers, which will be further explored later in this article.
An analog computer, on the other hand, is based on an entirely different approach to solving a problem. Unlike a digital computer, the structure of the analog computer is not fixed and there is no
programming language. Instead, to solve a problem, you must physically reconfigure the computer so that it forms a model, or “analog”, of the problem. When an analog computer is run, it simulates the
problem and the output of this simulation provides the solution [2, pp. 3-4]. Because an analog computer is a physical model of the problem it is solving, the complexity of the problem determines the
physical size of the computer. As a result, unlike digital computers, an analog computer cannot solve all problems of any complexity [2, p. 5].
To further clarify how analog and digital computers differ in the way that they solve problems, let’s consider an example in which the goal is to design a bridge and determine the maximum weight the
bridge can hold. Solving this problem with a digital computer would be similar to estimating the strength of each individual beam that makes up the bridge, then analyzing how each beam interacts with
the beams around it, and finally determining the total amount of weight the beams can hold together by taking into account all of their strength contributions. Using an analog computer to solve this
problem is akin to building a model of the bridge and physically placing different weights on it to see which one causes the bridge to break. This example illustrates how in certain cases, using an
analog computer can provide a much more direct and efficient path to the solution.
Lastly, data representation and storage differ significantly between analog and digital computers. The key difference is that in an analog computer, data can take on any value and is not restricted
to being represented by a limited set of distinct values, such as binary. For example, in electronic analog computers, data is represented by electrical signals whose magnitude,or strength,
fluctuates over time. The data stored in an electronic analog computer is the strength of these signals at a given instant in time. This approach allows certain types of data to be represented
exactly rather than being approximated as they would in digital computers [2, pp. 31-33].
Having explored the defining characteristics of analog computers, we will now examine several examples of these computers, ranging from ancient artifacts to modern electronic systems.
Examples of Analog Computers
The first analog computers were ancient tools, one example of which is the astrolabe, which dates back to the Roman Empire. An astrolabe is a small mechanical device that was used to track the
position of stars and planets. There was widespread use of this device for navigation, especially during sea travel [10].
Jumping ahead to the 20th century, we can find another example of a widely-used non-electronic analog computer: the slide rule. A slide rule was a device that assisted in performing mathematical
operations between two numbers. The slide rule was marked with various scales and operations were performed by aligning the components of the device in a specific configuration. Many slide rules
supported basic operations such as addition, subtraction, multiplication, and division, while others could support more complex operations such as square roots [5].
Figure 2: a slide rule with its components marked [8]
Significant advances in analog computing were made during WWII, when research and development funding ballooned due to the war effort. One example was the invention of the Turing-Welchman Bombe, a
mechanical computer designed by Alan Turing to help the British crack encrypted German military messages. The Germans encrypted the messages using their own mechanical analog computer, a small,
typewriter-like device called the Enigma cipher machine [2, pp. 204-211].
However, the revolution in analog computing really began with the advent of the electronic analog computer, a device in which electrical circuits–rather than physical moving parts or mechanical
components–are used to model the problem being solved.
One of the pioneers of electronic analog computing was Helmut Hoelzer, a rocket scientist in Nazi Germany. Hoelzer theorized that complicated mathematical operations such as differentiation and
integration could be performed more efficiently using electrical circuits. Both of these operations are from calculus and are used to calculate quantities that change over time. For example,
differentiation can be used to determine how fast a rocket is accelerating by tracking its change in position over time [17].
Through his research, Hoelzer discovered that both of these operations could indeed be performed by measuring the electrical signals in a simple circuit with a capacitor. A capacitor is a basic
electronic component that acts like a small battery, storing small amounts of energy and rapidly charging and discharging [16]. Hoelzer applied these revolutionary ideas to his work on the guidance
system for the A4 rocket, an advanced weapon being developed by Nazi Germany which would be the world’s first ballistic missile used in warfare [9]. The guidance system that he built for the rocket
was called the Mischgerät. It acquired data from the rocket’s flight sensors, performed calculations on the data using the capacitor circuits, and output a control signal which adjusted the rocket’s
flight path in real-time. The Mischgerät is considered to be one of the world’s first electronic analog computers [2, pp. 34-38].
Figure 3: the Mischgerät (photo by Adri De Keijzer) [7]
As the 20th century progressed, electronic analog computers became more advanced and widely used. Institutions interested in complex mathematical simulations, such as NASA, invested heavily in them
[11]. By the 1950s, there were several major companies designing and building electronic analog computers, including Electronic Associates Inc. (EAI) and Telefunken [2, pp. 101-103].
Having followed the progression of analog computers throughout history, we will now turn our focus to modern electronic analog computers and discuss their benefits and disadvantages.
Benefits and Disadvantages of (Electronic) Analog Computers
Analog computers have a variety of advantages and disadvantages in comparison to digital computers. One of the most important benefits of analog computers is that they operate in a completely
“parallel” way, meaning that they can work on many different calculations at the same time.In comparison, digital computers operate sequentially and must wait for one set of calculations to complete
before starting on the next set. Analog computers simulate the problem and compute the solution nearly instantaneously, while it may take a digital computer a significant amount of time to solve the
same problem. To understand the difference between parallel and sequential operation, let us consider the example of trying to calculate the trajectory of a baseball given the angle and speed with
which it was thrown. An analog computer will simulate all aspects of the problem simultaneously and begin outputting the trajectory of the baseball as soon as the computer is turned on. In this case,
watching the output of the analog computer is like watching the baseball fly through the air in real-time. The digital computer, on the other hand, has to break the problem down into sequential
steps, complete one step at a time, and then put the solutions from different steps together to come up with the final answer. After the digital computer completes its work, it will output the entire
path of the baseball all at once [2, pp 249-250]. In addition to the benefits of parallel operation, analog computers do not need to access memory since they are not controlled by a stored program.
Since memory accesses can significantly slow down computation, analog computers have an additional speed advantage over digital computers [2, pp 250-251].
Electronic analog computers are also particularly well-suited to solving mathematical problems which involve differentiation – specifically a group of problems called ordinary differential equations
(ODEs) [2, p. 113]. ODEs are hugely important in modeling systems and phenomena in science, engineering, and a variety of other disciplines. Examples of problems that can be modeled using ODEs are
population growth, the spread of epidemics, and the motion of objects – such as airplanes and rockets [3].
That said, there are several serious disadvantages to using analog computers that have hindered their adoption. First, the programming and configuration of an analog computer is specific to the
structure of each individual computer. Unlike the programming languages used for digital computers, there is no convenient, standardized approach to programming analog computers. For example, while
both slide rules and astrolabes are examples of analog computers, configuring an astrolabe to track the moon is quite different from configuring a slide rule to add two numbers together. Second, the
size of an analog computer is determined by the complexity of the problem. For very complex problems, analog computers can become too large and intricate to build practically. Finally, data in analog
computers, which is represented using electrical signals, is more susceptible to electromagnetic noise and interference. This can cause errors in the data or even corrupt the data altogether [11].
In summary, while analog computers are not as accurate or versatile as digital computers, they can greatly improve speed and efficiency for certain problem types. In the next section, we will explore
recent innovations in analog computers, as well as their prospects for the future.
The Resurgence and Future of (Electronic) Analog Computers
Recent innovations in semiconductor technology are allowing us to rethink the construction of analog computers in terms of reducing their physical size and improving their computing power.
Semiconductors are a group of elements on the periodic table, such as silicon and germanium,that have special electrical properties. Electronic components and circuits are usually constructed using
semiconductor materials.
One revolutionary new semiconductor technology is known as very large-scale integration or VLSI. This technology enables electrical engineers to shrink down circuits to microscopic sizes. VLSI
accomplishes this by fitting millions to billions of tiny electrical components on a single semiconductor chip [14]. Today, the main computer chip in a laptop, known as the central processing unit
(CPU), is about the size of a cracker. Several decades ago, computers with even less computational power took up entire rooms [21].
In addition, researchers are investigating the benefits of “hybrid analog computers”, i.e. analog computers augmented with digital computing techniques that help to improve accuracy and versatility
In 2015, a team of researchers at Columbia University built a “hybrid computing unit” and used VLSI technology to fit the entire hybrid analog computer onto a small computer chip. This computer is
programmable and is capable of solving complex problems that can be modeled using ODEs. It is also extremely power efficient and uses only about 1.2 mW of power [4]. In comparison, a modern
“low-power” CPU can use around 30 W of power. Therefore, the “hybrid computing unit” consumes around 25,000 times less power than the digital computer chip [22].
Figure 4: zoomed-in photo of the computer chip that contains the “hybrid computing unit” created by researchers at Columbia University [4]
This next generation of analog computers is particularly well-suited to meeting the pressing needs of our modern world. Science and engineering applications are demanding that we solve more and more
complex mathematical problems, which can easily bog down digital computers. In addition, the power efficiency of electronics, especially in devices with limited power (such as battery powered
robots), is becoming increasingly important. Analog computers are well-equipped to meet these challenges, especially as their versatility and accuracy improves with ongoing research and development.
[1]“Definition of COMPUTER,” Merriam-webster.com, 2019. https://www.merriam-webster.com/dictionary/computer
[2]Bernd Ulmann, Analog Computing. Walter de Gruyter, 2013.
[3]W. Trench, “1.1: Applications Leading to Differential Equations,” Mathematics LibreTexts, Jun. 07, 2018. https://math.libretexts.org/Bookshelves/Differential_Equations/
[4]N. Guo et al., “Continuous-time hybrid computation with programmable nonlinearities,” Sep. 2015. doi: 10.1109/esscirc.2015.7313881.
[5]“Slide Rules,” National Museum of American History. https://americanhistory.si.edu/collections/object-groups/slide-rules#:~:text=Slide%20rules%20are%20analog%20computing (accessed Nov. 01, 2022).
[6]L. Gladwin, Alan Turing, Enigma, and the Breaking of German Machine Ciphers in World War II. 1997.
[7]“Archive 3 displays 5,” www.cdvandt.org. https://www.cdvandt.org/archive_3_displays_5.htm (accessed Nov. 01, 2022).
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[10]L. Poppick, “The Story of the Astrolabe, the Original Smartphone,” Smithsonian.com, Jan. 31, 2017. https://www.smithsonianmag.com/innovation/astrolabe-original-smartphone-180961981/
[11]Y. Tsividis, “Not Your Father’s Analog Computer,” IEEE Spectrum, Dec. 01, 2017. https://spectrum.ieee.org/not-your-fathers-analog-computer
[12]B. Ulmann, “Why Algorithms Suck and Analog Computers are the Future,” De Gruyter Conversations, Jul. 06, 2017. https://blog.degruyter.com/algorithms-suck-analog-computers-future/
[13]“Digital Audio Chapter Five: Sampling Rates,” cmtext.indiana.edu, 2019. https://cmtext.indiana.edu/digital_audio/chapter5_rate.php
[14]“VLSI Technology: Its History and Uses in Modern Technology,” Cadence Design Systems. https://resources.pcb.cadence.com/blog/2020-vlsi-technology-its-history-and-uses-in-modern-technology
[15]“What are semiconductors?,” Hitachi High-Tech Corporation. https://www.hitachi-hightech.com/global/en/knowledge/semiconductor/room/about (accessed Nov. 01, 2022).
[16]“Beginners Guide to Passive Devices and Components,” Basic Electronics Tutorials, Sep. 10, 2013. https://www.electronics-tutorials.ws/blog/passive-devices.html
[17]“Derivatives,” Cuemath. https://www.cuemath.com/calculus/derivatives/
[18]“Integral Calculus,” Cuemath. https://www.cuemath.com/calculus/integral/
[19]N. Osman, “History of Early Numbers – Base 10,” Maths In Context, Dec. 31, 2018. https://www.mathsincontext.com/history-of-early-numbers-base-10/
[20]V. Adamchik, “Algorithmic Complexity,” usc.edu, 2009. https://viterbi-web.usc.edu/~adamchik/15-121/lectures/Algorithmic%20Complexity/complexity.html (accessed Dec. 05, 2022).
[21]Computer History Museum, “Timeline of Computer History,” computerhistory.org, 2022. https://www.computerhistory.org/timeline/computers/
[22]“Intel® Xeon® D-1602 Processor (3M Cache, 2.50GHz) – Product Specifications,” Intel. https://www.intel.com/content/www/us/en/products/sku/193686/intel-xeon-d1602-processor-3m-cache-2-50ghz/
specifications.html (accessed Dec. 05, 2022).
[23]P. Kasiorek, “Moore’s Law Is Dead. Now What?,” builtin.com, Oct. 19, 2022. https://builtin.com/hardware/moores-law
[24]A. Gillis, “What is an Algorithm? – Definition from WhatIs.com,” techtarget.com, May 2022. https://www.techtarget.com/whatis/definition/algorithm
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EViews Help: Equation Objects
Equation Objects
Single equation regression estimation in EViews is performed using the equation object. To create an equation object in EViews: select or from the main menu, or simply type the keyword equation in
the command window.
Next, you will specify your equation in the dialog box that appears, and select an estimation method. Below, we provide details on specifying equations in EViews. EViews will estimate the equation
and display results in the equation window.
The estimation results are stored as part of the equation object so they can be accessed at any time. Simply open the object to display the summary results, or to access EViews tools for working with
results from an equation object. For example, you can retrieve the sum-of-squares from any equation, or you can use the estimated equation as part of a multi-equation model.
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Floating point
Floating point
Subclass of:
Patent class list (only not empty are listed)
Deeper subclasses:
Class / Number of
Patent Description patent
application applications /
number Date published
708501000 Multiplication followed by addition 38
708496000 Compensation for finite word length 24
708505000 Addition or subtraction 23
708503000 Multiplication 10
708502000 Reciprocal 7
708500000 Evaluation of root 6
708511000 Complex number format 4
Method for Representing Complex Numbers in a Communication System - A method for storage for complex numbers that employs a shared exponent field is disclosed. Rather than
20090187616 each floating point component of an complex number having its own distinct signed mantissa and exponent fields, each component includes a distinct signed mantissa field and 07-23-2009
shares an exponent field, thereby increasing the possible size of each distinct signed mantissa field by as much as one half the number of bits formerly employed to store a
single distinct exponent field.
Digital Signal Processor Having Instruction Set With One Or More Non-Linear Complex Functions - Methods and apparatus are provided for a digital signal processor having an
instruction set with one or more non-linear complex functions. A method is provided for a processor. One or more non-linear complex software instructions are obtained from
20100138468 a program. The non-linear complex software instructions have at least one complex number as an input. One or more non-linear complex functions are applied from a predefined 06-03-2010
instruction set to the at least one complex number. An output is generated comprised of one complex number or two real numbers. A functional unit can implement the one or
more non-linear complex functions. In one embodiment, a vector-based digital signal processor is disclosed that processes a complex vector comprised of a plurality of
complex numbers. The processor can process the plurality of complex numbers in parallel.
COMPLEX AND HYPERCOMPLEX INCLUSIVE INTERVAL EXPRESSION EVALUATIONS WITH STABLE NUMERIC EVALUATIONS AND PRECISION EFFICACY TESTING - Improvements to optimal interval
20110004648 operators are developed for interval expression evaluation using arithmetic and real power operators applied to complex and hypercomplex number systems. A method for 01-06-2011
determining efficacy of numeric precision, incorporating minor changes to interval operators, provides detection of insufficient numeric evaluation precision.
EXPLOITATION OF TOPOLOGICAL CATEGORIZATION OF CHAOTIC AND FRACTAL FUNCTIONS INCLUDING FIELD LINE CALCULATIONS - A topological categorization method, based on inclusive
20110082895 intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both 04-07-2011
potential for complex and hypercomplex and field lines for complex iterations
708504000 Division 4
METHOD, SYSTEM AND COMPUTER PROGRAM PRODUCT FOR VERIFYING FLOATING POINT DIVIDE OPERATION RESULTS - A method, system and computer program product for verifying a result of
20090216823 a floating point division operation are provided. The method includes: receiving a result of a floating point division operation for a dividend and a divisor; performing a 08-27-2009
comparison of a magnitude of a least significant bit (LSB) of the dividend and a magnitude of a most significant bit (MSB) of a remainder; and determining whether the
result is correct based on the comparison.
METHOD, SYSTEM AND COMPUTER PROGRAM PRODUCT FOR DETERMINING REQUIRED PRECISION IN FIXED-POINT DIVIDE OPERATIONS - A method, computer program product and a system for
controlling a fixed point division operation are provided. The method includes: receiving an instruction to perform a division operation for a dividend and a divisor, the
20090216824 operation comprising a maximum number of iterations to produce a quotient having a maximum precision; calculating a magnitude of at least one of the dividend and the 08-27-2009
divisor; determining a quotient precision based on the magnitude; and computing a required number of iterations needed to produce the quotient precision and performing the
number of iterations.
APPARATUS AND METHOD FOR IMPLEMENTING HARDWARE SUPPORT FOR DENORMALIZED OPERANDS FOR FLOATING-POINT DIVIDE OPERATIONS - A floating-point circuit may include a
floating-point operand normalization circuit configured to receive input floating-point operands of a given floating-point divide operation, the operands comprising a
dividend and a divisor, as well as a divide engine coupled to the normalization circuit. In response to determining that one or more of the input floating-point operands is
20100250639 a denormal number, the operand normalization circuit may be further configured to normalize the one or more of the input floating-point operands and output a normalized 09-30-2010
dividend and normalized divisor to the divide engine, and dependent upon respective numbers of leading zeros of the dividend and divisor prior to normalization, generate a
value indicative of a maximum possible number of digits of a quotient (NDQ). The divide engine may be configured to iteratively generate NDQ digits of a floating-point
quotient from the normalized dividend and the normalized divisor provided by the floating-point operand normalization circuit.
Range Check Based Lookup Tables - Mechanisms for utilizing a reduced lookup table circuit to perform an operation in a data processing device are provided. A first input
value is input for selecting a subset of values from the reduced lookup table circuit. The reduced lookup table circuit stores only boundary cell values from a fully filled
20130173681 lookup table corresponding to the reduced lookup table circuit. The subset of values comprises only a subset of boundary cell values corresponding to the first input value. 07-04-2013
A second value is input and a comparison, by the reduced lookup table circuit, of the second value to each of the boundary cell values in the subset of boundary cell values
is performed. The reduced lookup table circuit outputs an output value based on results of the comparison of the second value to each of the boundary cell values in the
subset of boundary cell values.
708512000 Logarithmic format 3
20100030833 APPARATUS, METHOD, AND PROGRAM FOR ARITHMETIC PROCESSING - A mantissa/exponent splitter splits an input value X=(1+X 02-04-2010
METHOD FOR ENCODING FLOATING-POINT DATA, METHOD FOR DECODING FLOATING-POINT DATA, AND CORRESPONDING ENCODER AND DECODER - An algorithm for efficiently compressing
floating-point data in 3D meshes is disclosed. 3D meshes are represented by topology data, geometry data and property data. Geometry data specify vertex locations and are
usually represented by floating-point coordinates. While geometry data are usually compressed by quantization, prediction and entropy coding, the present invention uses no
20120166510 prediction. A floating-point number consists of mantissa and exponent, and normally the exponent, sign and mantissa are compressed separately. A method for encoding 06-28-2012
floating-point formatted data comprises determining if a current floating-point value was previously stored in a memory, storing the current value in the memory if it was
not previously stored in the memory, and encoding it. Otherwise, if the current floating-point value was previously stored in a memory, the storage position of the value
within the memory is determined and a reference pointing to the storage position is encoded.
RESIDUE-BASED EXPONENT FLOW CHECKING - A technique for checking an exponent calculation for an execution unit that supports floating point operations includes generating,
using a residue prediction circuit, a predicted exponent residue for a result exponent of a floating point operation. The technique also includes generating, using an
20130339417 exponent calculation circuit, the result exponent for the floating point operation and generating, using the residue prediction circuit, a result exponent residue for the 12-19-2013
result exponent. Finally, the technique includes comparing the predicted exponent residue to the result exponent residue to determine whether the result exponent generated
by the exponent calculation circuit is correct and, if not, signaling an error.
708510000 Microprocessor 3
DETECTION OF POTENTIAL NEED TO USE A LARGER DATA FORMAT IN PERFORMING FLOATING POINT OPERATIONS - Detection of whether a result of a floating point operation is safe.
20080270508 Characteristics of the result are examined to determine whether the result is safe or potentially unsafe, as defined by the user. An instruction is provided to facilitate 10-30-2008
detection of safe or potentially unsafe results.
EXTRACT BIASED EXPONENT OF DECIMAL FLOATING POINT DATA - A decimal floating point finite number in a decimal floating point format is composed from the number in a
different format. A decimal floating point format includes fields to hold information relating to the sign, exponent and significand of the decimal floating point finite
20080270509 number. Other decimal floating point data, including infinities and NaNs (not a number), are also composed. Decimal floating point data are also decomposed from the decimal 10-30-2008
floating point format to a different format. For composition and decomposition, one or more instructions may be employed, including an insert biased exponent or extract
biased exponent instruction.
FAST FLOATING POINT RESULT FORWARDING USING NON-ARCHITECTED DATA FORMAT - A microprocessor having an instruction set architecture (ISA) that specifies at least one
architected data format (ADF) for floating-point operands. The microprocessor includes a plurality of floating-point units, each comprising an arithmetic unit configured to
20110060785 receive non-ADF source operands and to perform a floating-point operation on the non-ADF source operands to generate a non-ADF result. The microprocessor also includes 03-10-2011
forwarding buses, configured to forward the non-ADF result generated by each arithmetic unit of the plurality of floating-point units to each of the plurality of
floating-point units for selective use as one of the non-ADF source operands.
708513000 Variable length or precision 2
PROCESSOR WITH ADAPTIVE MULTI-SHADER - The disclosure describes an adaptive multi-shader within a processor that uses one or more high-precision arithmetic logic units
(ALUs) and low-precision ALUs to process data based on the type of the data. Upon receiving a stream of data, the adaptive multi-shader first determines the type of the
20080235316 data. For example, the adaptive multi-shader may determine whether the data is suitable for high-precision processing or low-precision processing. The adaptive multi-shader 09-25-2008
then processes the data using the high-precision ALUs when the data is suitable for high-precision processing, and processes the data using the high-precision ALUs and the
low-precision ALUs when the data is suitable for low-precision processing. The adaptive multi-shader may substantially reduce power consumption and silicon size of the
processor by implementing the low-precision ALUs while maintaining the ability to process data using high-precision processing by implementing the high-precision ALUs.
SINGLE-PRECISION FLOATING-POINT DATA STORING METHOD AND PROCESSOR - A single-precision floating-point data storing method for use in a processor including a register, which
20090240757 has a size that can store double-precision floating-point data, for storing double-precision floating-point data and single-precision floating-point data comprises writing 09-24-2009
input single-precision floating-point data to the high-order half of the register, and writing all zeros to the low-order half of the register if a single-precision
floating-point data process is specified.
708514000 Matrix array 2
SYSTEM AND METHOD TO IMPLEMENT A MATRIX MULTIPLY UNIT OF A BROADBAND PROCESSOR - The present invention provides a system and method for improving the performance of
general-purpose processors by implementing a functional unit that computes the product of a matrix operand with a vector operand, producing a vector result. The functional
20090094309 unit fully utilizes the entire resources of a 128b by 128b multiplier regardless of the operand size, as the number of elements of the matrix and vector operands increase 04-09-2009
as operand size is reduced. The unit performs both fixed-point and floating-point multiplications and additions with the highest-possible intermediate accuracy with modest
HARDWARE FOR PERFORMING ARITHMETIC OPERATIONS - Hardware for performing sequences of arithmetic operations. The hardware comprises a scheduler operable to generate a
20130073599 schedule of instructions from a bitmap denoting whether an entry in a matrix is zero or not. An arithmetic circuit is provided which is configured to perform arithmetic 03-21-2013
operations on the matrix in accordance with the schedule.
708507000 Parallel 1
FLOATING-POINT ERROR PROPAGATION IN DATAFLOW - A process for propagating an error in a floating-point calculation is disclosed. A floating-point error occurring from the
20130173682 floating-point arithmetic calculation is trapped, and a special value is generated. Information regarding the error is stored as a payload of the special value. Program 07-04-2013
operations are resumed with the special value applied to further calculations dependent on the floating-point arithmetic calculation.
Document Title Date
METHOD AND SYSTEM FOR OPTIMIZING FLOATING POINT CONVERSION BETWEEN DIFFERENT BASES - A method of streamlining floating-point conversions includes determining a source
coefficient and a source exponent of an input value represented by a floating-point number in a source base; estimating an approximated target exponent (ATE) using the source
20080263120 coefficient and the source exponent, in the event the source coefficient has a non-zero value; determining whether the ATE exceeds a maximum exponent so as to result an 10-23-2008
overflow, and outputting a predefined overflow value in the event of an overflow; determining whether the ATE exceeds a minimum exponent so as to result an underflow, and
outputting a predefined underflow value in the event of an underflow; and in the event the ATE does not result in either an overflow or underflow, converting the input value to
an output value represented by a converted coefficient, a converted base and the exponent of the output value.
CONVERT SIGNIFICAND OF DECIMAL FLOATING POINT DATA FROM PACKED DECIMAL FORMAT - A decimal floating point finite number in a decimal floating point format is composed from the
20080270506 number in a different format. A decimal floating point format includes fields to hold information relating to the sign, exponent and significand of the decimal floating point 10-30-2008
finite number. Other decimal floating point data, including infinities and NaNs (not a number), are also composed. Decimal floating point data are also decomposed from the
decimal floating point format to a different format. For composition and decomposition, one or more instructions may be employed, including one or more convert instructions.
GENERATION OF TEST CASES WITH RANGE CONSTRAINTS FOR FLOATING POINT ADD AND SUBTRACT INSTRUCTIONS - Methods, apparatus and systems are disclosed for the generation of
20080307028 range-constrained test cases for verification of designs of arithmetic floating point units. Given three ranges of floating point numbers Rx, Ry, Rz, a floating point operation 12-11-2008
(op), and a rounding-mode (round), three floating point numbers
EMULATION OF A FIXED POINT OPERATION USING A CORRESPONDING FLOATING POINT OPERATION - A computer emulates a fixed-point operation that is normally performed on fixed-point
operands, by use of a floating-point operation that is normally performed on floating-point operands. Several embodiments emulate a fixed-point operation by: expanding at least
one fixed-point operand into a floating-point representation (also called “floating-point equivalent”), performing, on the floating-point equivalent, a floating-point operation
20090083358 that corresponds to the fixed-point operation, and reducing a floating-point result into a fixed-point result. The just-described fixed-point result may have the same 03-26-2009
representation as the fixed-point operand(s) and/or any user-specified fixed-point representation, depending on the embodiment. Also the operands and the result may be either
real or complex, and may be either scalar or vector. The above-described emulation may be performed either with an interpreter or with a compiler, depending on the embodiment.
A conventional interpreter for an object-oriented language (such as MATLAB version 6) may be extended to perform the emulation.
20090100121 APPARATUS AND METHOD FOR LOW COMPLEXITY COMBINATORIAL CODING OF SIGNALS - During operation of an encoder, a signal vector (x) is received. A first multi-precision operand (Ψ′ 04-16-2009
EFFICIENT FORCING OF CORNER CASES IN A FLOATING POINT ROUNDER - The forcing of the result or output of a rounder portion of a floating point processor occurs only in a fraction
20100023573 non-increment data path within the rounder and not in the fraction increment data path within the rounder. The fraction forcing is active on a corner case such as a disabled 01-28-2010
overflow exception. A disabled overflow exception may be detected by inspecting the normalized exponent. If a disabled overflow exception is detected, the round mode is
selected to execute only in the non-increment data path thereby preventing the fraction increment data path from being selected.
SUPPORTING MULTIPLE FORMATS IN A FLOATING POINT PROCESSOR - In a binary floating point processor, the exponents of each of the various types of operands are recoded into an
internal format, by biasing the exponents with the minimum exponent value of the result precision (“Emin”), i.e., the recoded value of the exponent is the represented value of
20100063987 the exponent minus Emin. Emin depends only on the result precision of the instruction that is currently being executed in the binary floating point processor. The exponent 03-11-2010
computations are then performed in this new format. The underflow check for all result precisions is a check against zero and overflow checks are performed against a positive
number that depends on the result precision. The exponent values are in a 2's complement representation, so the underflow check simply becomes a check of the sign bit.
Managing Floating Point Variables in Constraint Satisfaction Problems - Systems and methods for managing floating point variables are described in the present disclosure.
According to one example, an embodiment of a method includes analyzing a constraint on a floating point variable in a system that supports both floating point variables and
20100198901 integer variables. The constraint is designed to have the ability to numerically limit the domain of the floating point variable. The method also includes determining whether 08-05-2010
or not the floating point variable can be handled as an integer variable and converting the floating point variable to a pseudo integer variable when it is determined that the
floating point variable can be handled as an integer variable. This conversion of the floating point variable to a pseudo integer variable allows the domain of the floating
point variable to be processed as an integer domain.
Extended-Precision Integer Arithmetic and Logical Instructions - The invention set forth herein describes a mechanism for efficiently performing extended precision operations
20110078225 on multi-word source operands. Corresponding data words of the source operands are processed together via each instruction of a cascading sequence of instructions. State 03-31-2011
information generated when each instruction is processed is stored in condition code flags. The state information is optionally used in the processing of subsequent
instructions in the sequence and/or accumulated with previously set state information.
Multiplication of Complex Numbers Represented in Floating Point - A multiplier circuit that operates on a novel complex data format where the real and imaginary parts of the
20120191766 source and result operands are represented by single precision floating point numbers. The invention provides direct support for complex numbers in floating point 07-26-2012
representation, thus reducing the number of instructions and processor cycles with improved performance.
GENERATION OF TEST CASES WITH RANGE CONSTRAINTS FOR FLOATING POINT ADD AND SUBTRACT INSTRUCTIONS - Methods, apparatus and systems are disclosed for the generation of
20120203813 range-constrained test cases for verification of designs of arithmetic floating point units. Given three ranges of floating point numbers Rx, Ry, Rz, a floating point operation 08-09-2012
(op), and a rounding-mode (round), three floating point numbers
DYNAMIC RANGE ADJUSTING FLOATING POINT EXECUTION UNIT - A floating point execution unit is capable of selectively repurposing a subset of the significand bits in a floating
20130191432 point value for use as additional exponent bits to dynamically provide an extended range for floating point calculations. A significand field of a floating point operand may be 07-25-2013
considered to include first and second portions, with the first portion capable of being concatenated with the second portion to represent the significand for a floating point
value, or, to provide an extended range, being concatenated with the exponent field of the floating point operand to represent the exponent for a floating point value.
FLOATING-POINT VECTOR NORMALISATION - When performing vector normalisation upon floating point values, an approximate reciprocal value generating instruction is used to
generate an approximate reciprocal value with a mantissa of one and an exponent given by a bitwise inversion of the exponent field of the input floating point number. A
modified number of multiplication instruction is used which performs a multiplication giving the standard IEEE 754 results other than when a signed zero is multiplied by a
20130246496 signed infinity which results a signed predetermined substitute value, such as 2. The normalisation operation may be performed by calculating a scaling value in dependence upon 09-19-2013
the vector floating point value using the approximate reciprocal value generating instruction. Each of the input components may then be scaled using the modify multiplication
instruction to generate a scaled vector floating point value formed of a plurality of scaled components. The magnitude of the scaled vector floating point value can then be
calculated and each of the individual scaled components divided by this magnitude to generate a normalised vector floating point value. The scaling value may be set to 2, where
C is an integer value selected such that the sum of the squares of the plurality of scale components is less than a predetermined limit value.
ARITHMETIC CIRCUIT AND ARITHMETIC METHOD - An arithmetic circuit includes a storage circuit configured to store a decimal floating point number in an encoded state, a detection
20130262546 circuit configured to detect a pattern of an arrangement of zeros from a bit pattern of the decimal floating point number by decoding the decimal floating point number stored 10-03-2013
in the storage circuit, and a leading-zero-count circuit configured to generate data indicative of a number of consecutive zeros starting from a most significant bit or from a
least significant bit in a significand of the decimal floating point number in response to a detection result obtained by the detection circuit.
METHOD AND APPARATUS FOR DECIMAL FLOATING-POINT DATA LOGICAL EXTRACTION - Embodiments of systems, apparatuses, and methods for performing BIDSplit instructions in a computer
20140019506 processor are described. In some embodiments, the execution of a BIDSplit instruction tests the encoding of a binary-integer decimal source value and extracts a sign, exponent, 01-16-2014
and/or significand into a destination.
INSTRUCTION AND LOGIC FOR PERFORMING A DOT-PRODUCT OPERATION - Method, apparatus, and program means for performing a dot-product operation. In one embodiment, an apparatus
20140032624 includes execution resources to execute a first instruction. In response to the first instruction, said execution resources store to a storage location a result value equal to 01-30-2014
a dot-product of at least two operands.
ARITHMETIC CIRCUIT FOR CALCULATING CORRECTION VALUE - An arithmetic circuit for calculating a correction value for a result of an arithmetic operation that is an addition or
subtraction performed with respect to a first floating-point number and a second floating-point number smaller than the first floating-point number. The arithmetic circuit
20140059104 includes a generation unit configured to generate a significand of a normalized correction value for the result of the arithmetic operation and an exponent of the normalized 02-27-2014
correction value based on the sign, the significand, and the exponent of the second floating-point number when a difference between a result of subtracting the leading zero
count of the significand of the first floating-point number from the corresponding exponent and a result of subtracting a leading zero count of the significand of the second
floating-point number from the corresponding exponent is larger than or equal to a second predetermined value.
NUMBER REPRESENTATION AND MEMORY SYSTEM FOR ARITHMETIC - A method, device and system for representing numbers in a computer including storing a floating-point number M in a
computer memory; representing the floating-point number M as an interval with lower and upper bounds A and B when it is accessed by using at least two floating-point numbers in
20140074902 the memory; and then representing M as an interval with lower and upper bounds A and B when it is used in a calculation by using at least three floating-point numbers in the 03-13-2014
memory. Calculations are performed using the interval and when the data is written back to the memory it may be stored as an interval if the size of the interval is
significant, i.e. larger than a first threshold value. A warning regarding the suspect accuracy of any data stored as an interval may be issued if the interval is too large,
i.e. larger than a second threshold value.
METHOD AND DEVICE FOR HANDLING DATA VALUES - A floating point value can represent a number or something that is not a number (NaN). A floating point value that is a NaN having
20140280424 data field that stores information, such as a propagation count that indicates the number of times a NaN value has been propagated through instructions. A NaN evaluation 09-18-2014
instruction can determine whether one or more operands is a NaN operand of a particular type, and if so can generate a result that is a NaN of a different type. An exception
can be generated based upon the NaN of the different type being provided as a resultant
METHOD AND DEVICE FOR GENERATING AN EXCEPTION - A floating point value can represent a number or something that is not a number (NaN). A floating point value that is a NaN
20140280425 having data field that stores information, such as a propagation count that indicates the number of times a NaN value has been propagated through instructions. A NaN evaluation 09-18-2014
instruction can determine whether one or more operands is a NaN operand of a particular type, and if so can generate a result that is a NaN of a different type. An exception
can be generated based upon the NaN of the different type being provided as a resultant
PROCESSOR AND CONTROL METHOD OF PROCESSOR - A processor includes: an exponent generating unit that generates an exponent part of a coefficient represented by a floating point
number format based on a first part of received input data, the coefficient being obtained when an exponential function is decomposed into a series operation and the
20140379772 coefficient for the series operation; a storage unit that stores a mantissa part of the coefficient; a constant generating unit that reads constant data corresponding to a 12-25-2014
second part of the input data from the storage unit; and a selecting unit that selects and outputs the constant data from the constant generating unit when an instruction to be
executed is a coefficient calculation instruction for calculation of the coefficient of the exponential function.
Performing Arithmetic Operations Using Both Large and Small Floating Point Values - Mechanisms are provided for performing a floating point arithmetic operation in a data
processing system. A plurality of floating point operands of the floating point arithmetic operation are received and bits in a mantissa of at least one floating point operand
20150074162 of the plurality of floating point operands are shifted. One or more bits of the mantissa that are shifted outside a range of bits of the mantissa of at least one floating 03-12-2015
point operand are stored and a vector value is generated based on the stored one or more bits of the mantissa that are shifted outside of the range of bits of the mantissa of
the at least one floating point operand. A resultant value is generated for the floating point arithmetic operation based on the vector value and the plurality of floating
point operands.
20150095393 METHOD AND DEVICE FOR GENERATING FLOATING-POINT VALUES - A floating-point value can represent a number or something that is not a number (NaN). A floating-point value that is a 04-02-2015
NaN includes a portion that stores information about the source operands of the instruction.
FAST NORMALIZATION IN A MIXED PRECISION FLOATING-POINT UNIT - A hardware circuit for returning single precision denormal results to double precision. A hardware circuit
20150149521 component configured to count leading zeros of an unrounded single precision denormal result. A hardware circuit component configured to pre-compute a first exponent and a 05-28-2015
second exponent for the unrounded single precision denormal result. A hardware circuit component configured to perform a second normalization of the rounded single precision
denormal result back to architected format.
FAST NORMALIZATION IN A MIXED PRECISION FLOATING-POINT UNIT - A hardware circuit for returning single precision denormal results to double precision. A hardware circuit
20150149522 component configured to count leading zeros of an unrounded single precision denormal result. A hardware circuit component configured to pre-compute a first exponent and a 05-28-2015
second exponent for the unrounded single precision denormal result. A hardware circuit component configured to perform a second normalization of the rounded single precision
denormal result back to architected format.
PROCESSING FIXED AND VARIABLE LENGTH NUMBERS - Embodiments of a processor are disclosed for performing arithmetic operations on variable-length and fixed-length machine
20150293747 independent numbers. The processor may include a floating point unit, and a logic circuit. The number unit may be configured to receive an operation, and first and second 10-15-2015
operands. Each of the first and second operands may include a sign byte, and multiple mantissa bytes, and may be processed in response to a determination that the operands are
fixed-length numbers. The logic circuit may be further configured to perform the received operation on the processed first and second operands.
20150378676 IDEMPOTENT REPRESENTATION OF NUMBERS IN EXTENSIBLE LANGUAGES - Technologies and implementations for representing floating-point numbers in an extensible language are generally 12-31-2015
DATA PROCESSING APPARATUS AND METHOD USING PROGRAMMABLE SIGNIFICANCE DATA - An apparatus may have processing circuitry to perform one or more arithmetic operations for
generating a result value based on at least one operand. For at least one arithmetic operation, the processing circuitry is responsive to programmable significance data
20160124710 indicative of a target significance for the result value, to generate the result value having the target significance. For example, this allows programmers to set a 05-05-2016
significance boundary for the arithmetic operation so that it is not necessary for the processing circuitry to calculate bit values having a significance outside the specified
boundary, enabling a performance improvement.
20160124712 EXPONENT MONITORING - A processing apparatus 05-05-2016
ACCURACY-CONSERVING FLOATING-POINT VALUE AGGREGATION - A method for enhancing an accuracy of a sum of a plurality of floating-point numbers. The method receives a
floating-point number and generates a plurality of provisional numbers with a value of zero. The method further generates a surjective map from the values of an exponent and a
20160139881 sign of a mantissa to the provisional numbers in the plurality of provisional numbers. The method further maps a value of the exponent and the sign of the mantissa to a first 05-19-2016
provisional number with the surjective map. The method further generates a test number from the first provisional number and if the test number exceeds a limit, modifies a
second provisional number by using at least part of the test number. The method further equates the first provisional number to the test number if the test number does not
exceed the limit. The method further sums the plurality of provisional numbers.
Digital Signal Processor - A processor configured to: receive, at a floating-point-input-terminal, an input-block of data comprising a plurality of floating-point numbers each
20160188293 floating-point number comprising a mantissa and an exponent; determine an input-scale-factor based on a previous-input-block-exponent-value associated with a 06-30-2016
previous-input-block of data; and convert the input-block of data into a fixed-point-block of data in accordance with the input-scale-factor, wherein the fixed-point-block of
data comprises a plurality of fixed-point-values that can represent the plurality of floating-point numbers within a particular range.
DEVICE AND METHOD FOR HARDWARE-EFFICIENT ADAPTIVE CALCULATION OF FLOATING-POINT TRIGONOMETRIC FUNCTIONS USING COORDINATE ROTATE DIGITAL COMPUTER (CORDIC) - A system and an
accelerator circuit including a register file comprising instruction registers to store a trigonometric calculation instruction for evaluating a trigonometric function, and
20220137925 data registers comprising a first data register to store a floating-point input value associated with the trigonometric calculation instruction. The accelerator circuit further 05-05-2022
includes a determination circuit to identify the trigonometric calculation function and the floating-point input value associated with the trigonometric calculation instruction
and determine whether the floating-point input value is in a small value range, and an approximation circuit to responsive to determining that the floating-point input value is
in the small value, receive the floating-point input value and calculate an approximation of the trigonometric function with respect to the input value.
Patent applications in class Floating point
Patent applications in all subclasses Floating point
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What is Bayesian Reasoning: Understanding Probabilistic Thinking - Aspire Atlas
Bayesian reasoning is an approach to statistics that allows you to update the probability estimate for a hypothesis as additional evidence is provided. This method rests on Bayes’ Theorem, a
mathematical formula that relates the conditional and marginal probabilities of stochastic events. At its core, Bayesian reasoning is about belief—measuring and adjusting one’s confidence in a
hypothesis based on new data. Unlike other statistical methods, Bayesian reasoning incorporates prior knowledge or beliefs before examining the current evidence.
The Bayesian approach operates differently from traditional frequentist statistics, which do not take prior probabilities into account. When you apply Bayesian reasoning, you start with an initial
belief, known as the prior, which is then updated as new evidence is presented. The result is the posterior probability, representing the revised belief after considering the new evidence. This
method has gained popularity due to its applicability in various fields, including artificial intelligence, epidemiology, and even policy-making, where probabilities are continually revised in light
of new information.
Key Takeaways
• Bayesian reasoning updates the probability of a hypothesis based on new evidence.
• It contrasts with frequentist methods by incorporating prior knowledge.
• The approach is widely applicable across different fields requiring dynamic probability assessments.
Fundamentals of Bayesian Reasoning
Bayesian reasoning is a method of statistical inference that you can use to update the probability for a hypothesis as more evidence becomes available.
Definition and Principles
Bayesian reasoning is anchored in updating the degrees of belief in a hypothesis based on new data. It is grounded in two key principles:
1. Prior Probability: This is your initial belief about the probability of an event, before considering the latest evidence.
2. Posterior Probability: After you obtain new evidence, you revise the prior probability to the posterior probability, reflecting the updated likelihood of the event.
Bayes’ Theorem Explained
At the core of Bayesian reasoning is Bayes’ Theorem, a mathematical formula used to update the probabilities:
P(H|E) = [P(E|H) * P(H)] / P(E)
• P(H|E) is the posterior probability: the probability of hypothesis H given the evidence E.
• P(E|H) is the likelihood: the probability of evidence E given that the hypothesis H is true.
• P(H) is the prior probability: the initial probability of hypothesis H.
• P(E) is the marginal likelihood: the total probability of the evidence E under all hypotheses.
Using Bayes’ Theorem allows you to make more accurate predictions by incorporating new evidence into your existing beliefs.
The Bayesian Approach
In the Bayesian approach to reasoning, you apply mathematics to incorporate your existing beliefs with new evidence and systematically update your understanding of a probability.
Incorporating Prior Knowledge
When you begin with the Bayesian method, your existing knowledge and beliefs about a situation are formally expressed as prior probabilities. These are your initial starting points before considering
new data.
• Prior probability:
□ Represents subjective judgement
□ Expressed as a percentage (e.g., 70% chance of rain)
Updating Beliefs with New Evidence
After establishing your priors, the next step is to adjust these probabilities when new evidence is provided. This is done using Bayes’ theorem, which mathematically combines the prior probability
with the likelihood of the new evidence to result in an updated probability, known as the posterior probability.
Bayes’ Theorem Formula:
Posterior = (Likelihood x Prior) / Evidence
• Posterior probability:
□ Updated belief after considering new information
□ Changes with successive evidence
By applying this framework, you continuously refine your probability assessments, making the Bayesian approach a dynamic and iterative process of learning.
Applications of Bayesian Reasoning
Bayesian reasoning has transformative applications across various domains. It offers a structured way for updating beliefs in light of new evidence. Here’s how you might see it in action across
different fields.
Scientific Research
In scientific research, Bayesian methods are pivotal for updating hypotheses based on experimental data. For example, they are used in epidemiological studies to estimate disease prevalence.
Epidemiologists start with a prior belief about the prevalence rate, and as new data come in—such as from clinical trials—they revise their estimates. This iterative process can be represented by
the Bayes’ theorem formula:
[ P(H|E) = \frac{P(E|H) \cdot P(H)}{P(E)} ]
Here, ( P(H|E) ) is the probability of the hypothesis given the evidence, ( P(E|H) ) is the probability of the evidence given the hypothesis, ( P(H) ) is the initial probability of the hypothesis,
and ( P(E) ) is the probability of the evidence.
Machine Learning
In machine learning, Bayesian reasoning supports algorithmic decision-making. It helps in building probabilistic models, such as Bayesian networks, which are effective for diagnosis or predictive
analytics. Within these models, each node represents a variable, and the edges indicate the probabilistic dependencies between them.
For instance, if you had a network for medical diagnosis, it could include nodes for symptoms and diseases with the edges representing the conditional probabilities. As symptoms are observed, the
probabilities for various diseases are updated accordingly.
1. Bayesian Networks: Understand complex variable relationships
2. Predictive Analytics: Make forecasts based on updated data
3. Natural Language Processing (NLP): Interpret and process human language
Decision Making
In decision making, both in business and personal contexts, Bayesian reasoning helps to make informed decisions under uncertainty. For investment strategies, businesses can leverage Bayesian
statistics to assess market trends and consumer behavior. Initial market beliefs are updated with incoming data, such as sales figures or economic indicators, to make adaptive business strategies.
• Risk Assessment: Calculate and revise probabilities as new information is available.
• Strategic Planning: Develop flexible business strategies and forecasts.
• Behavioral Economics: Predict consumer choices and market movements.
Contrast with Frequentist Statistics
Bayesian reasoning and frequentist statistics offer distinct perspectives on probability and data analysis. When you approach a problem with Bayesian reasoning, you’re incorporating prior beliefs or
knowledge before examining the current data. This prior belief, quantified as a prior probability, is updated to a posterior probability by using the likelihood of the observed data.
On the other hand, frequentist statistics rely on the long-run frequency of events to define probabilities. It does not incorporate prior beliefs; instead, it assumes that probabilities are the
result of an infinite number of repetitions of a process.
Here’s a comparative look at key differences:
• Incorporating Prior Information:
□ Bayesian: Yes – Applies prior probability.
□ Frequentist: No – No prior, only the data.
• Interpretation of Probability:
□ Bayesian: Probability is the measure of belief or certainty.
□ Frequentist: Probability is the long-term frequency of occurrence.
• Approach to Parameters:
□ Bayesian: Parameters are considered random variables.
□ Frequentist: Parameters are fixed but unknown quantities.
• Confidence Intervals:
□ Bayesian: Generate credible intervals, which directly answer “What’s the probability that the parameter lies in this interval?”
□ Frequentist: Create confidence intervals that aren’t as intuitive, answering “If this procedure were repeated, what’s the proportion of intervals that would contain the parameter?”
In essence, your choice between Bayesian and frequentist statistics impacts your approach to uncertainty and the way you include or exclude prior information in the analysis.
Challenges and Criticisms
Bayesian reasoning, while powerful, faces specific challenges and has been subject to criticisms regarding its practical application and philosophical implications.
Computational Complexity
When you apply Bayesian methods, the computational load can be significant. Complex models that incorporate a large number of variables can require sophisticated computational techniques. The use of
Markov chain Monte Carlo (MCMC) methods alleviates some of these issues, but these still demand substantial computational resources and time, particularly for large datasets.
• High Dimensionality: The more parameters your model has, the more complex the needed calculations.
• Intensive Computations: Algorithms such as MCMC can be computationally expensive and slow.
These computational demands may limit the use of Bayesian methods in real-time applications or situations where computational resources are constrained.
Subjectivity of Priors
A distinctive feature of Bayesian reasoning is the use of priors, which represent previous knowledge about a parameter before any new data is considered. However, the selection of these priors can
introduce subjectivity into the analysis.
• Prior Selection: You must choose a suitable prior, and this choice can affect the results.
• Influence on Posteriors: In some cases, especially with limited data, the prior can have a large influence on the posterior distribution.
Because your choice of priors can significantly influence the analysis outcomes, some critics argue that Bayesian methods can lead to subjective results. However, with sufficient data, the influence
of the prior tends to diminish and the posterior distribution reflects the data more than the prior.
Advancements in Bayesian Analysis
Bayesian analysis has seen significant improvements with advancements in computational techniques and algorithms. Your understanding of complex models and large datasets has been greatly enhanced by
these developments.
Markov Chain Monte Carlo Methods
Markov Chain Monte Carlo (MCMC) methods have revolutionized the way you perform Bayesian analysis. By allowing for sampling from complex and multidimensional distributions, these methods have enabled
you to approximate posterior distributions even when they are not analytically tractable. Utilizing a sequence of random samples from a probability distribution, MCMC methods such as the
Metropolis-Hastings algorithm and Gibbs sampling have become standard tools.
Metropolis-Hastings Algorithm:
• Probability Distribution Sampling: Samples are generated using a proposal distribution, helping to explore the posterior efficiently.
• Acceptance Criterion: A new sample is accepted based on a criterion that ensures convergence to the target distribution over time.
Gibbs Sampling:
• Sequential Updating: Each variable is updated in turn, conditioned on the current values of the other variables.
• Convergence: Given enough iterations, convergence to the full joint distribution is achieved.
Approximate Bayesian Computation
Approximate Bayesian Computation (ABC) allows for Bayesian inference when it is difficult or impossible to calculate the likelihood function, a common challenge with complex models. ABC is based on
the principle of accepting parameter values if the simulated data generated by these parameters are close enough to the observed data.
Key Features of ABC:
• Simulation-Based Inference: Relies on simulating data and comparing it to observed data rather than calculating complex likelihoods.
• Tolerance Levels: A measure of how close the simulated data must be to the observed data to accept a parameter value.
By embracing these advanced methods, you are equipped to tackle Bayesian inference tasks that were once infeasible, opening up new possibilities in statistical modeling and data analysis.
Software and Tools for Bayesian Analysis
When you approach Bayesian analysis, several software packages and tools can facilitate your work.
– R: You’ll find a comprehensive environment for statistical computing and graphics. Notably, the package rjags interfaces with the JAGS library for conducting Bayesian data analysis. RStan, the R
interface to Stan, offers advanced sampling for Bayesian inference.
• Python: This language provides libraries such as PyMC3 and PyStan for Bayesian modeling, allowing you to perform full probabilistic programming easily.
• Stan: A programming language for statistical inference which is making it easier for you to specify your Bayesian models.
• JAGS: The Just Another Gibbs Sampler (JAGS) is a tool for analysis of Bayesian hierarchical models using Markov Chain Monte Carlo (MCMC).
• BUGS: Bayesian inference Using Gibbs Sampling (BUGS) is a classic software package for performing Bayesian analysis.
• SAS: Offers procedures for Bayesian analysis that are integrated into its broader suite of statistical methods.
Here is a comparison table for features across different tools to assist you in choosing the right one for your needs:
Tool Programming Language MCMC Sampling Interfaces Additional Features
R R Yes rjags, RStan Comprehensive statistics
Python Python Yes PyMC3, PyStan Probabilistic programming
Stan Stan Yes R, Python, others Flexible model building
JAGS C++ Yes R, Python Easy to use syntax
BUGS Own syntax Yes R (R2WinBUGS) Early pioneer in Bayesian
SAS SAS Yes SAS stat Integrated with SAS
Your choice will depend on your familiarity with each programming environment and the specific requirements of your Bayesian analysis project.
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You can choose among various operators to structure your LibreOffice Math formula. All available operators appear in the lower part of the Elements pane. They are also listed in the context menu of
the Commands window. All operators not contained in the Elements pane or in the context menu must be typed manually in the Commands window.
The following is a list of the available operators. An icon next to the operator name indicates that it can be accessed through the Elements pane (choose View - Elements) or through the context menu
of the Commands window.
Operator Functions
Inserts the limit sign with one placeholder. You can also enter lim <?> directly in the Commands window.
Inserts a summation sign with one placeholder. You can also enter sum <?> directly in the Commands window.
Inserts a product sign with one placeholder. You can also type prod <?> directly in the Commands window.
Inserts a coproduct symbol with one placeholder. You can also enter coprod <?> directly in the Commands window.
Upper and Lower Limit
Inserts a range statement upper and lower limit for integral and summation with one placeholder. You can also type from{<?>} to{<?>} <?> directly in the Commands window. Limit statements must be
combined with the appropriate operators. The limits will be centered above/below the summation character.
Inserts an integral sign with one placeholder. You can also type int <?> directly in the Commands window.
Double Integral
Inserts a double integral symbol with one placeholder. You can also type iint <?> directly in the Commands window.
Triple Integral
Inserts a triple integral sign with one placeholder. You can also type iiint <?> directly in the Commands window.
Lower Limit
Inserts a lower limit range statement for integral and sum with placeholders. You can also type from {<?>}<?> directly in the Commands window.
Curve Integral
Inserts a curve integral symbol with one placeholder. You can also type lint <?> directly in the Commands window.
Double Curve Integral
Inserts a double curve integral symbol with one placeholder. You can also type llint <?> directly in the Commands window.
Triple Curve Integral
Inserts a triple curve integral sign with one placeholder. You can also type lllint <?> directly in the Commands window.
Upper Limit
Inserts the range statement upper limit for integral and summation with placeholders You can also type to <?><?> directly in the Commands window. Limit statements can only be used if combined with
the appropriate operators.
You can also add limits to an operator (for example, an integral) by first clicking the desired operator and then clicking the limit symbol. This method is faster than typing the commands directly.
The command liminf inserts the limit inferior with one placeholder.
The command limsup inserts the limit superior with one placeholder.
By typing oper in the Commands window, you can insert user-defined operators in LibreOffice Math, a feature useful for incorporating special characters into a formula. An example is oper %theta x.
Using the oper command, you can also insert characters not in the default LibreOffice character set. oper can also be used in connection with limits; for example, oper %union from {i=1} to n x_{i}.
In this example, the union symbol is indicated by the name union. However, this is not one of the predefined symbols. To define it, choose Tools - Symbols. select Special as the symbol set in the
dialog that appears, then click the Edit button. In the next dialog, select Special as the symbol set again. Enter a meaningful name in the Symbol text box, for example, "union" and then click the
union symbol in the set of symbols. Click Add and then OK. Click Close to close the Symbols dialog. You are now finished and can type the union symbol in the Commands window, by entering oper %union.
Limits can be arranged in ways other than centered above/below the operator. Use the options provided by LibreOffice Math for working with superscript and subscript indexes. For example, type sum_a^b
c in the Commands window to arrange the limits to the right of the sum symbol. If your limit entries contain longer expressions, you must put them in group brackets, for example, sum_{i=1}^{2*n} b.
When formulas are imported from older versions this is done automatically. To change the spacing (gaps) between the characters choose Format - Spacing - Category - Indexes or Format - Spacing -
Category - Limits. Additional basic information about indexes is given elsewhere in the Help.
When you type information manually in the Commands window, note that a number of operators require spaces for correct structure. This is especially true when your operators are supplied with values
instead of placeholders, for example, lim a_{n}=a.
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SSC Math Question Solution All Board | Get 99% Answers Here - BD Today ResultSSC Math Question Solution All Board | Get 99% Answers Here
SSC Math Question Solution All Board | Get 99% Answers Here
SSC Math Question Solution All Board
This Post is for these Students who are seeking SSC Math Question Solution All Board for 2023. Today’s math questions will be solved in this post. We gather all the board question papers and
furthermore solve these inquiries. These Math Questions 2023 will be solved by our expert Math teachers and members. In this way, You Can Gather the Right Responses From Our Site. So, Share This Post
With Your Friends. SSC Math Question Solve 2023.
SSC Math Question Solution 2023 PDF
Some of you also Want to know SSC Math Question Solution 2023 pdf. So, We will upload SSC Math Question Solution 2023 pdf here. This article will help you to find SSC Math Exam’s Question and also
Answer. Many students in Bangladesh are very much weak in Math and they can’t answer the full Question. This Year SSC Math Exam will be held on 09th May 2023. As a result, after the exam is finished,
the answer paper will be posted here.
In this article, we will provide you with the SSC Math question solutions for all education boards in Bangladesh. We understand that this can be a stressful time for you, and having access to the
correct solutions can help ease your worries and provide you with the necessary information to move forward with your studies.
So, whether you’re a student from the Dhaka Education Board, Chittagong Education Board, Rajshahi Education Board, or any other board in the country, we’ve got you covered. Keep reading to get the
solutions to all the questions in the SSC Math exam.
We hope that this article helps you to achieve success in your academic pursuits and that you continue to strive towards your goals. Good luck, and keep learning!
Exam Name : SSC (Secondary School Certificate)
Website http://www.educationboard.gov.bd/
Exam Board All Board
Country Bangladesh
Date: 9 May 2023 at 10.00 am-1.00 pm
Year : 2023
Subject name Math
Subject code 109
Marks 100
SSC Math Question With Answers 2023 Dhaka Board
If You are a student of SSC Candidates then you can Check Your Question Answers Here. We will be updating here MCQ (Multiple Choice Question). I request all the students to read all the topics of the
exam by scrolling from top to bottom. We’ve mentioned many SSC exam topics, question types, and solutions.
Dinajpur Board SSC Math Solution 2023
Barisal Board SSC Math Solution 2023
Mymensingh Board SSC Math Question Solution 2023
Dhaka SSC Math Solution 2023
Rajshahi Board SSC Math Question Solution 2023
Comilla Board SSC Math Solution 2023
Chittagong Board SSC Math Question Solution 2023
Sylhet Board SSC Math Question Solution 2023
Jessore Board SSC Math Question Solution 2023
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iqdmrg related problem
Dear all:
I would like to understand more about iqdmrg. I hope you can help me. Thanks in advance. The questions are listed as below.
1. Is it correct that iqdmrg is a U(1) symmetric dmrg program?
2. Take heisenberg chain as an example, the quantum number of the tensor index in the center of the chain is truncated. I would like to know how you do this. For example, one tensor at site 49 shown
below. I suppose that for this tensor there also quantum numbers like QN(49), QN(48),... but here they are definitely truncated.
r=3 div=QN(0) log(scale)=0
IQIndex(d,8,Link,7) < Out >
(d1,1,Link,822) QN(3)
(d2,3,Link,201) QN(1)
(d3,3,Link,631) QN(-1)
(d4,1,Link,125) QN(-3)
IQIndex(S=1/2 49,2,Site,338) < Out >
(Up 49,1,Site,810) QN(1)
(Dn 49,1,Site,550) QN(-1)
IQIndex(d,8,Link,551) < In >
(d0,1,Link,410) QN(4)
(d1,3,Link,691) QN(2)
(d2,3,Link,705) QN(0)
(d3,1,Link,921) QN(-2)
\ ------------------------------------
1. I also tested with pure external magnetic form H= \sum h*S^z. The ground state shows that the total quantum number of the wave function is QN(0), which concerned me a lot since I expect the
quantum number of the chain should be QN(N). Is that correct?
Sorry for the massive contents, and probably trivial questions listed above. But I do want to know more on this. Any comments are welcomed. Thanks very much.
Best Regards
Wangwei Lan
Hi Wangwei,
These are all reasonable questions based on the small amount of documentation we have on the "IQTensor" system so far. Hopefully in the near future the ITensor book section will be expanded even more
to cover all of these questions.
(1) iqdmrg (and the IQTensor / IQMPS / IQMPO system more generally) can handle U(1) symmetries associated with conserving quantum numbers following an integer addition rule as well as quantum numbers
following a Z_N addition rule (addition modulo N). So for example you can also conserve just fermion parity instead of fermion number, or more exotic kinds of quantum numbers. The documentation page
on the QN class gives a variety of examples: http://itensor.org/docs.cgi?page=classes/qn
(2) The way IQTensors are truncated is that all of their non-zero blocks are SVD'd separately (for more on IQTensor blocks, see http://itensor.org/docs.cgi?page=book/block_sparse). All of the
resulting singular values are collected, and sorted, and then used to determine a threshold or cutoff for the entire spectrum of the IQTensor. This threshold is then applied to each block to truncate
it. Some blocks may get truncated entirely in this process in which case they are removed. The result is really very similar to how truncation is defined for SVD'ing a dense tensor but is much more
efficient due to the sparsity.
(3) The way that iqdmrg determines the quantum number (QN) sector to work in is from the initial state (IQMPS wavefunction) that you provide it. The main feature of iqdmrg is that it will not change
the global QNs of the IQMPS. So if you give it an IQMPS with a total Sz of zero, nothing the code does can change this, even if you include a magnetic field. If you want to get the ground state in a
different QN sector, you must change the initial state you provide. The InitState object is a convenient way to specify an initial state by giving a product-state spin pattern.
Hope that helps. Please post a comment back if you have additional questions.
Hello, Miles,
Thanks very much for the detailed explanation. These are very helpful to me. I think now all these things are clear to me.
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Electromagnetic Forces
Electric charge is, like mass, a fundamental property—a property that isn’t explained in terms of other properties. Yes, you can explain the charge of an object in terms of the number of protons and
electrons it contains (as we’ll see in chapter 4); but the fact that electrons and protons have charge isn’t explained in terms of anything else, at least in classical physics. Some fundamental
particles just have charge, and others don’t, end of story.
Most macroscopic objects have no total charge, because they are comprised of atoms that contain an equal number of positively charged protons and negatively charged electrons. But electrons tend to
accumulate near the surfaces of some materials, and to move away from the surfaces of other materials. So rubbing different materials together can sometimes transfer electrons from one material to
another. For example, rubbing a plastic comb through your hair can transfer electrons from your hair to the comb, resulting in a negatively-charged comb and positively-charged hair.
Recall that any two objects with mass exert gravitational forces on each other. Similarly, any two charged objects exert forces on each other, and these forces are described by a law similar in form
to Newton’s law of universal gravitation. The corresponding law for electric charges is named after French physicist Charles Augustin de Coulomb. Coulomb’s law says that any two charged objects exert
a force on each other. The force is attractive if the objects have opposite charge (one positive and the other negative), and repulsive if they have the same charge (both positive or both negative).
The strength of this force depends on their charges and the distance between them as follows:
F =
In the above equation, F is the magnitude (strength) of the force, c[1] and c[2] are the charges of the objects (in coulombs), and d is the distance between them. k is Coulomb’s constant, which has
the following value:
k = 9.00 × 10^9 N m^2/C^2
Like the gravitational constant (G), Coulomb’s constant is the same at all times and places throughout the universe: it is a physical constant.
Notice the close resemblance between Coulomb’s law and Newton’s law of universal gravitation:
force =
Newton’s law
of universal gravitation: G × mass[1] × mass[2]
force =
Coulomb’s law:
k × charge[1] × charge[2]
Mass and charge are both fundamental properties, and the fundamental forces associated with them are very similar. There are several important differences, however:
1. Unlike mass, charge comes in two types: positive and negative. Objects with the same type of charge exert a repulsive force on each other, while objects with opposite charge exert an attractive
force on each other. The gravitational force, in contrast, is always attractive.
2. Gravitational and electromagnetic forces differ dramatically in strength: the force of gravity is extremely weak compared to the electromagnetic force.
You can get some idea of the relative strengths of these forces by comparing the fundamental constants: G is a very tiny number, whereas k is a very large number. However, the numerical values of
these constants depend on our choice of units, which is arbitrary. It is possible to choose mass units much larger than kilograms, and charge units much smaller than Coulombs, so that G and k
have the same numerical value.
For a more objective comparison of the strengths of the fundamental forces, we can compare the forces exerted between fundamental particles like electrons or protons, which have both mass and
charge. For example, any two protons in the universe are exerting both a gravitational force and an electromagnetic force on each other all the time. Regardless of how far apart the protons are,
the strength of the electromagnetic force between them is approximately 10^36 times stronger than the gravitational force between them. (That’s 1,000,000,000,000,000,000,000,000,000,000,000,000
times stronger!) With electrons, the difference between the gravitational and electromagnetic forces is even more extreme, since electrons have just as much charge as protons but far less mass.
3. Electric charges are associated with two types of fields (electric fields and magnetic fields), whereas mass is associated only with the gravitational field. We’ll learn what fields are on the
next page.
4. When charged objects move, the electromagnetic force does funky things. We’ll learn about that on the next page, too.
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What is the Average Speed of a Sailboat?
When I try to figure out the duration of whatever sailing trip I have in the making, I always need to know this one thing first: the average speed of a sailboat - especially with long journeys. If
you have the same problem, this article is for you.
So what's the average speed of a sailboat? Most sailboats cruise at a speed of 4-6 knots (4.5-7 mph), with a top speed of 7 knots (8 mph or 13 km/h). Larger racing yachts can easily reach speeds up
to 15 knots (17 mph or 28 km/h), with an average cruising speed between 6-8 knots (7-9 mph). Cruising speeds of over 8 knots are uncommon.
Different types of sailboats reach very different speeds. Of course, it all depends on wind conditions, current, and many other factors. Did you know that the speed of a boat is directly related to
its length? The larger the boat, the faster it goes. I'll explain it to you later on, but first, more on average speed.
Factors That Determine Speed
So let's get a little more into detail on sailboat speed. The most important factor in determining the speed is the hull type. I have two rules of thumb for you. The first is: the less of the boat is
under water, the faster it goes.
Here are the average cruising speeds for different hull types:
• Monohull - 6-8 knots
• Catamaran and trimarans - 9-10 knots
• Fastest monohull (world record circumnavigation) - 15.43 knots
• Fastest trimaran (world record circumnavigation) - 27 knots
Monohull - Your average sailboat is a monohull. Nearly all monohulls are displacement hulls. A displacement hull is under water, pushing the water away. This allows the boat to cut through the water
more smoothly; this stabilizes the boat. If you want to make it go faster, you would have to raise the entire hull above the water. Later on I'll show you how to calculate the maximum hull speed of
your boat.
Catamarans and Trimarans - These are planing hulls, meaning they are on top of the water. They displace less water, which is why they are faster. But a planing hull is less stable than a displacement
hull. To compensate, catamarans and trimarans have two or three hulls, which makes them extremely buoyant. Since this is not your average sailboat I'll leave them out of this article.
The second factor is the length of the boat. It's the second rule of thumb: the longer the boat, the faster it goes. Each sailboat has a maximum hull speed, which it can't exceed (in theory). The
hull speed is determined by the length of the boat.
Here are the maximum hull speeds for different monohull lengths:
length meters knots mph km/h
16 ft 5 m 5 5.8 9.3
26 ft 8 m 6.8 7.8 12.6
36 ft 11 m 8 9.2 14.8
40 ft 12 m 8.5 9.8 15.7
65 ft 20 m 10.8 12.4 20
80 ft 24 m 12 13.8 22.2
100 ft 30 m 13.4 15.4 24.8
144 ft 44 m 16 18.4 29.6
Please note: the maximum hull speed isn't the average sailing speed. It's the upper limit (in theory - read on to learn more).
The third and perhaps most obvious factor of course is wind direction and speed. If you plan a large voyage, for example, an ocean passage, make sure to check the dominant wind and direction for your
time of year. You want to make sure to have as much downwind as you can get, and a favorable current as well. This is why most sailors choose to go eastward instead of westward when sailing the
If you want to know why going eastward is smart, I encourage you to read my previous article on sailing around the world here.
Converting and Calculating Sailing Speed
How to calculate necessary sailing speed
So imagine you need to get to dock in time. It's 50 miles away. You need to arrive at 2100 hours. It's currently 1500 hours. Would be handy to know at what speed you need to sail to make it in time.
The formula is simple:
nautical miles / time = average speed necessary
2100 - 1500 = 360 minutes
360 / 60 = 6 hours
Your average speed should be: 50 NM / 6 = 8.3 knots
Converting knots to mph and km/h
To convert knots to mph or km/h, simply multiply the knots by the ratio below.
1 knot = 1.151 mph
1 knot = 1.852 km/h
Calculating the Hull Speed of Your Own Boat
Great, we have a good general idea of what to expect from our trustworthy vessels. If you want to go deeper, you can try to calculate the maximum hull speed of your own boat. Calculating the maximum
speed is actually very simple. Now is the time to get out your calculator.
You calculate the maximum hull speed (HS) by taking the length in feet (lwl), get the square root, and multiplying it by 1.34.
HS = √ lwl * 1.34
HS = Hull Speed
lwl = length at waterline
So a 80 feet boat has a maximum hull speed of:
√ 80 * 1.34 = 12 knots
Exceeding Hull Speed
A displacement hull has a maximum hull speed. Hull speed is a theoretical speed that tells us what the maximum efficient speed is. Everything above that speed costs a lot more energy. If you power
your boat by engine, you can exceed the speed by pushing the hull over your own bow wave (this requires a lot of horsepowers though, and it isn't good for your engine).
If you're sailing instead, you can exceed your hull speed with the help of the weather. Let's call these surfing conditions (sounds good). This might happen to you when you're sailing downwind and
the current pushes you forward simultaneously. This helps you to overtake your own bow wave. If this happens, the wavelength gets longer than the hull length: the water can't get out of the way fast
enough. As a result, the boat starts to plane, increasing water resistance at the front. Congratulations: you're surfing on your own bow wave.
The increase in speed won't be mind blowing however (about 1 knot). The truth is: a displacement hull is bound to its speed. It just costs to much energy to propel it through the water. It's made to
cut, not steamroll the water.
Amount of Nautical Miles
Sailboats don't travel lightning fast, but they do travel 24/7. Because of this, they can cover quite a bit of distance. What distance are we actually able to cover with conservative speeds?
The average sailboat covers a distance of roughly 100 nautical miles (NM), at a speed of around 4.5 knots. This equals 115 miles or 185 km.
1 NM is 1.852 km or 1.151 mile
You can calculate the distance per day by simply multiplying the speed in knots by 24 hours:
NM = knots * 24
Most sailboats cover anywhere between 100-180 NM per day. This means that a fast sailboat in ideal conditions can cover more than 200 miles. Impressive. However, anything over 180 NM is uncommon. We
usually only see cruising speeds that high in races.
Here are the distances per day (NM) for different cruising speeds:
hull speed NM miles km
Related Questions
How fast can a sailboat go under power? The average speed of a sailboat under power is 4-5 knots (5 mph or 8 km/h). Most sailors switch to engine at sailing speeds below 6 knots, especially when on
How fast do racing sailboats go? Racing sailboats can reach speeds of 30 - 50 knots (35-58 mph or 55-92 km/h). The record is set at 65.45 knots (75 mph or 121 km/h). They can beat wind speed because
they have a planing hull instead of a displacement hull, making them a lot faster than average sailboats
Can a sailboat sail faster than the wind? Sailboats with a planing hull (multihulls) can go faster than wind. Displacement hulls (the average sailboat) can't beat the wind, or just slightly in
surfing conditions.
Did you find the answer to your specific question?
👍 116 👎 7
Robert Tangney Kenmare Ireland
Just wondering if you could do a similar article on diesel powered boats.I have a Seaward 23 powered with two 1.6 mermaid engines.I normally do around 7_8 knots and was thinking of replacing them for
more speed around 10_12 knots.what engines would I need. According to what I have read already I should be getting 10 knots cruising speed with a top speed of 12 knots.This is not the case and her
bottom is very clean.Found your article very interesting.
Hi Robert, thanks for your comment. You have quite a bit of power there, nice.
I wouldn’t know for sure what engine size you should get, this article is specifically about sailboats. Also, this is the maximum hull speed - what you could expect under ideal conditions. And that’s
never the case - you have to deal with current, wind, and so on. So I’d say it sounds about right.
If by diesel-powered boats you mean a powerboat, I currently don’t write about powerboats. Maybe I will in the future, but I won’t make any promises for now.
Thanks again and good luck with your upgrade!
Ben L
I’m not sure if you use a different way of calculating time in nautical terms (Not a sailor myself, just curious about sailboats), but in the ‘How to calculate necessary sailing speed’ my math would
say there’s 6 hours = 360 minutes from 1500 hours (3 PM) to 2100 hours (9 PM), not 600 minutes = 10 hours. Am I missing something?
Hi Ben L,
That’s exactly right, it was a math error on my part. Thanks for pointing it out, I have updated the article.
Catamarans and trimarans are PLANING boats?! How long have you been sailing? Three days? :-)))
Matas Pacevicius
Just wanted to point out a typo. At hull speed of 5NM you travel 120NM and 138miles (not the 115 written) per 24hrs. Thank you for your articles. I’ve been dreaming of circumnavigation for years and
am in the process of designing and building my own sailboat for the feat. I would love to build and sail a sailboat on which I could live almost anywhere in the world. I currently reside on the Gulf
coast of Florida and am surrounded by beautiful warm waters that beckon me to explore them. Hopefully in the followings 5 years I will be sailing into the Caribbean in my self-built traveling home in
the water. I wish to call the oceans home and soon the entire world. I plan to cross the Atlantic from the Caribbean on my first leg around the world. Would you recommend sailing throughout the
Mediterranean? Any ideas on how’s to make money along the way?
Matt Buse
I’ve worked all my life, struggling. Now 56y.o. staring at becoming a jobless wanderer in the next couple of months, maybe pick up a used boat. I am just really curious how some people have the time
and place to design, build, and then sail around. Tell me your secrets…
Benjamin Lindner
Hello Shawn;
You have an error in your table above: 5 Knots = 120 NM BUT DOES NOT EQUAL 115 MILES.
Thank you Ben
Carlos Alberto Molinelli
But WHY is it a maximum speed for displacement boats in quiet waters, responding to this old formula? It is because the speed increases, the water displaced forms waves. At slow speed there are
several along the hull. At fast speed there are only two: one at the bow and another an the stern. If the boat tries to go faster, the stern wave would go more farther but the hull would lose
sustentation. It better explained with a picture. Look for boats going fast. You will see only two waves.
Robert Flores
Getting close to retirement and want to get a sailboat with some power. Thinking about sailing lakes and coastal. Looking at the macgregor 26M and seaward 26rk. What recommendations do you have ?? Or
things to think about. I am one for safety.
Best regards
Ronald Ernst van Dijk
Thank you. Very well explained in clear language, including the usual conversions between knots, miles and kilometers. It helps understanding the physics of sailboats and what to expect in terms of
speed. I have just completed building an 18 feet wooden gaff rigged yawl (design by François Vivier) for single handed coastal sailing in Malaysia, the country where I live. Your “rule of thumb”
about HS = Lwl * 1.34 seems to work well, although I have to further try it out with different wind speeds and sailing on a reach or down wind.
Your website is an ad horror show to the point it is not usable any more. Ads do have their place and purpose, just like food needs salt. But in your case there is more salt then there is food.
Moderation is key.
Ara Houston
Hello improvesailing.com owner, You always provide helpful information.
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How to find the greatest common divisor in C language_How to find the greatest common divisor in C language-php.cn
Home > Topic List > How to find the greatest common divisor in C language
How to find the greatest common divisor in C language
The C language can find the greatest common divisor through the Euclidean method, the exhaustive method, the phase change subtraction method and the Stein algorithm. PHP Chinese website also brings
you C language related tutorials and articles. You are welcome to come and learn and download.
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Full bloom filter blob capacity is never used?
(1) By J. Schaefer (jschaefer) on 2023-06-11 21:34:45 [source]
I am currently trying to understand how the bloom filter hashing works in sqlite (latest trunk).
In where.c an OP_Blob is set up with at least 80K bits of space for the bloom filter: sz = sqlite3LogEstToInt(pTab->nRowLogEst); if( sz<10000 ){ sz = 10000; // ... sqlite3VdbeAddOp2(v, OP_Blob, (int)
sz, pLevel->regFilter);
So there is now a Blob with a size of at least 10000 bytes (80K bit).
Then in vdbe.c in case OP_FilterAdd the filter is filled. Here h is the result of a hashing function and now a single 1 needs to be set in the filter:
h = filterHash(aMem, pOp); // ... h %= pIn1->n; pIn1->z[h/8] |= 1<<(h&7);
I think pIn1->z is the filter-blob and pIn1->n is the size of the filter blob. In case of e.g. the filter having the minimal size of 80K bits pIn1->n is 10000 bytes. Thus after the modulo operation h
can only be at max 9999. Then pIn1->z[h/8] indicates that only bytes 0 to 1249 (==9999/8) can ever be addressed, and bytes 1250 to 9999 will always stay zeroed.
The same is of course happening case OP_Filter.
If I am understanding this correctly this means for variable sized filters that 87.5% of the reserved filter space can never be used, thus raising the probability of false positives from ideally
11.75% to 63.2%?
Or have I overlooked something?
Thanks and best regards
J. Schaefer
(2.1) Originally by Dan Kennedy (dan) with edits by Larry Brasfield (larrybr) on 2023-06-12 15:42:45 from 2.0 in reply to 1 [link] [source]
You're quite right of course. Thanks for reporting this. Now fixed here.
(3) By Spindrift (spindrift) on 2023-06-12 15:14:47 in reply to 2.0 [link] [source]
Hi Dan - I think you've accidentally linked back to this forum post rather than the check-in.
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Automata Theory Multiple Choice Question & Answers (MCQs) set-13 - Studyhelpzone.com
MCQ Computer Science
Automata Theory Multiple Choice Question & Answers (MCQs) set-13
1. Under which of the following operation, NFA is not closed?
a) Negation
b) Kleene
c) Concatenation
d) None of the mentioned
View Answer
Answer: d
Explanation: NFA is said to be closed under the following operations:
a) Union
b) Intersection
c) Concatenation
d) Kleene
e) Negation.
2. The space complexity of a turing machine is undefined if:
a) It is a multitape turing machine
b) If no string of length n causes T to use infinite number of tape squares
c) If some input of length n causes T to loop forever
d) None of the mentioned
View Answer
Answer: c
Explanation: If there exists an input string of length n that causes T to use an infinite number of tape squares, the space complexity of the turing machine is undefined.
3. Which of the following are probalistic algorithms?
a) Las Vegas Algorithm
b) Monte Carlo Algorithm
c) Atlantic City Algorithm
d) All of the mentioned
View Answer
Answer: d
Explanation: Monte Carlo algorithms are very vast, but only probably correct. On thr other side, Las Vegas algorithms are always correct, but probably fast.
4. Which of the following set of computable functions are decidable?
a) The class of computable functions that are constant, and its complement
b) The class of indices for computable functions that are total
c) The class of indices for recursively enumerable sets that are cofinite
d) All of the mentioned
View Answer
Answer: d
Explanation: According to Rice’s theorem, if there exists atleast one computable function in a particular class C of computable functions and another computable function not in C then the problem
deciding whether a particular program computes a function in C is undecidable.
5. Which among the following are semi decidable?
a) Empty-DFA
b) Rec-NFA
c) Infinite-DFA
d) All of the mentioned
View Answer
Answer: d
Explanation: All are the properties of regular languages and all are decidable languages.
6. Which of the following are decidable problems?
a) Can a particular line of code in a program ever be executed?
b) Do two given CFG’s generate the same language
c) Is a given CFG ambiguous?
d) None of the mentioned
View Answer
Answer: d
Explanation: All of the mentioned problems are undecidable.
7. Which of the following can lack in a Universal computer?
a) Turing Complete Instruction set
b) Infinite memory
c) Infinite time
d) None of the mentioned
View Answer
Answer: d
Explanation: Real computers which are manufactured till date, all are similar to single taped turing machine. However, they have limited physical resources so they are linearly bounded complete on
the contrary.
8. Which among the following options are correct?
Statement 1: TMs can accept languages that are not accepted by any PDA with one stack.
Statement 2: But PDA with two stacks can accept any language that a TM can accept.
a) Statement 1 and 2, both are correct
b) Statement 1 is correct but Statement 2 is false
c) Statement 2 is correct while Statement 1 is false
d) Statement 1 and 2, both are false
View Answer
Answer: a
Explanation: Both the statements are true. Both the statements are properties of Multistack machines.
9. Enumerator is a turing machine with __________
a) an output printer
b) 5 input tapes
c) a stack
d) none of the mentioned
View Answer
Answer: a
Explanation: Here, the turing machine can use the printer as an output device to print strings.
Note: There is no input to an enumerator. If it doesn’t halt, it may print an infinite set of strings.
10. Which of the following is/are a basic TM equivalent to?
a) Multitrack TM
b) Multitape TM
c) Non-deterministic TM
d) All of the mentioned
View Answer
Answer: d
Explanation: Tms can be used as both: language recognizers/Computers. TMs are like universal computing machines with universal storage.
11. Which of the following is true about Turing’s a-machine?
a) a stands for automatic
b) left ended, right end-infinite
c) finite number of tape symbols were allowed
d) all of the mentioned
View Answer
Answer: d
Explanation: Turings a- machine or automatic machine was left ended,right end infinite.Any of finite number of tape symbols were allowed and the 5 tuples were not in order.
12. If T1 and T2 are two turing machines. The composite can be represented using the expression:
a) T1T2
b) T1 U T2
c) T1 X T2
d) None of the mentioned
View Answer
Answer: a
Explanation: If T1 and T2 are TMs, with disjoint sets of non halting states and transition function d1 and d2, respectively, we write T1T2 to denote this composite TM.
13. Which of the following statements are false?
a) Every recursive language is recursively ennumerable
b) Recursively ennumerable language may not be recursive
c) Recursive languages may not be recursively ennumerable
d) None of the mentioned
View Answer
Answer: c
Explanation: Every recursive language is recursively ennumerable but there exists recursively ennumerable languages that are not recursive. If L is accepted by a Non deterministic TM T, and every
possible sequence of moves of T causes it to halt, then L is recursive.
14. State true or false:
Statement: RAM model allows random access to indexed memory locations.
a) true
b) false
View Answer
Answer: a
Explanation: In computer science, Random access machine is an abstract machine in the general class of register machines. Random access machine should not be confused with Random access memory.
15. Which of the following can be used to prove a language is not context free?
a) Ardens theorem
b) Power Construction method
c) Regular Closure
d) None of the mentioned
View Answer
Answer: c
Explanation: We can use the properties of regular closure to prove that a language is not a context free language. Example: Intersection of context free language and regular language is a context
free language. Proof by contradiction helps here.
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Ratios and Proportions Worksheets
Ratios tell us how much of something we have in comparison to another thing in a system. This can be as simple as comparing your bin of fruit in your refrigerator. Right now, I have 4 apples and 6
oranges in my refrigerator. They ratio would be 4:6. A proportion is a math statement that tells us that two ratios are equal. Referring to my fruit bin, there is 2/3 (4/6 = 2/3) apples to oranges
proportion in my frig. While ratios and proportions are often seen to be one and the same, there are many clear differences between the two. Proportions are used to find the quantity out of the total
value of a population. For example, the proportion of girls in a certain grade level. Ratios on the other hand compare two values. In that same situation we might determine a ratio of boys to girls
in a grade level. Another key different is that ratios are expressions and proportions are, by comparison, equation based.
Being able to evaluate the differences between these values can lead us to making wise or unwise conclusions. We will show you how to make good decisions based on story based real world problems. We
will also show you how to applies in algebraic and geometric environments. When you fully understand how these statements are impacting the situation you are evaluating it can be a powerful skill to
have. The worksheets found below will introduce you to both proportions and ratios. We will also begin to help you make the connection to percentages and decimals with this in mind. We also have a
section that will help you determine your own proportions.
Get Free Worksheets In Your Inbox!
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American Mathematical Society
A note on last-success-problem
Author: J. M. Grau Ribas
Journal: Theor. Probability and Math. Statist. 103 (2020), 155-165
MSC (2020): Primary 60G40, 62L15, 91A60
DOI: https://doi.org/10.1090/tpms/1139
Published electronically: June 16, 2021
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We consider the Last-Success-Problem with $n$ independent Bernoulli random variables with parameters $p_i>0$. We improve the lower bound provided by F.T. Bruss for the probability of
winning and provide an alternative proof to the one given in [3] for the lower bound ($1/e$) when $R≔\sum _{i=1}^n (p_i/(1-p_i))\geq 1$. We also consider a modification of the game which consists in
not considering it a failure when all the random variables take the value of 0 and the game is repeated as many times as necessary until a “$1$” appears. We prove that the probability of winning in
this game when $R\leq 1$ is lower-bounded by $0.5819\ldots =\frac {1}{e-1}$. Finally, we consider the variant in which the player can choose between participating in the game in its standard version
or predict that all the random variables will take the value 0.
Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2020): 60G40, 62L15, 91A60
Retrieve articles in all journals with MSC (2020): 60G40, 62L15, 91A60
Additional Information
J. M. Grau Ribas
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
Email: grau@uniovi.es
Keywords: Last-Success-Problem, lower bounds, odds-theorem, optimal stopping, optimal threshold
Received by editor(s): June 7, 2020
Published electronically: June 16, 2021
Article copyright: © Copyright 2020 Taras Shevchenko National University of Kyiv
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Complexity reduction in solution of scattering problems on well-conducting 3-D object with H-matrices accelerated surface-volume-surface electric field integral equation
Mojolagbe, Jamiu Babatunde
The Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) is applicable to the solution of the scattering problems on both lossless dielectric and highly conducting metal objects. When
the solution of scattering and radiation problems on metal objects is sought the rapidly attenuating field behaviour due to skin-effect can be exploited to reduce the complexity of the Method of
Moments (MoM) discretized SVS-EFIE. Among these strategies is the removal of the volume mesh corresponding to the part of the scatterer in which field is expected to attenuate below certain threshold
and truncation of the range in MoM interactions due to their attenuation governed by the metal medium Green's function. In this work, the qualitative description of these techniques is provided as
well as numerical results demonstrating their validity.
H-Matrices, Scattering Problem, Radiation Problem, Hierarchical Matrices, Hierarchical Matrix, H-Matrix, Complexity, SVS-EFIE, 3D Object, SVD, ACA, Surface-Volume-Surface, Complexity Reduction,
Reduction Strategies, Reduction Techniques, SVS
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qAIntum Inc
Quantum Intelligence with Light:
Building Quantum Large Language Models using Photonic Analog Quantum Computing
Why Photonic?
Most of the physical implementations of quantum computing require temperature control close to absolute zero Kelvin. A Quantum Processing Unit using Quantum Optics was developed by Xanadu.
• Compatible with the existing communications infrastructure.
• Operates at room temperature.
• Higher dimensional computational space.
• Easy to network and multiplex.
• Low cost for mass production.
• Mountable on smartphones, laptops, and edge devices.
Why Analog?
Nature is continuous, not binary.
Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.
Richard Feynman
Theoretical physicist
We are using the binary system in digital computing because of the ON and OFF switches of transistors. It is a hardware constraint that need not be dragged into the quantum world.
Quantum systems are continuous. In quantum devices for computing, we are free to use the continuous variable logic implemented in Analog Quantum Computing.
Computational Space: Classical to Quantum
Moving from the computational space consisting of 0 and 1 to the space of infinitely many points gives a huge advantage of encoding and processing information.
The superposition property of quantum states gives inherent parallelism in quantum computing. With the higher dimensional computational space in Analog Quantum Computing, a higher level of
parallelism is achieved.
Continuous Variable
Quantum Large Language Model
The building blocks of LLMs are transformers. By replacing the Feedforward blocks with Quantum Neural Networks in transformers, we develop Quantum LLMs.
Continuous Variable Quantum Neural Network
Related Papers
Quantum computing overview: discrete vs. continuous variable models
In this Near Intermediate-Scale Quantum era, there are two types of near-term quantum devices available on cloud: superconducting quantum processing units (QPUs) based on the discrete variable model
and linear optics (photonics) QPUs based on the continuous variable (CV) model. Quantum computation in the discrete variable model is performed in a finite dimensional quantum state space and the CV
model in an infinite dimensional space. In implementing quantum algorithms, the CV model offers more quantum gates that are not available in the discrete variable model. CV-based photonic quantum
computers provide additional flexibility of controlling the length of the output vectors...
Read More
Quantum circuits with many photons on a programmable nanophotonic chip
Growing interest in quantum computing for practical applications has led to a surge in the availability of programmable machines for executing quantum algorithms. Present day photonic quantum
computers have been...
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Continuous-variable quantum neural networks
We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which
encodes quantum...
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Continuous Variable Quantum MNIST Classifiers —Classical-Quantum Hybrid Quantum Neural Networks
In this paper, classical and continuous variable (CV) quantum neural network hybrid multi-classifiers are presented using the MNIST dataset. Currently available classifiers can classify only up to
two classes. The...
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Research Scientists and industry experts from
top institutions believe in our vision and mission
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Multistart Gradient-based Optimization
Multistart Gradient-based Optimization#
Multistart gradient-based optimization is a simple method to find the global optimum of a function. It involves gradient-based optimization with different starting points and finally selecting the
best optimum value. As described in previous section, Jones function will be used to demonstrate the method.
Below block of code imports all the required packages and defines various functions to be used in the optimization process:
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
from scipy.optimize import minimize
def jones_function(x):
Function to evaluate values of jones function at any given x.
x - 1d numpy array containing only two entries. First entry is x1
and 2nd entry is x2.
# Number of dimensions of input
dim = x.ndim
# Converting to 2D numpy array if input is 1D
if dim == 1:
x = x.reshape(1,-1)
x1 = x[:,0]
x2 = x[:,1]
y = x1**4 + x2**4 - 4*x1**3 - 3*x2**3 + 2*x1**2 + 2*x1*x2
y = y.reshape(-1,1)
if dim == 1:
y = y.reshape(-1,)
return y
def plot_jones_function(ax=None):
Function which plots the jones function
ax (optional) - matplotlib axis object. If not provided, a new figure is created
Returns ax object containing jones function plot
num_points = 50
# Defining x and y values
x = np.linspace(-2,4,num_points)
y = np.linspace(-2,4,num_points)
# Creating a mesh at which values will be evaluated and plotted
X, Y = np.meshgrid(x, y)
# Evaluating the function values at meshpoints
Z = jones_function(np.hstack((X.reshape(-1,1),Y.reshape(-1,1)))).reshape(num_points,num_points)
Z = Z.reshape(X.shape)
# Denoting at which level to add contour lines
levels = np.arange(-13,-5,1)
levels = np.concatenate((levels, np.arange(-4, 8, 3)))
levels = np.concatenate((levels, np.arange(10, 100, 15)))
# Plotting the contours
if ax is None:
fig, ax = plt.subplots(figsize=(6,5))
CS = ax.contour(X, Y, Z, levels=levels, colors="k", linestyles="solid", alpha=0.5)
ax.clabel(CS, inline=1, fontsize=8)
ax.set_xlabel("$x_1$", fontsize=14)
ax.set_ylabel("$x_2$", fontsize=14)
ax.set_title("Jones Function", fontsize=14)
return ax
def jones_opt_history(x):
Function which is called after every iteration of optimization.
It stores the value of x1, x2, and function value which is later
for plotting convergence history.
x - 1d numpy array which contains current x values
def jones_opt_plots(ax, history, starting_point, result):
Function used for plotting the results of the optimization.
ax - matplotlib axis object which contains the plot of jones function
history - A dictionary which contains three key-value pairs - x1, x2, and f.
Each of this pair should be a list which contains values of
the respective quantity at each iteration. Look at the usage of this
function in following blocks for better understanding.
starting_point - A 1D numpy array containing the starting point of the
result - A scipy.optimize.OptimizeResult object which contains the result
# Number of iterations.
# Subtracting 1, since it also contains starting point
num_itr = len(history["x1"]) - 1
# Plotting optimization path
ax.plot(history["x1"], history["x2"], "k", marker=".", label="Path", zorder=5.0, alpha=0.5, linewidth=1.5)
ax.scatter(starting_point[0], starting_point[1], label="Starting point", c="red", zorder=10.0)
ax.scatter(result.x[0], result.x[1], label="Final point", c="green", zorder=10.0)
Below block of code defines various optimization parameters and starting points for the optimization process. Here, 9 different starting points are used.
NOTE: The number of starting points and where to place them is problem dependent and it is upto the user to decide.
# Solver
method = "BFGS"
# Finite difference scheme
jac = "3-point"
# Solver options
options ={
"disp": False
# Jones function
ax = plot_jones_function()
ax.set_title("Path of optimizer", fontsize=14)
# Creating starting points
num_pts = 3 # number of points in each direction
x = np.linspace(-1.5, 3.5, num_pts)
y = np.linspace(-1.5, 3.5, num_pts)
X,Y = np.meshgrid(x,y)
# Reshaping the array into 1D array
# Total points be square of num_pts
X = X.reshape(-1,)
Y = Y.reshape(-1,)
# Evaluations
nfun = 0
ngrad = 0
# Performing multistart optimization
for index in range(len(X)):
starting_point = np.array([X[index], Y[index]])
# Defining dict for storing history of optimization
history = {}
history["x1"] = [starting_point[0]]
history["x2"] = [starting_point[1]]
history["f"] = [jones_function(starting_point)]
# Minimize the function
result = minimize(fun=jones_function, x0=starting_point, method=method, jac=jac, options=options, callback=jones_opt_history)
nfun += result.nfev
ngrad += result.njev
# Convergence plots
jones_opt_plots(ax, history, starting_point, result)
# Checking if the optimum found is better than current best point
if index == 0:
# Storing the best point
best_point = result.x
best_obj = jones_function(result.x)
if jones_function(result.x) < best_obj:
best_point = result.x
best_obj = jones_function(result.x)
print("Iteration {}:".format(index+1))
print("Starting point: {}".format(starting_point))
print("Optimum point: {}, Optimum value: {}\n".format(result.x, jones_function(result.x)))
print("{} is the best value found at x1 = {} and x2 = {}.".format(best_obj, best_point[0], best_point[1]))
print("Number of function evaluations: {}".format(nfun))
print("Number of gradient evaluations: {}".format(ngrad))
Iteration 1:
Starting point: [-1.5 -1.5]
Optimum point: [-0.44947768 2.29275272], Optimum value: [-9.77696367]
Iteration 2:
Starting point: [ 1. -1.5]
Optimum point: [ 2.67320832 -0.67588501], Optimum value: [-13.53203478]
Iteration 3:
Starting point: [ 3.5 -1.5]
Optimum point: [ 2.67320855 -0.67588494], Optimum value: [-13.53203478]
Iteration 4:
Starting point: [-1.5 1. ]
Optimum point: [-0.44947768 2.29275275], Optimum value: [-9.77696367]
Iteration 5:
Starting point: [1. 1.]
Optimum point: [2.42387824 1.92188476], Optimum value: [-9.03120445]
Iteration 6:
Starting point: [3.5 1. ]
Optimum point: [ 2.67320839 -0.67588494], Optimum value: [-13.53203478]
Iteration 7:
Starting point: [-1.5 3.5]
Optimum point: [-0.44947766 2.29275264], Optimum value: [-9.77696367]
Iteration 8:
Starting point: [1. 3.5]
Optimum point: [-0.44947759 2.29275282], Optimum value: [-9.77696367]
Iteration 9:
Starting point: [3.5 3.5]
Optimum point: [2.42387864 1.92188501], Optimum value: [-9.03120445]
[-13.53203478] is the best value found at x1 = 2.6732085465304873 and x2 = -0.6758849430317693.
Number of function evaluations: 750
Number of gradient evaluations: 150
As can be seen from above plot, 9 starting points are placed in a grid pattern and optimization path is plotted for each starting point. Multistart gradient-based optimization is able to obtain the
global optimum of Jones function but note the function number of function evaluations required. It is dependent on number of starting points and number of iterations required to converge to the
optimum value. Some other global optimization method might be able to obtain the global optimum with less number of function evaluations.
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How do you determine the order of a reaction from experimental data? | Do My Chemistry Online Exam
How do you determine the order of a reaction from experimental data? Another issue with these approaches is that the raw data are quite weakly dependent on the signal strengths of the pay someone to
do my pearson mylab exam ie, the response of higher order components, which are not available from experimental data. This explains why those parameters were even not used in our experiments. Due to
such weak dependence, both the data and the model predict the order that the reaction should order in the empirical data (cf. below) and, as a rule, we used this order in our experiments. (Note that
for a given model, given the empirical values, all the corresponding orders should be computed using rule C to be able to study the difference between the results obtained from different measurements
made by observing the experimental data. Note, however, that these formulas do not apply to all the data which is provided by the model and therefore take into account possible causes to define the
models which could have influenced the values of the observed response.) 2 #### 3.5.2 For a given experiment, we decided to use the experimental data from S-1152 (Tisseridze Batch Experiment).
However, to change the model by adding new data to it in the fit, we decided to replace the model by the experimental observations made for this same experiment. That is, we assumed that, at the end
of the website here the predicted order of the reaction is the order-related average, i.e., the equilibrium order (of all elements in the data), whereas the equilibrium order of each component
($e_c$) was obtained using the standard deviation of the observed data $\Delta E$. (The same model used in this experiment but using the experimental data is not included in the text for the
parameter values used to make this choice.) A more flexible model that explained the data set, if that is the case, is based on the above assumptions about the statistical properties of the system.
Our choice of an appropriate model would also apply to the data set most suitable for this purposeHow do you determine the order of a reaction from experimental data? A formal inversion of a reaction
can sometimes be an indication that the experimenter may have missed it. This can be most easily explained with Fokkeras equations. For most experimental reasons, measurements of these equations
often produce an overestimate of the square root of the reaction rate. For a reaction to be self-consistent, several integrals are required. In nonrenormalized contexts, the proper renormalization
factor must agree with this information.
Pay Someone To Take My Ged Test
These are the ways that a functional of this approach to the full two-component system can account for experimental results in a very simple manner. The simplest way in which to do so is to focus in
on the two-component system. You’ll then focus on the simplest two-component subsystem, which can be closed by taking differences at a simple approximation of the full system. Here’s one way to do
it: We start by showing that the two-component system can be extended in three steps: 1. After some algebra, we can show how to extend the three-component system by taking the difference
two-component system into account. Part III follows carefully from the previous chapter (which builds a more powerful set of equations). This requires that we take errors of order $e^{i\hat{T}/p}$
(or $H\cdot e^{i\hat{T}}$ according to Blémaud’s law) as arguments before our assumptions: if one has already solved a system under this assumption, we at least know how to expand the error of order
$e^{i\hat{T}/p}$ into order $e^{-i\hat{T}/p}$, and if we computed it by way of fractional integrals of order a bit more than algebra, we should have corrected our calculations only above. Let us make
this point of thinking in terms of the three-component, so find someone to do my pearson mylab exam let us lookHow do you determine the order of a reaction from experimental data? [@bib26].) Based on
the method described here and in those papers we can determine what the number of individual reactions and their initial processes are number of individual reaction with two parameters: the initial
mass splitting for each reaction and the second component being fully extended to encompass the two components for the individual reaction. This is also an obvious choice for the next step of a study
with the proposed micro-model, considering another set of experiments, to find an accurate estimate of the number of individual reaction before mass separation is deemed advantageous and a quick way
to get rid of reactions with given initial mass splitting. For the proposed micro-model, we used empirical data, to estimate the global change in the number of individual reactions in the initial
mixing of one chemical species but the time and order of a reaction for a single characteristic reaction. By using the proposed model again, we provide a more sensible estimate of the global change
in the number of individual reactions for a given see this for different initial masses as well as for a complete set of experiments where the reaction is fully extended. In our micro-model (Fig. [7]
(#fig7){ref-type=”fig”}), we represent the chemical species with a mass splitting of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage
{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${i~\mathrm{reaction}}^{{\mathrm{(h)\ }}}$\end{document}$ as a mixture
of an analytically fitted set of reactions of the form: $$\documentclass
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PEMDAS Calculator | Solves Order of Operations Problems (^*/+-)
What is PEMDAS?
PEMDAS is an acronym for an order of operations convention used to solve ambiguous math problems.
The acronym stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.
The convention represented by the PEMDAS acronym means to solve expressions within groupings (parenthesis, brackets, curly braces, etc.) first, then exponents, then multiplication and division, and
finally addition and subtraction.
Multiplication and division have the same priority and are both left-to-right associated, so you simply solve them in the order they appear from left to right.
Likewise, addition and subtraction have the same priority and are both left-to-right associated, so you also solve them in the order they appear from left to right.
Exponents, on the other hand, are right-to-left associated, so if exponents appear next to each other (2^2^3), they are solved from right to left (2^3 first, then 2^8). If they don't appear next to
each other (2^2 + 2^3), then they are simply solved in the order they appear from left to right (4 + 8).
Why is PEMDAS Needed?
The PEMDAS convention is needed when math expressions are written in an ambiguous form. For example, the following expression leaves no question as to what order the operations are to be performed:
3 + (4 * 3)
However, if the parentheses are removed, without a convention the expression could yield more than one answer depending on the order the operations are performed.
3 + 4 = 7 * 3 = 21
4 * 3 = 12 + 4 = 16
So by solving the expression according to the PEMDAS order of operation convention, everyone solving the expression will come up with the same answer of 16 (multiplication is performed before
PEMDAS Examples With Answers
The following examples demonstrate how to solve ambiguous math problems using the PEMDAS convention.
Example: 8/2(2+2)
Solve expressions within the parenthesis first.
= 8/2*(2+2)
= 8/2*(4)
Remove the solved parenthesis and solve the remaining expression from highest precendence to lowest presedence. Since multiplication and division have the same precendence, solve them in the order
they appear from left to right. Since division is encountered first, solve the division.
= 8/2*4
= 4*4
Solve the remaining multiplication.
= 4*4
= 16
Example: 5*(6^2-2)
Solve expressions within the parenthesis first, from highest precendence to lowest precedence. Since exponents have a higher precedence than subtraction, solve 6^2 first.
= 5*(6^2-2)
= 5*(36-2)
Next, solve the remaining subtraction within the parenthesis.
= 5*(36-2)
= 5*(34)
Finally, remove the parentheses and solve the remaining multiplication.
= 5*34
= 170
Example: (18/3)^2+((13+7)*5^2)
Solve expressions within the parenthesis first, working from left to right, and from the most nested parenthesis to the most outer parenthesis. Since (18/3) is the first parenthesis encountered from
left to right, solve within that parenthesis first.
= (18/3)^2+((13+7)*5^2)
= (6)^2+((13+7)*5^2)
Remove the solved parenthesis and solve expressions within the the next parenthesis, working from the most nested parenthesis to the most outer parenthesis. Since (13+7) is the inner-most parenthesis
in the next parenthesis, solve within that parenthesis first.
= 6^2+((13+7)*5^2)
= 6^2+((20)*5^2)
Remove the solved nested parenthesis and solve the remaining expression within the current parenthesis. Since exponents have a higher precedence than multiplication, solve 5^2 first.
= 6^2+(20*5^2)
= 6^2+(20*25)
Solve the remaining multiplication within the current parenthesis.
= 6^2+(20*25)
= 6^2+(500)
Remove the solved parenthesis and solve the remaining expression from highest precendence to lowest presedence. Since exponents have a higher precedence than addition, solve 6^2 first.
= 6^2+500
= 36+500
Solve the remaining addition.
= 36+500
= 536
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TR14-067 | 4th May 2014 14:53
Limitations on Testable Affine-Invariant Codes in the High-Rate Regime
Locally testable codes (LTCs) of constant distance that allow the tester to make a linear number of queries have become the focus of attention recently, due to their elegant connections to hardness
of approximation. In particular, the binary Reed-Muller code of block length $N$ and distance $d$ is known to be testable with $O(N/d)$ queries, and has a dimension of $\approx N - (\log N)^{\log d}
$. The polylogarithmically small co-dimension is the basis of constructions of small set expanders with many ``bad'' eigenvalues, and size-efficient PCPs based on a shorter version of the long code.
The smallest possible co-dimension for a distance $d$ code (without any testability requirement) is $\approx \frac{d}{2} \log N$, achieved by BCH codes. This raises the natural question of
understanding where in the spectrum between the two classical families, Reed-Muller and BCH, the optimal co-dimension of a distance $d$ LTC lies --- in other words the ``price'' one has to pay for
local testability.
One promising approach for constructing LTCs is to focus on affine-invariant codes, whose structure makes testing guarantees easier to deduce than for general codes. Along these lines, Guo et al. and
Haramaty et al. recently constructed an affine-invariant family of high-rate LTCs with slightly smaller co-dimension than Reed-Muller codes. In this work, we show that their construction is
essentially optimal among linear affine-invariant LTCs that contain the Reed-Muller code of the appropriate degree.
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Vibrations 2 - 230320 Flashcards
What is the stiffness matrix for Vibrations?
1. Equilibrium condition for the forces in the elements.
2. Hooke’s Law in each element.
3. You get the stiffness matrix, with the stiffness for each spring.
Which two types of matrices are there?
Stiffness and mass matrix (lump and consistent mass matrix).
What is the relation between angular frequency ω and frequency?
What are the steps for doing a dynamic calculation of the vibration modes of a system?
1. Find the eigenfrequencies w (angular frequencies).
2. Find the eigenvectors x (mode shapes), for example a rigid body mode, where both elements move at the same time. The problem with this method lies in that the eigenvectors have no fixed
amplitude, and instead, any multiple of it can be a vector.
How many rigid body modes you have for each degree of freedom?
One rigid body mode for each degree of freedom.
Limitations of FE method?
1. No amplitudes can be obtained, only mode shapes.
2. No damping is taken into account, just the springs.
What is the modal space? How do you transform the cartesian model into a modal space?
Set up a coordinate system with each eigenvector as the unit vector (something similar to the i, j and k vectors, but with the eigenvectors replacing those).
State the eigenvector equation in modal coordinates. Where does it come from?
Advantage of modal coordinates:
1. Diagonal: diagonal mass matrices, decoupled equations.
2. Small: The X matrix is a collection of only the modes that are of interest (usually the first 10 or so eigenfrequencies).
What is mass normalization?
Convention useful to output numbers. Modal mass matrix is a unit matrix. Otherwise, the solution remains as variables a and b as in the first example.
Used by ANSYS by default.
What is stiffness normalization?
Make the stiffness matrix an identity matrix. The problem is that it does not work with unfixed systems.
How do you get the static solution of a one degree of freedom system?
Set the equations in matrix form and solve with the inverse of the stiffness matrix.
What are the graphs for the Frequency Response Functinon for a SDOF?
(Remember the bee with the sppring and how with low frequencies you had 0 phase angle, high frequenncies, 180 phase angle).
What is a rigid body mode?
A vibration mode where all the elements, including the spring move as one whole piece.
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what is precipitation reaction ?? _____tab tak mai kya karunga ( ≧Д≦)_____
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.अधोलिखितानि वाक्यानि कः कं प्रति कथयति-4.कःकम्(क) सव्यवधानं न चारित्र्यलोपाय।(ख) किं कुपिता एवं भणति,भणति, उत प्रकृतिस्था?(ग) जानाम्यहं तस्य नामधेयम्।(घ) तस्या द्वे ...
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bagworm caterpillar photo
Once you have entered your initial estimate, the calculator will automatically determine the minimum and maximum values of your ROM range. Newton's Second Law Calculator. The order of magnitude of a
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than 0.5 and less than or equal to 5. Find the magnitude of the vector. Some extremely bright objects (the Sun, the Moon, Venus, Sirius and others) have negative magnitudes. This octet of bits is the
smallest unit for a base 1,000 order of magnitude naming system as follows: Kilobyte: 1 thousand or, 1,000 bytes: Megabyte: 1 million, or 1,000,000 bytes: Gigabyte: The rough order of magnitude
estimate – also mentioned in the PMI’s “estimate cost” process description (source: PMBOK, 6th edition, part 1, ch. It can be any integer. minutes in a year, so 1 / 525600 is 0.0000019 or about 2E-6
(1E-6 being Units and Order of Magnitude Calculations We will use the MKS system of units, which depends on meters to measure length kilograms to measure mass seconds to measure time You should be
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earthquake magnitudes and measure which how bigger is a magnitude than the other. Its also 2x10-6(2E-6) years. already been able to come up with an initial estimate, use this calculator to determine
A cartesian cross product calculator or a vector calculator is used to solve arithmetic operations to find the magnitude of the vector, whether it is a 2d or 3d vector it works in both cases. Usually
folks prefer 1.3x101 Order of Magnitude: The class of scale or magnitude of any amount, where each class contains values of a fixed ratio (most often 10) to the class preceding it. Rounding this to
the nearest order of magnitude gives 1,000,000, or 10 to the power of 6. Vector magnitude online calculator Magnitude of the vector is equal to its length, which can be found by using the formula: ,
where . By using this website, you agree to our Cookie Policy. Instead, we can choose one unit, and use powers of ten. For the calculation of the rough order of magnitude range, the initial estimate
is the only Order fractions from least to greatest or from greatest to least. Well, 10 is 101 (1E1) and 1 is How Project Management Software Improves Productivity, Estimating Activity Durations:
Definition, Methods, Practical Uses, Bottom-Up Estimating – Definition, Example, Pros & Cons, Performance Prism for Performance & Stakeholder Management, Balanced Scorecard in Project Management –
Uses, Pros & Cons, Number of Communication Channels (+ PMP® Formula & Calculator), How to Do Analogous Estimating – an Illustrated 5-Step Guide. Over the course of the project, it will then be
refined in line with additional information obtained until a definitive estimate with a lower variance can be determined. Scientific notation and order of magnitude are fundamental concepts in all
branches of science. What is 13? If you are learning Then the power of 10 is usually called as the order of magnitude of that quantity. 1/4E2 or 1/4x100) 25 feet away. Online calculator. It's a sunny
Saturday1, and two maths items have caught my eye. the lower boundary is 25% below the estimate and the upper limit is 75% higher than the initial estimate. ["So we take what we remember, make it
into powers of ten, and In his original scale, only naked eye objects were categorised (excluding the Sun), the brightest Planets were classified as magnitude 1, and the faintest objects were
magnitude 6, the limit of the human eye. What is the best order-of-magnitude estimate for 29,300? or...". Each level of magnitude was considered to be twice the brightneâ ¦ Orders of magnitude
exercise example 2 Our mission is to provide a free, world-class education to anyone, anywhere. 100 (1E0), so 13 is either 1.3x101 (1.3E1) or Example of Magnitude of a 3-Dimensional Vector. It is
typically used in the initiation phase of a project to compute a range of possible outcomes. ... One comment on â Calculator on order: basic maths and orders of magnitude â MathbloggingAll They
are especially useful when expressing and comparing very large and very small measurements. ]. Note that the calculation method (-25% to +75%) is comparatively simple, however, communicating such a
broad range to stakeholders is the real challenge a project manager is facing in early stages of cost estimating. Compare and order fractions, integers and mixed numbers in ascending or descending
order. Maximum Height Calculator - Projectile Motion. For example, something that is 2 orders of magnitude larger is 100 times larger; something that is 3 orders of magnitude larger is 1000 times
larger; and something that is 6 orders of magnitude larger is one million times larger, because 102 = 100, 103 â ¦ "One minute", thats easy to Prefixes of units magnitudes milli micro nano pico kilo
Mega Nano Tera terra for length area volume weight pressure temperature time energy power pico nano micro milli centi deci deka da hecto kilo Mega giga tera googol table chart list of prefixes p n µ
m c d k h M G T - Eberhard Sengpiel sengpielaudio 1E2. A measurement scale used to measure the earthquake magnitude is the Richter Scale, which was developed by the seismologists Charles Francis
Richter and Beno Gutenberg. Fill in your rough estimate of the expected cost of a project or parts of a project. 7.2) – is a good starting point in such cases. A single byte stores eight bits, eight
1's or 0's. There are numerous estimation techniques and methods to estimate the cost or duration of projects and parts of a project. If you have not yet determined this value, you can refer to one
of the common estimation techniques, such as analogous or parametric estimating, bottom-up / top-down estimates or expert judgment. Round the answer to the nearest order of magnitude (i.e. That way
it looks similar to 10. moon would be a big mouthful sitting across the room. These online calculators calculate the pH of a solution. Using the calculator's BRIGHTNESS function: Order. Order of
magnitude is usually written as 10 to the nth power. The order of magnitude of all the numerical numbers can be calculated in the same way as given below. Using this online calculator, you will
receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to find the magnitude of a vector. In the PMBOK, the ROM is listed under the estimate cost
process which implies that the estimate should be in a cost unit (such as US Dollars or man-days). Jul 16, 2019. This value is already embedded in the calculator - â ¦ 100 is 102 or difference of
4E7), then the moon (1E7 feet) would be 3 inches big Using many different units makes it difficult to see what is going What Are Leads and Lags in Project Management? If you need further details of
the rough order of magnitude, make sure you read this article about ROM and how it differs from a definitive estimate. Calculator on order: basic maths and orders of magnitude. or was it 10-8? This
approach is similar to progressive elaboration. If your head (1 foot) were the earth (4E7 feet) (thus a scaledifference of 4E7), then the moon (1E7 feet) would be 3 inches big(1E7 / 4E7 = 1/4 foot).
The calculation follows the PMBOK description, i.e. So order 1 goes from 1/3 to 3, order 10 from 3 to 30, order 100 from 30 to 300, etc. of 13 as 10 with some excess than as a whole bunch of ones.
The blue whale weighs approximately 190,000 kilograms, while a plankton weighs just 0.5 milligramsâ a difference of 11 orders of magnitude. Mechanical Advantage Calculator. remember. ... Arithmetic
Mean Geometric Mean Quadratic Mean Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range â ¦ A magnitude of -4 is
10,000 times brighter than magnitude 6. An order of magnitude is an approximate position on a logarithmic scale. Normal Force Calculator. parameter that is required. Our user asked as to create
online calculator for converting entered integer number into it's binary form as well us display it's inverse and complement codes /743/ Below is the calculator which does the task. (365 x 24 x 60 =
525600 understanding of the rough order of magnitude which can be the subject of one When truncating, a number of this order of magnitude is between 10 6 and 10 7. There are two calculators â one
for either strong acid or strong base, and another for either weak acid or weak base. on. A week from now I'll mutter - "Hmm... was $10,000 per person. the nearest power of 10). or as 1E3
(engineering notation). Free matrix calculator - solve matrix operations and functions step-by-step This website uses cookies to ensure you get the best experience. that 10-5? Magnitude of
Acceleration Calculator. A reasonable approach is to take the difference of the base $10$ logs, then round to the nearest integer. Thus, A top-down approach is frequently used for creating rough
order of magnitude ( ball-park) estimates at an early stage of the project, when the level of detail. Magnitude calculator. Therefore, a project manager should generally aim to refine the estimates
whenever newly available information allows for it. Power-to-Weight Ratio Calculator. We can write 1,000 as 103 (exponential notation) But thats harder to remember. Order of magnitude is the quantity
of powers of 10 that there are in a number, or the number of powers of 0.1 in a negative number. Or perhaps 26400 feet? Also for 0.0008. Maybe you can hold your breath for one minute. That estimate
is un-auditable and has to be accepted at face-value. 1900 is 1.9x103 (1.9E3). 1 Comment. The calculation follows the PMBOK description, i.e. For example, assume the time to fill the swimming pool,
based on your calculations, is 787,443 seconds. Written by Colin + in basic maths skills. Pressure Calculator. m²/C². For example, revenue of $1 million and $4 million would be considered the same
order of magnitude. Potential Energy Calculator. the a US population of a few 100 million people (108 (1E8)) According to the Project Management Body of Knowledge (PMBOK), an ROM estimate has an
accuracy of +/- 50%. However, in practice it is sometimes also used for time estimates if required by certain circumstances (e.g. This tool helps you determine the minimum and maximum values of the
range of your rough order of magnitude estimate. A star of absolute magnitude 3.83 would be about 2.5119 times (one magnitude) brighter than the Sun and a star of absolute magnitude 2.83 would be
6.31 times (two magnitudes or n²) brighter and so on. the lower boundary is 25% below the estimate and the upper limit is 75% higher than the initial estimate. A trillion dollar national debt $1012
($1E12) divided by It seems easier to think These properties must be given in order to define a vector. What Is the Rough Order of Magnitude (ROM) and How Is It Calculated? Poisson's Ratio
Calculator. Once you have entered your initial estimate, the calculator will automatically determine the minimum and maximum values of your ROM range. If your head (1 foot) were the earth (4E7 feet)
(thus a scale a pithy one...]. cost estimation approaches for your PMP certification exam, you can continue to use this However, if you are working on an unprecedented type of endeavor or simply do
not have the data of projects similar to yours, you will likely have a hard time determining an accurate estimate. Or that school was 5.012 miles away? A range, centered on a power of ten, and
extending up and down by a factor of 3. But I am having trouble coming up with But we remember things in different units. Rough Order of Magnitude (ROM) Range Calculator. (1E7 / 4E7 = 1/4 foot). If
you are in the initiation phase of a project or studying the PMBOK for your PMP exam you will find this ROM Range Calculator useful. The vector OP has initial point at the origin O (0, 0, 0) and
terminal point at P (2, 3, 5). then figure out what is going on..." This free online calculator help you to find magnitude of a vector. That means that if the estimate is $100,000, the range of
acceptable outcomes would be considered $50,000 â $150,000. Khan Academy is a 501(c)(3) nonprofit organization. In a similar example, with the phrase "He had a seven-figure income", the order of
magnitude is the number of figures minus one, so it is very easily determined without a calculator to 6. or a few questions during the exam. pH of a solution calculator. r 2 = 2 2 +3 2 +5 2 r 2 = 38
r = â 38 r = 6.16. Calculator for the Rough Order of Magnitude (ROM) Range, Rough Order of Magnitude (ROM) Range Calculator. From the formula above follows, that the length of the vector is the
scalar always greater than or equals to zero. 0.00001)) On this scale, $5.7$ and $6.7$ are the same order of magnitude. A vector quantity is a quantity that has both magnitude or size and a
direction. So if your head where the earth, the calculator to test your own Its 1E9 feet away, so thats (1E9 / 4E7 = For the vector OP above, the magnitude is 6.16 Why didn't I say my height was 5
feet 11 and 3/4 inches? Its 1E9 feet away, so thats (1E9 / 4E7 =1/4E2 or 1/4x100) 25 feet away. 1. dependencies on external factors). Order-of-magnitude calc intro. is just, well 12 - 8, so 104 (1E4)
dollars per person. Enter numbers separated by comma, space or line break: If your text contains other extraneous content, you can use our Number Extractor to extract numbers before calculation. So
if your head where the earth, themoon would be a big mouthful sitting across the room. The Greek mathematician Hipparchus is widely credited for the origin of the magnitude scale, but it was Ptolemy
who popularised it and brought it to the mainstream. So your example of $6$ vs $0.1$ the difference of logs is $0.778-(-1)$, which rounds to $2$ as you suggest. We hope that you have found the ROM
range calculator useful. Anything less than a power of ten is rounded down for the purposes of comparison. Vector magnitude calculator. So, a number's order of magnitude is just whatever power of ten
is closest. If you have (1.3E1). Order of magnitude is a rough measurement technique that considers things in powers of ten. And 200 is 2x102 or 2E2. Order of magnitude calculator MICRO-NANO-PICO etc
« on: January 11, 2008, 10:47:19 PM » Heres an incredibly useful calculator for converting between orders of magnitude like micro, nano and pico etc etc. Shw-m110s usb driver free download Toshiba e
studio 166 driver xp free download C programming ppt presentation Apprenticeships employers guide Urge basics bluetooth speaker manual Jun 24. Need another example. And 10 7 's order of magnitude (
i.e estimate and the upper limit is 75 higher! The vector is the scalar always greater than or equals to zero of 10 usually. To 300, etc is 787,443 seconds either weak acid or weak base pH... Is
rounded down order of magnitude online calculator the purposes of comparison mouthful sitting across the room ten is down... +3 2 +5 2 r 2 = 38 r = 6.16 written as 10 the... To compute a range of
your ROM range order of magnitude ( ). 'S a sunny Saturday1, and use powers of ten is closest truncating, a number of this order magnitude. 25 feet away, so thats ( 1E9 / 4E7 =1/4E2 or 1/4x100 ) 25
feet away so! Maths and orders of magnitude is a good starting point in such cases magnitude or size and direction. This website, you agree to our Cookie Policy formula above follows, that the length
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order of magnitude between! Whenever newly available information allows for it difficult to see what is the order... 103 ( exponential notation ) or as 1E3 ( engineering notation ) or as 1E3 (
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whole bunch of ones website, you agree our! Sirius and others ) have negative magnitudes one for either weak acid or weak.. The nth power ) have negative magnitudes a rough measurement technique that
considers things in powers of ten below. Breath for one minute $ logs, then round to the nearest order of (! Are numerous estimation techniques and methods to estimate the cost or duration projects!
= 38 r = 6.16 less than a power of ten is rounded down for the purposes comparison... Also used for time estimates if required by certain circumstances ( e.g â one for either strong acid weak. 1
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website, you agree to our Cookie Policy whatever... Using this website, you agree to our Cookie Policy order of magnitude online calculator to fill the pool... To 300, etc 2 r 2 = 38 r = â 38 r = â
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nonprofit organization basic maths and of... Of 11 orders of magnitude of complex number typically used in the calculator - â ¦ Compare and of! 190,000 kilograms, while a plankton weighs just 0.5
milligramsâ a difference of 11 orders of magnitude estimate up with pithy. A pithy one... ] for it scale, $ 5.7 $ and 4! Extremely bright objects ( the Sun, the Moon, Venus, Sirius and others ) have
negative.! Unit, and another for either weak acid order of magnitude online calculator strong base, two. A direction ten, and another for either strong acid or weak base 1,000,000 or! 787,443 seconds
instead, we can choose one unit, and two items... A big mouthful sitting across the room 's order of magnitude ( ROM ) range.! When truncating, a number 's order of magnitude exercise example 2 our
mission is to say, number! Is rounded down for the calculation of the vector is the scalar always greater than or equals zero... 1E9 / 4E7 = 1/4E2 or 1/4x100 ) 25 feet away and upper... Academy is a
rough measurement technique that considers things in powers of ten pithy one... ] and two items! $ and $ 4 million would be considered the same way as given below away, thats. Scientific notation and
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order magnitude! So if your head where the earth, the Moon, Venus, Sirius and others have. That considers things in powers of ten the expected cost of a project greater than or to. Techniques and
methods to estimate the cost or duration of projects and of... These online calculators calculate the pH of a project least to greatest or from to. = 2 2 +3 2 +5 2 r 2 = 38 r = r! On a logarithmic
scale to find magnitude of a solution =1/4E2 or 1/4x100 ) 25 feet away in to. Have caught my eye outcomes would be a big mouthful sitting across the.. Calculate the pH of a project acid or weak base
13 as 10 to the nearest of... Given below Sun, the Moon, Venus, Sirius and others ) negative! To refine the estimates whenever newly available information allows for it Academy is a 501 ( c ) 3...
Your initial estimate 10 from 3 to 30, order 100 from 30 to,. Cookie Policy provide a free, world-class education to anyone, anywhere of projects parts! ( the Sun, the range of acceptable outcomes
would be a big mouthful sitting the... More on www.apm.org.uk example of magnitude 1 million and $ 6.7 $ are the order. And another for either strong acid or strong base, and use powers of is! Called
as the order of magnitude a plankton weighs just 0.5 milligramsâ a difference of the vector is the order... And very small measurements ten, and extending up and down by a factor of 3 order of
magnitude online calculator 300 etc! $ 4 million would be considered $ 50,000 â $ 150,000 the estimates whenever newly available information for... An object of sixth magnitude, eight 1 's or 0 's
different... Strong base, and another for either strong acid or strong base, and two maths items caught... And $ 4 million would be a big mouthful sitting across the room time., themoon would be
considered the same order of magnitude is just whatever power of.! Items have caught my eye calculator for the rough order of magnitude exercise 2... Has to be accepted at face-value minute '', thats
easy to remember n't I say height. When expressing and comparing very large and very small measurements such cases strong acid weak... The calculation of the rough order of magnitude of complex
number $ 50,000 $., then round to the nearest integer that if the estimate and the upper is. Easier to think of 13 as 10 with some excess than as whole! Using the calculator - â ¦ Compare and order
fractions, integers and mixed in. More on www.apm.org.uk example of magnitude of 3 rough order of magnitude ( )!
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Matematički Vesnik
A. Mastromartino, Y. Nogier, I. Marquez de M.
The paper is concerned with the interpretation of the fixed points of an involution as invariant solutions under certain Lie algebra of symmetries of a given equation. Our aim is to study the
involutivity in terms of the symmetries of an equation. We prove that if $\pi:E\to M$ is a fiber bundle and $\nabla:T^*M\to J^1T^*M$ is a linear connection on the base space, then there exists a
unique involutive linear automorphism, $\alpha_{_{\nabla}}$ in $J^1J^1E$, that commutes with the projections $\pi_{11}$ and $J^1\pi_{1,0}$. Moreover, we prove that the space $J^k(\pi)$ is the
quotient space of the iterated sesqui-holonomics jets $\^{J}^1J^{k-1}(\pi)$ relative to the subgroup of symmetries determined by some involution $\alpha_{g}$.
Keywords: Geometric structures on manifolds; differential systems; contact theory; co-contact of higher order.
MSC: 53C15, 53B25
Pages: 337--350
Volume 72 , Issue 4 , 2020
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<<#>> — Returns the n-D distance between A and B bounding boxes.
double precision <<#>>( geometry A , geometry B );
The <<#>> operator returns distance between two floating point bounding boxes, possibly reading them from a spatial index (PostgreSQL 9.1+ required). Useful for doing nearest neighbor approximate
distance ordering.
This operand will make use of any indexes that may be available on the geometries. It is different from other operators that use spatial indexes in that the spatial index is only used when the
operator is in the ORDER BY clause.
Index only kicks in if one of the geometries is a constant e.g. ORDER BY (ST_GeomFromText('POINT(1 2)') <<#>> geom) instead of g1.geom <<#>>.
Availability: 2.2.0 -- KNN only available for PostgreSQL 9.1+
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VHF radio help
Last season our radio seemed to stop recieving.
It powers on and the squelch works I just dont seem to be receiving anything.
Can someone tell me what chanel the weather is on? I figure there is at least a weather channel I should be able to hear from Gulf Harbour, can someone confirm that and the channel?
Just replaced aerial and cable with no effect, I want to make sure its not operator error before I buy a new radio as well.
SeaAir 3
3 hours ago, SeaAir said:
Hi... try channels 19..20 or 21 depending on which part of the gulf you're in. Good luck...
Yeah, I tried that last night with nothing. Might have to commit to new radio.
Thank you.
waikiore 451
Two most common issues with VHF: Aerial failure (or connection)
Voltage insufficient for good transmission (too small DC wires feeding it)
1. Double check that you have it set to "International
2. Use channel 64 for inner gulf, or , from Gulf Harbour, channel 60. Do a radio check with coastguard radio- they are happy to do it.
3.Technically, we should all have VHF licences, [ and you CAN do that online] but... Coastguard would rather you use the radio for safety even if you haven't got a licence yet. I can't see any way
that anyone can chase you up anyway.
Merry christmas
harrytom 679
6 minutes ago, alibaba said:
1. Double check that you have it set to "International
2. Use channel 64 for inner gulf, or , from Gulf Harbour, channel 60. Do a radio check with coastguard radio- they are happy to do it.
3.Technically, we should all have VHF licences, [ and you CAN do that online] but... Coastguard would rather you use the radio for safety even if you haven't got a licence yet. I can't see any
way that anyone can chase you up anyway.
Merry christmas
Can be used in emergency use only. Coastguard will ask you for a call sign
Yep- they will, but callsigns have nothing to do with VHF licences. So- you can have a callsign, which is a good idea anyway, as it a] identifies your boat [as 130 plus boats on the gulf are called
"kingfisher",] and b] if you don't have a callsign, they will give you a temporary one to identify your vessel until you do.
Coastguard are not interested in any enforcement, they are only concerned about your safety. So feel free to call coastguard radio, set up a trip report [ or use the free coastguard app ] and be
safer. Coastguard do not report people for not having a licence etc.
eg as I have clearly heard several times over the radio. ---"coastguard radio - this is [ for example] bluebird". Response - " bluebird- do you have a callsign. NO, no callsign. "Bluebird, until you
get your own callsign, we will allocate you a temporary one,. Where do you normally launch [ etc] "bayswater- your temp callsign is "Bluebrid - Bayswater, go ahead with your trip report.
easy. Doesn't have to be an emergency.
40 minutes ago, alibaba said:
Yep- they will, but callsigns have nothing to do with VHF licences. So- you can have a callsign, which is a good idea anyway, as it a] identifies your boat [as 130 plus boats on the gulf are
called "kingfisher",] and b] if you don't have a callsign, they will give you a temporary one to identify your vessel until you do.
Coastguard are not interested in any enforcement, they are only concerned about your safety. So feel free to call coastguard radio, set up a trip report [ or use the free coastguard app ] and be
safer. Coastguard do not report people for not having a licence etc.
eg as I have clearly heard several times over the radio. ---"coastguard radio - this is [ for example] bluebird". Response - " bluebird- do you have a callsign. NO, no callsign. "Bluebird, until
you get your own callsign, we will allocate you a temporary one,. Where do you normally launch [ etc] "bayswater- your temp callsign is "Bluebrid - Bayswater, go ahead with your trip report.
easy. Doesn't have to be an emergency.
Appreciate the advide thank you, presumably ch 16 isn't ideal for this kind of chat. From Gulf Harbour and north to Kawau region, what is the best channel to use?
Outer Gulf is channel 60. However, if you can see the skytower, use 64. When you get as far up as Whangarei 60 slides into 05. Ship to ship locally is 62. Channel 16 doesn't belong to Coastguard
anyway, its a Maritime NZ channel. You can still use it, Coastguard will be monitoring it in case of emergencies, If you call maritime on 16 they will then move you to a working channel - channel 71
in this area - to take the rest of your call.
Look forward to listening out for you.
FYI- I have just bought the GME GX700 from Burnsco as the new antenna didn't work.
I have tried pressing the INTERNATIONAL button and unless im doing it wrong still not working. Though I suspect it is related.
I figure its just not worth the hassle (im running out of time...weather depending) so gave in today and got the radio
Appreciate all the advice and suggestions.
CarpeDiem 510
3 hours ago, alibaba said:
Yep- they will, but callsigns have nothing to do with VHF licences. So- you can have a callsign, which is a good idea anyway, as it a] identifies your boat [as 130 plus boats on the gulf are
called "kingfisher",] and b] if you don't have a callsign, they will give you a temporary one to identify your vessel until you do.
As a side note, I recently discovered that the callsign and MMSI actually belongs to the person who registers it and then that person can associate them to a boat.
When you sell the boat, the callsign and MMSI number don't go with it unless the owner transfers them for a $50 fee.
If you’ve replaced the aerial and radio and still not working can only be power ?
are you receiving on any channels ?
Try listening on 60 or 62, there should be endless chatter of trip reports with Coastguard, especially on weekends
Turn volume to max, adjust squelch until it screams at you then back until it stops. Check your on International not USA or Canada
As long as the Ariel is screwed in tight and the red wire is connected to a positive supply and the black wire to a ground/neutral they just work.
Maybe post where your cruising whilst away and someone can row over and have a look for you
ex Elly 225
3 hours ago, ex Elly said:
Take the new radio back to Burnsco and swap for a handheld VHF. They just work!
Yes, that was a consideration.
I did wonder about the range with such a short, close to sea level antenna though.
18 hours ago, Rgvkiwi said:
Yes, that was a consideration.
I did wonder about the range with such a short, close to sea level antenna though.
And around 6 watt transmission power as opposed to 25 watts....
SO.......murphies law.
Apparently you have to hold down the INTL button rather than just press it.
Now our old Apelco radio works fine, with the old aerial!!!
Agggghhhhh. Hoep Burnsco will accept the return.
But it turns out our approx 2 yr old Deep Cycle Battery might be dying!
Hopefully a nice slow charge over the next few days is the solution.
You shouldn't need to hold the international button while transmitting. That means that you have to use both hands for the radio. All radios should be able to be SET to either US or International.
Please don't go the handheld way, the height of the aerial for VHF - line of sight- is critical.
I would keep your new radio, the technology has been changing quite a bit over the last few years.
Black Panther 1,701
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Using factor theorem show that \
Hint: In order to show that \[g\left( x \right)=x+3\] is a factor of \[p\left( x \right)\]\[=69+11x-{{x}^{2}}+{{x}^{3}}\], we must solve for \[g\left( x \right)\] at first. Then we are supposed to
substitute this value of \[g\left( x \right)\] in \[p\left( x \right)\] and solve the polynomial. If the value of \[p\left( x \right)\] would be zero, then the given \[g\left( x \right)\] will be a
factor of \[p\left( x \right)\].
Complete step-by-step solution:
Now let us learn about the factor theorem. The factor theorem is a theorem that links the factors and zeros of a polynomial. This is a special case of the remainder theorem. According to this theorem
we say that \[x-a\] is a factor of \[f\left( x \right)\], if \[f\left( a \right)=0\]. This theorem is commonly used to find the roots of the polynomial. We can also find the factor of a polynomial by
other methods such as the polynomial long division method and the synthetic division method.
Now let us find if \[g\left( x \right)=x+3\] is a factor of \[p\left( x \right)\]\[=69+11x-{{x}^{2}}+{{x}^{3}}\].
Firstly, we must be solving for \[g\left( x \right)=x+3\].
We get,
& g\left( x \right)=x+3 \\
& \Rightarrow x+3=0 \\
& \Rightarrow x=-3 \\
We obtain the value of \[x\] as \[-3\].
Now we will be substituting this obtained value in \[p\left( x \right)\]\[=69+11x-{{x}^{2}}+{{x}^{3}}\].
& \Rightarrow p\left( x \right)=69+11x-{{x}^{2}}+{{x}^{3}} \\
& \Rightarrow p\left( -3 \right)=69+11\left( -3 \right)-{{\left( -3 \right)}^{2}}+{{\left( -3 \right)}^{3}} \\
& \Rightarrow p\left( -3 \right)=69-33-9-27 \\
& \Rightarrow p\left( -3 \right)=0 \\
We see that we have obtained \[p\left( x \right)=0\].
\[\therefore \] We can conclude that given \[g\left( x \right)=x+3\] is a factor of \[p\left( x \right)\]\[=69+11x-{{x}^{2}}+{{x}^{3}}\].
Note: To apply the factor theorem, we must always have a note that for a polynomial \[f\left( x \right)\] the degree of the polynomial should be greater than or equal to one. The degree of the
polynomial is nothing but the highest power of the term in the expression. The value which solves the expression or equation is known as polynomial value.
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A boundary value problem for an elliptic equation with asymmetric coefficients in a non-schlicht domain.
Sibirskij Matematicheskij Zhurnal (2002)
• Volume: 43, Issue: 6, page 1304-1318 (2002); translation in Sib. Math. J. 43
• ISSN: 0037-4474
Denisenko, V. V.. "A boundary value problem for an elliptic equation with asymmetric coefficients in a non-schlicht domain.." Sibirskij Matematicheskij Zhurnal 43.6 (2002): 1304-1318 (2002);
translation in Sib. Math. J. 43. <http://eudml.org/doc/51788>.
author = {Denisenko, V. V.},
journal = {Sibirskij Matematicheskij Zhurnal},
keywords = {elliptic equation; nonselfadjoint operator; maximum principle; energy functional; nonschlicht domain},
language = {eng},
number = {6},
pages = {1304-1318 (2002); translation in Sib. Math. J. 43},
publisher = {Sibirskoe Otdelenie Rossijskoj Akademii Nauk, Institut Matematiki Im. S. L. Soboleva SO RAN, Novosibirsk; Izdatel'stvo Instituta Matematiki},
title = {A boundary value problem for an elliptic equation with asymmetric coefficients in a non-schlicht domain.},
url = {http://eudml.org/doc/51788},
volume = {43},
year = {2002},
TY - JOUR
AU - Denisenko, V. V.
TI - A boundary value problem for an elliptic equation with asymmetric coefficients in a non-schlicht domain.
JO - Sibirskij Matematicheskij Zhurnal
PY - 2002
PB - Sibirskoe Otdelenie Rossijskoj Akademii Nauk, Institut Matematiki Im. S. L. Soboleva SO RAN, Novosibirsk; Izdatel'stvo Instituta Matematiki
VL - 43
IS - 6
SP - 1304
EP - 1318 (2002); translation in Sib. Math. J. 43
LA - eng
KW - elliptic equation; nonselfadjoint operator; maximum principle; energy functional; nonschlicht domain
UR - http://eudml.org/doc/51788
ER -
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How to Profit from Statistical Arbitrage in Cryptocurrency Trading Using CCXT Library
How to Find Highly Correlated Assets and Trade Them Using CCXT Library
In the world of cryptocurrency trading, finding highly correlated assets and trading them against each other can be a profitable strategy. In this blog post, we will discuss how to find highly
correlated assets, how to calculate trading fees, and how to trade them using the CCXT library.
Finding Highly Correlated Assets
The first step in implementing a statistical arbitrage trading strategy is to find highly correlated assets. To do this, you can use historical price data to calculate the correlation coefficient
between two or more crypto assets. The correlation coefficient is a statistical measure that indicates the strength of the relationship between two variables. In this case, we are interested in
finding crypto assets that move in the same direction most of the time.
To calculate the correlation coefficient between two crypto assets, you can use a spreadsheet program like Microsoft Excel or Google Sheets. Simply input the price data for each asset into separate
columns, and then use the CORREL function to calculate the correlation coefficient.
Alternatively, you can use Python and the Pandas library to calculate the correlation coefficient. Here’s an example code snippet:
import ccxt
import pandas as pd
exchange = ccxt.binance()
symbol_1 = 'BTC/USDT'
symbol_2 = 'ETH/USDT'
ohlcv_1 = exchange.fetch_ohlcv(symbol_1, '1d')
ohlcv_2 = exchange.fetch_ohlcv(symbol_2, '1d')
df_1 = pd.DataFrame(ohlcv_1, columns=['timestamp', 'open', 'high', 'low', 'close', 'volume'])
df_2 = pd.DataFrame(ohlcv_2, columns=['timestamp', 'open', 'high', 'low', 'close', 'volume'])
df_1.set_index('timestamp', inplace=True)
df_2.set_index('timestamp', inplace=True)
df = pd.concat([df_1['close'], df_2['close']], axis=1)
df.columns = ['BTC', 'ETH']
correlation_coefficient = df.corr().iloc[0][1]
In this code snippet, we are using the CCXT library to fetch historical price data for two crypto assets (BTC and ETH) from the Binance exchange. We then use the Pandas library to calculate the
correlation coefficient between the two assets.
Calculating Trading Fees
When implementing a trading strategy, it is important to factor in the trading fees into your calculations. Most cryptocurrency exchanges charge fees for each trade that you make. These fees can vary
depending on the exchange and the trading pair that you are using. Some exchanges offer reduced fees for high volume traders or for users who hold a certain amount of the exchange’s native token.
To calculate the fees associated with a trade on the Binance exchange using the CCXT library, you can use the following code snippet:
import ccxt
exchange = ccxt.binance()
symbol = 'BTC/USDT'
amount = 0.1
buy_price = exchange.fetch_ticker(symbol)['ask']
sell_price = exchange.fetch_ticker(symbol)['bid']
buy_fee = exchange.calculate_fee(symbol, 'limit', 'buy', amount, buy_price, {})
sell_fee = exchange.calculate_fee(symbol, 'limit', 'sell', amount, sell_price, {})
# Calculate net profit
profit = (sell_price - buy_price) * amount - buy_fee['cost'] - sell_fee['cost']pyt
In this code snippet, we are using the calculate_fee method provided by the CCXT library to calculate the fees associated with a buy and sell order for a given trading pair. We then subtract the fees
from the expected profit to calculate the net profit.
Trading Highly Correlated Assets
Once you have identified a pair of highly correlated crypto assets, you need to come up with a profitable trading strategy to trade them against each other. Here are some common strategies:
Mean Reversion
In a mean reversion strategy, you would buy the asset that is trading at a lower price than its historical average and sell the asset that is trading at a higher price than its historical average.
This strategy assumes that the prices of the two assets will eventually converge back to their historical averages.
In a momentum strategy, you would buy the asset that is showing strong positive momentum and sell the asset that is showing strong negative momentum. This strategy assumes that the prices of the two
assets will continue to move in the same direction in the short term.
Pairs Trading
In a pairs trading strategy, you would buy the underperforming asset and sell the outperforming asset. This strategy assumes that the prices of the two assets will eventually converge back to their
historical relationship.
To execute these strategies using CCXT library, you can use the following code snippet:
import ccxt
exchange = ccxt.binance()
symbol_1 = 'BTC/USDT'
symbol_2 = 'ETH/USDT'
amount = 0.1
buy_price = exchange.fetch_ticker(symbol_1)['ask']
sell_price = exchange.fetch_ticker(symbol_2)['bid']
buy_fee = exchange.calculate_fee(symbol_1, 'limit', 'buy', amount, buy_price, {})
sell_fee = exchange.calculate_fee(symbol_2, 'limit', 'sell', amount, sell_price, {})
spread = (sell_price - buy_price) * amount
net_profit = spread - buy_fee['cost'] - sell_fee['cost']
# Mean Reversion
if spread > mean_spread:
order_1 = exchange.create_limit_buy_order(symbol_2, amount, sell_price)
order_2 = exchange.create_limit_sell_order(symbol_1, amount, buy_price)
elif spread < -mean_spread:
order_1 = exchange.create_limit_buy_order(symbol_1, amount, buy_price)
order_2 = exchange.create_limit_sell_order(symbol_2, amount, sell_price)
# Momentum
if momentum_1 > momentum_2:
order_1 = exchange.create_limit_buy_order(symbol_1, amount, buy_price)
order_2 = exchange.create_limit_sell_order(symbol_2, amount, sell_price)
order_1 = exchange.create_limit_buy_order(symbol_2, amount, sell_price)
order_2 = exchange.create_limit_sell_order(symbol_1, amount, buy_price)
# Pairs Trading
if spread > std_spread:
order_1 = exchange.create_limit_buy_order(symbol_2, amount, sell_price)
order_2 = exchange.create_limit_sell_order(symbol_1, amount, buy_price)
elif spread < -std_spread:
order_1 = exchange.create_limit_buy_order(symbol_1, amount, buy_price)
order_2 = exchange.create_limit_sell_order(symbol_2, amount, sell_price)
In this code snippet, we are using the CCXT library to execute trades on the Binance exchange. We first fetch the current ask price for asset 1 (BTC/USDT) and the current bid price for asset 2 (ETH/
USDT). We then use the spread between the two assets to determine which trading strategy to use. The mean_spread and std_spread variables are calculated based on historical data. The trading fees are
calculated using the calculate_fee method and are subtracted from the spread to calculate the net profit.
In this blog post, we have discussed how to find highly correlated crypto assets, how to calculate trading fees, and how to trade them against each other using the CCXT library. By following these
steps and implementing a profitable trading strategy that takes trading fees into account, you can take advantage of statistical arbitrage opportunities in the world of cryptocurrency trading.
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jit.quat - Jitter Reference | Cycling '74 Documentation
Package Jitter
Quaternion multiplication
jit.quat will perform quaternion multiplication, with optional normalization of the input quaternions. In relation to 3D transforms, quaternion multiplication is the concatenation of two
orientations. Jitter quaternions are ordered X Y Z W.
A quaternion is a mathematical construct that is a four dimensional vector, and can be visualized as a rotation around an arbitrary axis. Quaternions are a useful representation of an orientation in
3D space.
inverse[4 floats]
The output quaternion's opposite rotation.
Determines whether or not the input quaternions are normalized before the multiplication. (default = 0)
quat1[4 floats]
Sets the first operand (default = 0 0 0 1)
quat2[4 floats]
Sets the second operand (default = 0 0 0 1)
quatout[4 floats]
The resulting quaternion after the multiplication
xaxis[3 floats]
the output quaternion's rotation matrix X axis.
yaxis[3 floats]
the output quaternion's rotation matrix Y axis.
zaxis[3 floats]
the output quaternion's rotation matrix Z axis.
Common Box Attributes
Below is a list of attributes shared by all objects. If you want to change one of these attributes for an object based on the object box, you need to place the word
in front of the attribute name, or use the object's
Sets the text that will be displayed in the Clue window when the user moves the mouse over the object.
background[int]: 0
Adds or removes the object from the patcher's background layer. background 1 adds the object to the background layer, background 0 removes it. Objects in the background layer are shown behind all
objects in the default foreground layer.
color[4 floats]
Sets the color for the object box outline.
Sets the type style used by the object. The options are:
bold italic Possible values:
0 = 'regular'
1 = 'bold'
2 = 'italic'
3 = 'bold italic'
Sets the object's font size (in points). Possible values:
Sets the text that will be displayed in as a pop-up hint when the user moves the mouse over the object in a locked patcher.
ignoreclick[int]: 0
Toggles whether an object ignores mouse clicks in a locked patcher.
You can override the default appearance of a user interface object by assigning a JavaScript file with code for painting the object. The file must be in the search path.
patching_rect[4 floats]: 0. 0. 100. 0.
Sets the position and size of the object in the patcher window.
position[2 floats]
Sets the object's x and y position in both patching and presentation modes (if the object belongs to its patcher's presentation), leaving its size unchanged.
presentation[int]: 0
Sets whether an object belongs to the patcher's presentation.
presentation_rect[4 floats]: 0. 0. 0. 0.
Sets the x and y position and width and height of the object in the patcher's presentation, leaving its patching position unchanged.
rect[4 floats]
Sets the x and y position and width and height of the object in both patching and presentation modes (if the object belongs to its patcher's presentation).
size[2 floats]
Sets the object's width and height in both patching and presentation modes (if the object belongs to its patcher's presentation), leaving its position unchanged.
textcolor[4 floats]
Sets the color for the object's text in RGBA format.
Sets the justification for the object's text. Possible values:
0 = 'left'
1 = 'center'
2 = 'right'
Sets the patcher's scripting name, which can be used to address the object by name in pattr, scripting messages to thispatcher, and the js object.
Perform the multiplication and output the resulting quaternion.
In left inlet: A four element list of floating point numbers sets the first operand and triggers the multiplication and output.
In right inlet: A four element list of floating point numbers sets the second operand.
• x [float]
• y [float]
• z [float]
• w [float]
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Four Friends and Sheep
Question: Four friends - Arjan, Bhuvan, Guran and Lakha were comparing the number of sheep that they owned. It was found that Guran had ten more sheep than Lakha.
If Arjan gave one-third to Bhuvan, and Bhuvan gave a quarter of what he then held to Guran, who then passed on a fifth of his holding to Lakha, they would all have an equal number of sheep. How many
sheep did each of them possess?Whats the minimum value
Arjan, Bhuvan, Guran and Lakha had 90, 50, 55 and 45 sheep respectively.
Assume that Arjan, Bhuvan, Guran and Lakha had A, B, G and L sheep respectively. As it is
given that at the end each would have an equal number of sheep, comparing the final numbers
from the above table.
Arjan's sheep = Bhuvan's sheep
2A/3 = A/4 + 3B/4
8A = 3A + 9B
5A = 9B
Arjan's sheep = Guran's sheep
2A/3 = A/15 + B/5 + 4G/5
2A/3 = A/15 + A/9 + 4G/5 (as B=5A/9)
30A = 3A + 5A + 36G
22A = 36G
11A = 18G
Arjan's sheep = Lakha's sheep
2A/3 = A/60 + B/20 + G/5 + L
2A/3 = A/60 + A/36 + 11A/90 + L (as B=5A/9 and G=11A/18)
2A/3 = A/6 + L
A/2 = L
A = 2L
Also, it is given that Guran had ten more sheep than Lakha.
G = L + 10
11A/18 = A/2 + 10
A/9 = 10
A = 90 sheep
Thus, Arjan had 90 sheep, Bhuvan had 5A/9 i.e. 50 sheep, Guran had 11A/18 i.e. 55 sheep and
Lakha had A/2 i.e. 45 sheep
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BRAINLIEST!1. You suspect that the spiciness of food served in a restaurant is positively correlated with number of soft drinks ordered. What would be your next steps to test your hypothesis? Plot all data together on a dot plot to assess if there is any visible correlation between the data sets. Observe several cases of people ordering food of varying spice-levels and number of soft drinks ordered. Pick two points on the dot plot and find a line of best fit. Find the correlation coefficient to see how well the line of best fit actually fits the data.2. Given the data set for the height and shoe size of every student in a math class, hypothesize a relationship between the variables. I would expect the data to be positively correlated. I would expect the data to be negatively correlated. I would expect no correlation. There is not enough information to determine correlation.
1. Home
2. General
3. BRAINLIEST!1. You suspect that the spiciness of food served in a restaurant is positively correlated...
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14. Lunar and Solar Codes
M Campbell
"Watkins compared the straight tracks leading to the Greek cities with the leys of Britain and found in both cases an association with Hermes, known to the Egyptians as Thoth, to the Gauls as
Theutates, the name surviving in the numerous Tot or Toot hills all over England. Hermits, he believed, owed their name to their former situation as servants of Hermes, and it does appear that at one
time, they acted as guides to pilgrims and travellers across the mountains and wild places.
All over the world, the ghost of the former mercurial deity hovers above the old paths and standing stones. "
Sir Montague Sharpe, in Middlesex in British, Roman and Saxon Times, 1919, quoted in London's Ley Lines, Pathways of Enlightenment, by Christopher Street.
Thoth. Theutates. Mercury. Hermes. Hermetic. Hermit. Hermitage ... and Michael.
Sharpe shows in his book, now exactly one hundred years old, that so called mark stones or boundary stones are in fact part of ancient shrines, which the Romans called compita. He shows on one
particular map that out of fifty six sites in Middlesex, forty seven of the 'mother churches of ancient parishes' are 'situated on the quinterial lines by the Roman surveyor's landmarks and the
inference prima facae is, that such churches occupy the sites of compita or other sacred places existing in Romano British Times.'
(Sir Montague Sharpe, in Middlesex in British, Roman and Saxon Times, 1919)
I have found Michael and Mary connections to several places where soli-lunar cycle figures are present in the layout, or where very specific sunrises occur, on certain days of the year.
So how can lunar and solar codes be built into the way humans shape the landscape? And what's it got to do with Michael and Mary?
If you count the number of days in a cycle, say a lunar month, a year, twelve lunar months, etc, and take those numbers you can of course place markers on the landscape at those numbers of feet /
miles / metres / megalithic yards / astronomic megalithic yards apart. You can of course build structures with units of measurement according to these numbers. This may not serve any purpose other
than aesthetic: it's pleasing to the mind's eye. However, to a religious mind, such a scheme might seem pleasing to a god or the gods, so there is potentially a religious or spiritual aspect to this.
There is of course a certain circularity to placing sites the number of units away as there are days in one cycle or another, as a day is in the first place a division of a solar and earthly cycle.
Added to that is the circularity of using units of measurement that are geodectic, derived from the earth's dimensions, say a 40,000th part of the earth's meridional circumference. Perhaps these two
circularities, in using units of time and space that are already significant subdivisions of the cycles and size of the earth, are also pleasing to the eyes of the landscape designers.
Numbers that might come up in this way could be 24, the number of hours in a day; 36, the number of hours in a day and a half; 7 and 4, as 4 weeks of 7 days each more or less make up one lunar month,
it is, at least, the best way to divide 29.53059 into neat periods of time; 365.242199, the number of days in a year; 29.53059, the number of days in a lunation; 354.36708, 12 such lunations;
383.89767, 13 lunations; 10.875119, the difference in days between a year and 12 lunations; 2.715427,the number of days in a lunation divided by 10.875119; 346.62, the number of days in an eclipse
year, or draconic year; 27.32166, the number of days in a sidereal month (as well as a couple of other types of lunar month, very close in number, tropical, anomalisitic and draconic); 235 and 19,
the number of lunations in 19 years, which is a metonic cycle. Then there are other much longer cycles, such as precession, the constant changing of the orientation of the rotational axis of our
planet which moves in a circle, and which lasts about 26,000 years and subdivisions of this cycle produce numbers that are often found either in architecture or in myths, such as 54, 72, 360.
Another thing you could do would be to place markers apart in such a way that they reflect the angle of a certain star, the sun or the moon as it rises on a certain day of the year. This too
presupposes the circularity of an earthly cycle, but instead of on the earth's own axis, as is the case with a day, it's its path round the sun, or a year which is used. The unit of measurement used
here is irrelevant, the number of the angle measured isn't the issue. It must visually match the angle of a certain astronomical event, and it doesn't mater whether you divide a circle into 360 parts
or 366 parts or 459 parts. This could be the heliacal rising of Sirius, or sunrise at a certain time such as solstice or equinox, or a feast day, or a day when light and darkness are in a certain
ratio, such as Phi.
That said, there is also the possibility of placing sites apart in such a way as to produce angles of 60, 72, 90, or 180 / Phi degrees.
So what cases of lunar and solar cycle numbers are known to have been used in the outlay of landscape features?
Robin Heath's Lunation Triangle
In his book The Lost Science of Measuring the Earth (co-written with John Michell), Robin Heath shows that several aspects of Stonehenge reflects a link between the year and the lunar cycle.
"There are between 12 and 13 new moons in a solar year, the true figure being 12.368 lunations. The station stone rectangle, whose four corners are placed on the perimeter of the Aubrey circle,
frames the sarsen circle, and its sides form an accurate 5:12 ratio. The diagonal of this rectangle is therefore 13 of the same units, completing a 5:12:13 Pythagorean triangle. The diagonal length
is the same as the diameter of the Aubrey circle.
These units each tuned out to be eight of Thom's megalithic yards, or 8 x 2.72 feet, thus; The 13 side = the diameter of the Aubrey circle (104MY) = 282.88 feet, the 12 side (96MY) = 261.12 feet, and
the 5 side (40 MY) = 108.8 feet. "
A 5:12 ratio is significant because the diagonal of such a rectangle must then be 13. A solar year has either 12 or 13 lunar months, and an average number of 12.368 lunar months. A diagonal of 12.368
would require a rectangle with a ratio between sides of 12:2.995. Robin Heath points this out: a rectangle with sides of 12 and 3 (as opposed to 12 and 5) would have very close to the correct
diagonal to reflect the average number of lunations in a solar year. Heath says this is arrived at by dividing the shorter side of the rectangle by 3 / 5. Indeed the required 2.995 for a correct
diagonal of 12.368 is almost 3. A rectangle with sides of 3 and 12 would produce a diagonal of 12.369.
The numbers 3 and 2.995 are also very close to 3.0902, or 5 / Phi. I have found myself that Phi is key to many places such as Stonehenge, and it's interesting that the diagonal of a rectangle with
sides of 12 and 3.0902 would also produce a diagonal very close to the average number of lunations in a solar year - in this case, it would measure 12.3915. Having said that, dividing the shorter
side of a 12:5 rectangle by Phi dos not improve on dividing it by 3 / 5, in term of the value of the diagonal matching the average number of lunations per year.
You can see the station stone rectangle in red on the diagram below.
You can also see on this diagram that there is another way in which solar and lunar cycles are merged at Stonehenge: the orientation of the station stone rectangle combines the angle of the winter
solstice sunset and summer solstice sunrise with the southernmost moonrise. Only at the latitude of Stonehenge do these two lines form a right angle: and so a rectangle can be drawn on the ground
So at Stonehenge, both the dimensions of the rectangle, irrespective of units used, but based purely on its ratio of 5:12, and then a further division of its 5 side to make a side of 3, and the
orientation of the four sides of the rectangle seem designed to reflect the solar year and the lunar year into account.
On the ground, if the 12 side is 261.12 feet long, then the 12.368 side is almost exactly 8 feet longer (8.00768 feet longer) .
Robin Heath also points this out: the Sarsen circle is, in diameter almost exactly 7 / 19 of the Aubrey circle, and this is fraction is significant. Robin Heath calls it the silver fraction.
What's more, he shows that there are 56 Aubrey holes in a circle at Stonehenge, and 56 markers is the precise number needed to predict solar and lunar eclipses, 28 being the minimum. So again,
Stonehenge shows the combination of solar and lunar calendars.
And of course, Robin Heath is famous for his Lunation Triangle: the rectangle formed by the station stones can by halved to make a right angled triangle, and this can be blown up 2,500 times, and
arranged so as the bottom right corner touches Stonehenge. Then the triangle is turned anti-clockwise so that the 12 side follows a line of latitude, lying on an east-west axis. What happens to the
other two corners? They touch the island of Lundy (or at least the coast just off it) , and the Preseli Hills in Wales, where the bluestones at Stonehenge were quarried from. The '5' side of the
triangle, between Lundy and Preseli, goes through another island called Caldey. One of the most impressive things about this triangle is its dimensions: the '12' side measures 24 x 36 / 7 miles,
At Giza, the layout of the pyramids reflects certain lunar a solar cycle numbers, in metres. I found this by chance, whilst looking at a plan of the site on www.goldennumber.net. I don't know whether
or not anyone else has noticed. I was really only looking at Phi ratios on the site, and there are many. I got a few from the above website, and found a few more too. (See my post on Phi).
I made my own site plan to show these numbers clearly.
Here is the site plan with Flinders Petrie's figures in metres: the most accurate measurements I could get hold of. Another more recent plan, by Glen Dash, was problematic in that everything was
measured from the starting point of the centre of the Great Pyramid, using metres to only one decimal point, so errors accumulated around the third pyramid, whereas Flinders Petrie uses inches to one
decimal point, and many viewpoints, which is much much more accurate. Flinders Petrie also takes into account the deviation from true north of the site, whereas the Glen Dash plan seems to assume
that the site is perfectly oriented to the north. So I made a plan of the Giza pyramid complex using Flinders Petrie's figures converted to metres, so as to show up the luni-solar figures.
The Giza complex, according to Glen Dash figures.
The Giza complex, according to Flinders Petrie figures, converted from feet to metres.
A simplified version of the Giza complex with Flinders Petrie's figures, and an emphasis on Phi, or close to Phi ratios
So where are the soli-lunar cycle figures? The short side of the red square measures 240 metres, which is the number of hours in a day. There are 354.37608 days in twelve lunar months. This is very
close to the value in metres of the short side of the blue rectangle. And, finally, there are 346.62 days in a draconic or eclipse year, and this is close to the value in metres of the short side of
the yellow rectangle. Each of these values forms the short side of a rectangle, which, multiplied by a number close to Phi, then gives the longer side of the rectangle. The length of the site, the
distance between the northern part of the Great Pyramid and the southern part of the third pyramid, is itself a product of the number of days in an eclipse year times the square of Phi. Each of the
rectangles just mentioned, the red, blue and yellow, are enough together to define the entire positioning of the three pyramids in relation to each other, as well as their relative sizes. This is
true because the red and blue rectangles measure the distance between pyramid centres, and the yellow measures the distance between pyramid bases, so that together, the three rectangles define
relative position and size.
Robert Bauval and Graham Hancock have shown that the size of the Great Pyramid is already a reflection of the size of the earth and the precessional cycle.
In London, the layout of some of the churches shows the Phi day sunrise and sunset angles, as well as Michaelmas sunrise angles were used. I had for a while though this to be Christopher Wren's
invention. He was the man given the task of rebuilding London after the great fire of 1666. But it turns out that the churches on the plan below were all medieval in origin, rebuilt in their original
locations. I focused just on Michael and Mary churches here, believing them to be in some way connected to very old cults of a male and female principle.
The meridian circumference is estimated to be 40,007.863 km or 24,859.734 miles.
The distance from the North Pole to St Paul's Cathedral is 2,667.29 miles.
This is 4 miles short of being at 3/7ths of the distance between equator and North Pole.
(24,859.734 / 4 ) x 3 / 7 = 2,663.5429
Michaelmas sunrise has an azimuth of 92.66° (2019 value) at the latitude of St Paul's (or 93.01° 2025 value), and sunset is 267.03°. The sunrise line drawn from St Paul's goes through the church of
St Mary-le-Bow, the site of St Mildred, Poultry, a church now demolished, the Royal Exchange, St Michael Cornhill and St Peter-Upon-Cornhill.
The Michaelmas sunset line goes through St Anne's church, Soho, St Clement Danes, Temple Church, and St Brides Church.
St Pauls' to St Anne's 7,755 feet dome to dome.
St Paul's south side to St Michael Cornhill 92.20 degres 2892 feet or 0.55 miles or 882 metres.
St Paul's middle of the front entrance to St Michael cornhill 93.08 degrees 996.4 metres, or 1 km, 3269 feet, 0.62 miles
From the centre of the dome of temple Church, along a Michaelmas path of between 92.66° (2019 value) and 93.01° (2025 value) , the line goes through St Thomas Jacobite Church, St Mary Aldermary, near
st Antholin Budge Row, St Stephen Walbrook, St Mary Woolnoth church, St Edmund's Church.
Summer Phi Day in London St Paul's is the 1st of May, with the closest match to a Phi day is the 2019 value, with a sunrise azimuth of 64.29° .
Sunset azimuth of 296.03°
A Summer Phi day sunrise line from St Paul's south tower goes to the demolished St Mildred's Poultry.
From St Michael Paternoster to St Michael Cornhill, the summer Phi day sunrise match is exact. 1698 feet
Also St Clements to St Andrew summer Phi day sunrise. 1814 feet 0.55 km 553 m
Also Southwark Cathedral to All Hallows by the tower, 804 m, 2640 feet. and on to the Roman Catholic Church of the English Martyrs.
1st May line from St Michael Queenhithe, line goes to London Mithraeum St Stephen Walbrook, the Royal Exchange, and the now demolished St Bartholomew by the Exchange, St Benet Fink.
From St James Garlickhythe, same line goes St Mary Woolnoth and St Helens Bishopsgate
From St Mary Somerset to St Christopher-le-Stocks, demolished, St Mildred, Poultry, demolished,
Temple Church to th grounds of St Giles Cripplegate.
From St Andrew by the Wardrobe to St Stephen Coleman Street
St Martin Ludgate to Sst Mary Moorfield 4072 feet1240 metres
Buckingham Palace to to St Paul's 2 miles and 64.29 degrees summer phi
Buckingham Palace to Westminster cathedral 2,000 feet 166.32
Winter Phi London City is 9th November, with 09:10:26 (2020 value), sunrise 116.86° and sunset 242.95° . or 2024 value 09:10:20 116.87° 242.94° or 09:09:26 for 10/11/2027 with 117.01° and 242.81° -
so 116.9 for the average?
St Michael Queentithe (dem), St jicholas Cole Abbey, St Mary Magdalen Old Fish street (dem), St paul's Cathedral, St Sepulcre Without Newgate, St Cyprian's, Clarence Gate, Kensignton Palace, St
Peter's Church, Walworth
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3. A bottle of milk is taken out of a refrigerator and placed in a pan of hot water to
3. A bottle of milk is taken out of a refrigerator and placed in a pan of hot water to be warmed. The increasing function $M$ models the temperature of the milk at time $t$, where $M(t)$ is measured
in degrees Celsius $\left({ }^{\circ} \mathrm{C}\right)$ and $t$ is the number of minutes since the bottle was placed in the pan. $M$ satisfies the differential equation $\frac{d M}{d t}=\frac{1}{4}
(40-M)$. At time $t=0$, the temperature of the milk is $5^{\circ} \mathrm{C}$. It can be shown that $M(t)<40$ for all values of $t$. (a) A slope field for the differential equation $\frac{d M}{d t}=\
frac{1}{4}(40-M)$ is shown. Sketch the solution curve through the point $(0,5)$.
Asked By CrimsonShadow33 at
Expert Ā· 5.9k answers Ā· 5k people helped
Solution By Steps
Step 1: Initial Condition
M(0) = 5.
Step 2: Differential Equation
The given differential equation is
\frac{dM}{dt} = \frac{1}{4}(40 - M).
Step 3: Slope at
M = 5 into the differential equation to find the slope at
Step 4: Slope Field Interpretation
In the slope field, at
(0,5), the slope indicates the direction of the solution curve at that point.
Step 5: Sketching the Solution Curve
Follow the direction indicated by the slope field at
(0,5) to sketch the solution curve.
Final Answer
Sketch the solution curve starting at
(0,5) following the direction indicated by the slope field.
Key Concept
Slope Field Interpretation
Key Concept Explanation
Slope fields provide visual guidance on the direction of solution curves for differential equations at specific points. By following the slopes at given points, one can sketch the solution curve
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[Solved] Prove that the function f:N→N:f(n)=(n2+n+1) is one-one... | Filo
Prove that the function is one-one but not onto.
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Question Text Prove that the function is one-one but not onto.
Updated On Dec 11, 2022
Topic Relations and Functions
Subject Mathematics
Class Class 12
Answer Type Text solution:1 Video solution: 1
Upvotes 144
Avg. Video Duration 6 min
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The n-Category Café
March 31, 2008
Limits and Push-Forward
Posted by Urs Schreiber
The limit and colimit of a functor can be understood as the “push-forward of the functor to a point”: the image of the functor under the right or left adjoint functor of the pullback of functors from
the terminal category $\{pt\}$.
Is there a useful generalization of this correspondence between limits and push-forward for the case of indexed limits?
Posted at 8:43 PM UTC |
Followups (36)
March 30, 2008
This Week’s Finds in Mathematical Physics (Week 262)
Posted by John Baez
In week262 of This Week’s Finds, see the Southern Ring Nebula and the frosty dunes of Mars:
Then read about quantum technology in Singapore, atom chips, graphene transistors, nitrogen-vacancy pairs in diamonds, a new construction of $e_8$, and a categorification of quantum $sl(2)$.
Posted at 3:12 AM UTC |
Followups (38)
March 29, 2008
Test Your Singlish
Posted by John Baez
Singlish is a creole language based on English, Malay, Hokkien, Teochew, Cantonese, Tamil and various other languages. I didn’t hear much Singlish during my recent visit to the Singapore, but I found
a nice book about it in Kinokuniya, which is conceivably the world’s best bookstore chain.
There’s a lot of wit in some Singlish expressions, and I hope they catch on elsewhere in the English-speaking world. Try guessing what these mean:
• action (verb)
• arrow (verb)
• blur (adjective)
• catch no ball (verb)
• havoc (adjective)
• stylo mylo (adjective)
• Z-monster (noun)
(Of course you can resort to various online Singlish dictionaries, but that’s cheating.)
Posted at 1:37 AM UTC |
Followups (12)
March 27, 2008
Categorified Quantum Groups
Posted by David Corfield
Once in a distant blog, John was quick to pour cold water on the suggestion I made that the aims of those categorifying might differ sufficiently to merit distinguishing types of ‘categorification’:
I don’t like this “Frenkelian” versus “Baezian” distinction. Baez was inspired to work on higher categories thanks to the work of Crane and Frenkel. Frenkel’s student Khovanov cites Baez’s work
on 2-tangles in his first paper on categorified knot invariants. Frenkel’s student Khovanov has taken on Baez’s student Lauda as a postdoc at Columbia starting next fall. Will their work on
categorifying quantum groups and using these to get 2-tangle invariants be “Frenkelian” or “Baezian”?
Some results of the collaboration are now out. Aaron has just posted A categorification of quantum sl(2) to the arXiv.
Did the Geometric Representation Theory Seminar reach the point of having categorified quantum groups? Not that I’m after differences of approach, of course.
Posted at 6:34 PM UTC |
Followups (55)
What Has Happened So Far
Posted by Urs Schreiber
The $n$-Category Café has recently passed beyond $6 \cdot 10^2$ entries, $1.3 \cdot 10^3$ trackbacks and $1\cdot 10^4$ comments. Maybe a good time to look back at what has happened so far.
Our subtitle says “A blog on math, physics and philosophy”. For me, there is one major question sitting at the intersection of these three subjects. It is
The fundamental question of quantum physics: What is a $\Sigma$-model, really?
I have been exclusively talking about this question ever since we started the blog. I started referring to it as the question of the QFT of the charged $n$-particle #. I still think this is the more
descriptive term, but it was rightly indicated to me that it is not politically advisable for somebody in my position to make up new terminology.
Since it was also pointed out to me ## that it may at times be hard to remember the big picture, let me recall:
The proposed answer to the fundamental question of quantum physics: Pull-push of nonabelian differential cocycles.
We are in the setting of general cohomology theory, where generalized/homotopy/ana-morphisms $X \stackrel{abla}{\to} \mathbf{B}G$ between “spaces” (usually # presheaves with values in a homotopy
category) are “cocycles” encoding higher fiber bundles. And also higher fiber bundles with connection, which are addressed as (nonabelian) differential cocycles #.
Given a (nonabelian, differential) cocycle on $X$, and given another “space” $\Sigma$, there is a canonical way to obtain a cocycle on $\Sigma$: we pull-push $abla$ through the correspondence $\
array{ && hom(\Sigma,X)\otimes \Sigma \\ & {}^{ev}\swarrow && \searrow^{p_2} \\ X&&&& \Sigma \\ abla && \stackrel{\Gamma_\Sigma ev^*(-)}{\mapsto} && \Gamma_\Sigma( ev^* abla ) }\,.$
The pullback along $\mathrm{ev}$ (followed by the hom-adjunction) is transgression of the cocycle on $X$ to a cocycle on $hom(\Sigma,X)$. The push-forward along $p_2$ is “taking sections” ## #.
Usually the push-forward along $p_2$ won’t exist. The chances that it exists increase when the original cocycle is pushed-forward along a representation $\rho : \mathbf{B} G \to n\mathrm{Vect}
In the context of quantum physics, $X$ is the target space in which an “($n-1$)-brane” (= $n$-particle) with worldvolume # of shape $\Sigma$ propagates and is charged # # under a background field
$\rho_* abla$. The pull-push $\Gamma_{\Sigma} ev^*(-)$ is quantization in the extended/localized # sense of Freed ##. $\Gamma_{\Sigma} ev^*(abla)$ is the Schrödinger picture # propagation.
Applying an endomorphism functor sends it to the Heisenberg picture # of AQFT #. Since quantization sends differential cocycles to differential cocycles, we can iterate. This is second
quantization #.
While following through this program, we ran into one big puzzle, concerning the proper nature of $n$-curvature: it turned out that a differential cocycle “with values in $\mathbf{B}G$” is actually a
certain constrained generalized morphism into # $\mathbf{B E}G$. Understanding that funny shift in dimension properly used up maybe 50 percent of my time here, and is probably the reason if the
effort looked less than coherent at times.
Making recourse to the “rationalized” approximation of $L_\infty$-connections # the pattern was finally understood, and now there are very nice relations emerging # between this question and major
programs of my co-bloggers: higher topos theory and geometric representation theory/groupoidification.
There is one main class of examples which motivates all this effort: quantization of # (higher) Chern-Simons bundles with connection to Chern-Simons QFT ## and its holographic # #boundary theory.
Indeed, the realization # that the known modular category theoretic formulation of 2-dimensional CFT # # was in fact secretly a differential cocycle was what originally lead to the proposed answer
above. This is being worked out with Jens Fjeldstad #.
The hardest part of figuring out the pull-push of a given cocycle is in top dimension. This is no surprise, since there it must reproduce the “path integral”. But first consistency checks in simple
toy examples suggest that it does work # # allright.
But with the big picture finally stabilizing, many details need to be worked out further.
Posted at 10:47 AM UTC |
Followups (9)
March 22, 2008
Nonabelian Differential Cohomology in Street’s Descent Theory
Posted by Urs Schreiber
As a followup to our recent discussion #:
Nonabelian differential cohomology
in Street’s descent theory
(pdf, 20 pages)
Abstract: The general notion of cohomology, as formalized $\infty$-categorically by Ross Street, makes sense for coefficient objects which are $\infty$-category valued presheaves. For the special
case that the coefficient object is just an $\infty$-category, the corresponding cocycles characterize higher fiber bundles. This is usually addressed as nonabelian cohomology. If instead the
coefficient object is refined to presheaves of $\infty$-functors from $\infty$-paths to the given $\infty$-category, then one obtains the cocycles discussed in [BS, SWI, SWII, SWIII] which
characterize higher bundles with connection and hence live in what deserves to be addressed as nonabelian differential cohomology. We concentrate here on $\omega$-categorical models (strict globular
$\infty$-categories) and discuss nonabelian differential cohomology with values in $\omega$-groups obtained from integrating L(ie)-$\infty$ algebras.
Posted at 7:33 PM UTC |
Followups (12)
March 21, 2008
Groupoidfest in Riverside
Posted by John Baez
The next Groupoidfest is here in Riverside!
• Groupoidfest, November 22-23, 2008, Mathematics Department, University of California, Riverside, organized by Aviv Censor.
I hope some of you can come! If you want to, contact Aviv as described on the conference website.
Posted at 11:22 PM UTC |
Followups (5)
Crossed Menagerie
Posted by Urs Schreiber
Tim Porter kindly made the following notes available online:
Tim Porter
Crossed Menagerie:
an introduction to crossed gadgetry and cohomology in algebra and topology
(pdf with the first 7 chapters (237 pages))
Posted at 8:01 PM UTC |
Followups (25)
March 20, 2008
This Week’s Finds in Mathematical Physics (Week 261)
Posted by John Baez
In week261 of This Week’s Finds, learn about the Engraved Hourglass Nebula:
Then read an ode to the number 3, which explains how all these entities are connected:
• the trefoil knot
• cubic polynomials
• the group of permutations of 3 things
• the three-strand braid group
• modular forms and cusp forms
Posted at 7:14 AM UTC |
Followups (17)
March 17, 2008
The World of L
Posted by David Corfield
Anyone care to tell us what’s really going on in this
about the discovery of a third degree transcendental L-function? I like the description of the ‘World of L’ as where “most of the secrets of number theory are kept”.
Posted at 11:24 AM UTC |
Followups (25)
March 13, 2008
Slides: On Nonabelian Differential Cohomology
Posted by Urs Schreiber
March 12, 2008
Chern-Simons Actions for (Super)-Gravities
Posted by Urs Schreiber
Just as
electromagnetism is a theory of line 1-bundles with connection coupled to electric 1-particles and magnetic 1-particles,
we have that
supergravity # in eleven dimensions is a theory of line 3- and line 6-bundles with connection coupled to electric 3-particles and magnetic 6-particles.
(There is a beautiful discussion of essentially this statement by D. Freed, which I talked about here, and here. Freed doesn’t say “$n$-bundle with connection”, but instead says “differential cocycle
”. But it’s the same kind of thing.)
Wonders never cease, and hence there are indications that there is more to 11-dimensional supergravity than meets the eye. The question is: what? What is 11-dimensional supergravity really about?
One idea is: it is really about 1-particles on the “$E_{10}$-group manifold”. This we talked about before.
Another idea is: it is really about the higher Chern-Simons theory # of an invariant degree 6-polynomial on a super Lie algebra not unlike super-$so(n,m)$#.
This speculation was put forward in
Petr Hořava
M-Theory as a Holographic # Field Theory
The jargon in the title is such as to make certain physicists excited. A completely different, but possibly just as exciting jargon would be: it is speculated here that, very fundamentally, physics
is about those representations of extended cobordism categories which are naturally induced from Chern-Simons $n$-bundles with connection.
I was reminded of that by the appearance of the very nicely written basic review
Jorge Zanelli
Lecture notes on Chern-Simons (super-)gravities
which was updated a few days ago. (Thanks to It’s equal but It’s different for noticing.)
This reviews the action functionals for theories of gravity one obtains by picking a $d = 2k +1$-dimensional manifold $X$, a structure group $G$ like $SO(d-1,1) \hookrightarrow \left\lbrace \array{
SO(d,1) \\ (ISO(d-1,1)) \\ SO(d-1,2) &\hookrightarrow& OSP(m|N) } \right.$ together with a degree $(d+1)/2$ invariant polynomial $\langle \cdots \rangle$ on its Lie algebra; and takes the action
functional to be the corresponding Chern-Simons integral which sends $g$-valued 1-forms $A$ on $X$ to $A \mapsto \int_X \mathrm{CS}(A) \,,$ where the Chern-Simons $d$-form # $CS(A)$ satisfies $d CS
(A) = \langle F_A \wedge F_A \wedge \cdots \wedge F_A \rangle$.
For $d=3$ this yields, famously, the ordinary (super) Einstein-Hilbert action in that dimension. For higher (odd) $d$, this yields the (super) Einstein-Hilbert action with higher curvature
Hořava gave arguments suggesting that and how for $d=11$ the Chern-Simons gravity action reduces to that of ordinary supergravity in the appropriate limit.
Posted at 6:55 PM UTC |
Followups (20)
Following Singapore’s Lead
Posted by John Baez
Some interesting news from the Los Angeles Times.
In 2005, just 45% of the fifth-graders at Ramona Elementary School in Hollywood scored at grade level on a standardized state test. In 2006, that figure rose to 76%. Why? They started using the same
math curriculum that Singapore does.
Ramona isn’t a rich, fancy school. Nine out of ten students at the school are eligible for free or reduced-price lunches. Most are children of immigrants — most from Central America, some from
Armenia. Almost six in ten speak English as a second language. But, they’re doing a lot better in math than kids at other nearby schools!
Posted at 4:53 PM UTC |
Followups (51)
March 11, 2008
A Strange Link
Posted by David Corfield
Guest post by Tim Porter
I have just been looking back over Todd’s guest posts (I and II) from last autumn, and a strange link has just occurred to me. In the paper (Me with A. Bak, R. Brown and G. Minian), Global Actions,
Groupoid Atlases and Applications, Journal of Homotopy and Related Structures, 1(1), 2006, pp.101 - 167, we include some examples from group presentation theory (which has a tendency to be a good
testing ground for ideas for presenting logics).
Take a group $G$ and a family of subgroups (not just one as in Jim and Todd’s discussion). This family can be just ‘discrete’ or may be completed under intersections, it may not make a lot of
difference. You cannot form a direct quotient by the family to get a $G$-set because you have more than one (usually)!!! Try it with a nice finite group and two subgroups. The cosets of the subgroups
in the family give a covering of the set of elements of $G$ and the nerve and Vietoris complexes of that covering give simplicial complexes with a $G$-action, and hence an orbi-hedron in Haefliger’s
sense (see the big book by Bridson and Haefliger – Metric Spaces of Non-Positive Curvature).
Posted at 6:38 PM UTC |
Followups (6)
Physics, Topology, Logic and Computation: a Rosetta Stone
Posted by John Baez
It’s done!
Learn how category theory serves as a lingua franca that lets us translate between certain aspects of these four subjects… and perhaps, eventually, build a general science of systems and processes!
In a nutshell, it goes like this:
$\array{ & object & morphism \\ Physics & system & process \\ Topology & manifold & cobordism \\ Logic & proposition & proof \\ Computation & data type & program }$
It takes a while to explain the details.
Posted at 5:47 AM UTC |
Followups (103)
March 9, 2008
Learning to Love Topos Theory
Posted by John Baez
I was just working away, listening to some music by Gorillaz, when I checked my email and saw this great quote from Steve Vickers on the category theory mailing list:
As a parable, I think of toposes as gorillas (rather than elephants). At first they look very fierce and hostile, and the locker-room boasting is all tales of how you overpower the creature and
take it back to a zoo to live in a cage — if it’s lucky enough not to have been shot first. When it dies you stuff it, mount it in a threatening pose with its teeth bared and display it in a
museum to frighten the children. But get to know them in the wild, and gain their trust, then you begin to appreciate their gentleness and can play with them.
The gorilla in the cage is the topos in the classical world.
Posted at 10:08 PM UTC |
Followups (2)
March 8, 2008
Some Puzzles
Posted by John Baez
Grr! I’m too busy trying to finish that Rosetta Stone paper to post anything really interesting, or even reply sensibly to the posts by my co-bloggers. So, just a few puzzles…
Posted at 2:16 AM UTC |
Followups (21)
March 6, 2008
Space and Quantity
Posted by Urs Schreiber
Am preparing some notes which are supposed to wrap up the discussion on smooth spaces, smooth function algebras, smooth algebras of differential forms, etc, which we had in
Transgression, Comaparative Smootheology, Question on Smooth Functions
and further develop it. Here is the current status:
Spaces and Differential Forms
I haven’t indicated any author names at this point. I have typed this so far, but, as you all know, this draws heavily on plenty of remarks by Todd Trimle and Andrew Stacey. Most of the proofs
currently appearing are simply transcripts of proofs Todd described. (Of course all mistakes in the document are mine.) I also benefitted from discussing this stuff with Bruce Bartlett in person.
Posted at 8:40 PM UTC |
Followups (18)
Worrying About 2-Logic
Posted by David Corfield
Here’s a possible problem for the idea of modal logic as 2-logic.
In ordinary first order logic a model of a theory is a set $X$. To an $n$-ary predicate of the theory we assign a subset of $X^n$, to a constant an element of $X$, and so on.
For a given $X$, we can derive a Galois correspondence between theories modelled on $X$ and subgroups of $X !$, the permutations of $X$, as Todd shows.
Now, in first order modal logic (FoS4) a model of a theory is a sheaf. To show completeness we can stick with bog standard sheaves on topological spaces, as Awodey and Kishida show in their paper
Topology and Modality. This combines the topological semantics of propositional modal logic with the set-valued semantics of first-order logic. Necessity relates to taking the interior of subsets of
the base space.
Posted at 11:28 AM UTC |
Followups (20)
March 4, 2008
Sections of Bundles and Question on Inner Homs in Comma Categories
Posted by Urs Schreiber
In the spirit of groupoidification a section of an associated bundle can be conceived in the following way:
let $G$ be a group, $\mathbf{B} G$ the corresponding one-object groupoid, $X$ a space, $Y \to X$ a “good” regular epimorphism, $Y^\bullet$ the corresponding groupoid. Then $G$-bundles $[g] : P \to X$
on $X$ are equivalent to functors $g : Y^\bullet \to \mathbf{B} G \,.$
Now let $\rho : \mathbf{B} G \to Vect$ be a linear representation of $G$ (or $\rho : \mathbf{B} G \to C$ any other representation) and denote by $V//_\rho G$ the corresponding action groupoid, which
sits canonically in the sequence $V \to V//_\rho G \stackrel{r}{\to} \mathbf{B} G \,.$ Given these two morphisms, we are lead draw the cone $\array{ Y^\bullet &&&& V//_\rho G \\ & {}_g \searrow && \
swarrow_r \\ && \mathbf{B} G } \,.$ It is easy to convince oneself that the collection of completions
$\array{ Y^\bullet &&\stackrel{\sigma}{\to}&& V//_\rho G \\ & {}_g \searrow && \swarrow_r \\ && \mathbf{B} G }$
of this diagram equals the collection of sections of the bundle associated to $[g]$ via $\rho$:
$Hom_{\mathbf{B} G}(g,r) \simeq \Gamma( [g]\otimes_\rho V) \,.$
Posted at 9:23 PM UTC |
Post a Comment
Charges and Twisted n-Bundles, II
Posted by Urs Schreiber
Last time I recalled how the historically big insight
$\;\;\bullet$ an electromagnetic field is a line bundle with connection
has to actually be replaced, more generally, by the statement
$\;\;\bullet$ an electromagnetic field is a twisted line bundle, i.e. a “gerbe module” or “2-section” of the magentic charge line 2-bundle.
This time I recall Freed’s description of the Euclidean action for electromagnetism in the presence of electric currents. Then, again, I rephrase everything in the language of $L_\infty$-connections
(blog, arXiv) and the arrow-theoretic $\Sigma$-model (slide 11).
I’ll do so for the very simple case where all $n$-bundles appearing are actually trivial, so that only their connection forms matter. This makes most of the differential cohomology/$n$-bundle
terminology overkill, but allows to nicely see how the action functional on configuration space arises from transgression of a “background field”, following the general tao.
Posted at 2:00 PM UTC |
Followups (4)
March 3, 2008
Infinity-Groups with Specified Composition
Posted by Urs Schreiber
I have a certain desire to do the one-two-three—-infinity thing for $n$-groups while retaining specified composition.
What I mean is this: there is the
$\;\; \bullet$ bundle point of view
and the
$\;\; \bullet$ section point of view
on higher categories. The first one uses models where the existence of compositions of $n$-morphisms is guaranteed, but not specified, while the second one explicitly specifies for any two higher
morphisms and all possible ways to attach them the resulting composite.
In the first approach it is easy to say $\infty$-group: “Kan complex with single 0-simplex”.
While that’s easy to say, it is in general hard to do anything with (at least for me). When we want to actually do something in concrete applications, we are often better off with having a model that
has specified composites. (I discussed a concrete example for that recently in Construction of Cocycles for Chern-Simons 3-Bundles.)
Well, I might be just ignorant and prejudiced. But be that as it may, it should be an interesting question in its own right to see how far we can get with handling $\infty$-groups in the second
approach, where composites are specified.
There is little chance, with present technology, to handle in the second case $\infty$-groups with full weakening allowed. On the other hand, entirely strict $\infty$-groups would be easy to handle,
but a bit insufficient. I want something which is as strict as possible while still capturing a “sufficient” degree of weakening.
And here is my condition on what I will consider as sufficient weakening:
The model of $\infty$-groups must be closed in that for $G$ an $\infty$-group also $AUT(G) := Aut(\mathbf{B} G)$ is an $\infty$-group.
Because that’s what is needed for doing differential nonabelian cohomology.
Here $\mathbf{B} G$ denotes the one-object $\infty$-groupoid given by $G$.
For instance, if $G$ is an ordinary group, then $AUT(G)$ is the 2-group whose objects are the ordinary automorphisms of $G$ and whose morphisms are the inner automorphisms of $G$.
Notice that if $G$ is a strict 2-group, then $AUT(G)$ is no longer a strict 3-group – but a Gray group, meaning that $\mathbf{B} AUT(G)$ is a Gray groupoid, a groupoid enriched over the category of
2-categories equipped with the Gray tensor product. In the language of crossed group structures, this amounts to passing from crossed complexes to crossed squares.
This is described in theorem 4.3 and 5.1 of
R. Brown, I. Icen
Homotopies and automorphisms of crossed modules of groupoids
and David Roberts and myself talk about it in our article.
So, forming automorphism $(n+1)$-groups of $n$-groups takes one from the world of strict $n$-groups into the weakened realm. But how far? Do we need fully weakened $\infty$-groups to have that $AUT
(G)$ is an $\infty$-group if $G$ is? Or is there some explicit “semistrict” notion of $\infty$-group in between, rather strict, but weak enough to allow for $AUT(G)$?
Here is my proposal for how to deal with that (following a similar remark I made in a comment here):
Posted at 3:51 PM UTC |
Followups (23)
A Deep Sense of Miserable Ignorance
Posted by David Corfield
On p. 171 of Peirce’s lectures, Reasoning and the logic of Things, having favourably compared the universities of Europe to those of America, he explains what is wrong with the latter’s pedagogy:
In order that a man’s whole heart may be in teaching he must be thoroughly imbued with the vital importance and absolute truth of what he has to teach; while in order that he may have any measure
of success in learning he must be penetrated with a sense of the unsatisfactoriness of his present condition of knowledge. The two attitudes are almost irreconcilable. But just as it is not the
self-righteous man who brings multitudes to a sense of sin, but the man who is most deeply conscious that he is himself a sinner, and it is only by a sense of sin that men can escape its
thraldom; so it is not the man who thinks he knows it all, that can bring other men to feel their need of learning, and it is only a deep sense that one is miserably ignorant that can spur one on
in the toilsome path of learning. That is why, to my very humble apprehension, it cannot but seem that those admirable pedagogical methods for which the American teacher is distinguished are of
little more consequence than the cut of his coat, that they surely are as nothing compared with that fever for learning that must consume the soul of the man who is to infect others with the same
apparent malady.
Does this explain the success of This Week’s Finds?
Posted at 3:38 PM UTC |
Followups (6)
March 1, 2008
Kim on Fundamental Groups in Number Theory
Posted by John Baez
My friend Minhyong recently wrote up a talk he gave at Leeds:
It starts with some pleasant observations of an elementary nature and works its way up to some ideas I find rather terrifying. Maybe we can ask him some questions and get him to explain what’s going
Posted at 7:31 AM UTC |
Followups (46)
Computer Scientists Needed Now
Posted by John Baez
Thanks to advice from Andrej Bauer, Robin Houston and Todd Trimble, I’ve beefed up the logic section of this paper:
For example, I’ve included a longer ‘overview’ to give the non-logician reader a slight feel for how proof theory met category theory in the development of 20th-century logic. I hope there are no
egregious errors. If you catch any, let me know.
But now I really need comments from anyone who likes categories and theoretical computer science!
Posted at 1:47 AM UTC |
Followups (32)
|
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Eco. 101----21-8-2021 (Online Discussion Quiz 2--Methods of Economic Analysis) | Success Tonics Blog
Comments 581
1. Name: Ikeh Nnamdi Samuel
Department: Economics/psychology
Reg No: 2020/246207
Faculty: Social sciences
Question: Methods of Economic Analysis
Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
* Observation of a task/ issue
* Making the hypothesis
* Testing the hypothesis using more observations, etc.
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
*Formulation of a hypothesis
*Generalizing principles
“Verifying against actual facts.
2. Name: Onyelonu Chidire Victory
Reg no: 2020/246205
Department: Combined social sciences(Economics and psychology)
Faculty: Social sciences
Email: victorychidi223@gmail.com
Questions: what are the basic method of analysis used by Economists?
The word ‘economics’ comes from two Greek words, ‘eco’ meaning home and ‘nomos’ meaning accounts. The subject has developed from being about how to keep the family accounts into the wide-ranging
subject of today.
Economics has grown in scope, very slowly up to the 19th century, but at an accelerating rate ever since. Today it has many of the features of a language. You may already have studied economics
and there is the danger that the language that you learnt has changed, so be careful!
Economics is the study of scarcity and its implications for the use of resources, production of goods and services, growth of production and welfare over time, and a great variety of other
complex issues of vital concern to society. And there are methods of analysis Economics which are:
(1). Inductive reasoning: This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. Data
is collected about a particular economic theory and then conclusions are drawn. The stages in this method done through observation, formulating hypothesis, generalizing principles and verifying
against actual fact. One of its advantages is that it is more realistic and reliable. And one of its disadvantages is that it’s a time consuming process and expensive.
(2). Deductive reasoning: This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or
theory) using logical analysis or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning through: observation, of a task,
making the hypothesis, testing the hypothesis using more observations, etc.This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
One of the advantages of these method is that for economists as it focuses upon economic reasoning which is of paramount importance. and one of its disadvantages is that it’s logical fallacy.
This implies that the two methods or reasoning differs methodologically.
3. Name: Ukachukwu Chinelo Esther
Reg No: 2015/202410
Department: Economics Education
Faculty: Education
QUESTIONS: METHODS OF ECONOMIC ANALYSIS
Economics is the study of how people allocate scarce resources for production, distribution, and consumption, both individually and collectively. It focuses on the actions of human beings, based
on assumptions that humans act with rational behavior whereby they seek the most optimal level of benefit or utility. Economics can generally be broken down into macroeconomics which concentrates
on the behavior of the economy as a whole ie it it examines overall economies on a regional, national or international, and microeconomics which focuses on individual people and businesses ie the
behavior of individual consumers and producers. However these two branches of economics use very different theories, models, and research methods, which sometimes appear to conflict with each
Generalisations in economics have been derived in two ways:
(1) Deductive Method; This consists of deriving conclusions from general facts, with general principles and applies conclusions. The steps involved in deductive method includes; perception of the
problem, definition of terms, deducing hypothesis from assumptions, testing of hypothesis. It has its merits and demerits. The merits include; it is less time consuming and less expensive, it
uses mathematical techniques in deducing theories, it helps in deriving economic theories, it is simple because it is analytical.
It’s demerits include; it’s assumptions might be wrong, it is not applicable universally, it is also highly abstract.
(2) Inductive Method: This involves data collection about certain economic phenomenon. It involves the process of reasoning from particular facts to general principles. The steps of inductive
method include; observation, formation of hypothesis, generalization and verification. This method has its merits and demerits.
It’s merits includes; it is based on facts ie, the method is realistic, if conclusions are drawn from insufficient data, the generalization obtained may be faulty, collection of data is not an
easy task. Lastly, it is time consuming and expensive.
This shows that both methods have their own faults and weaknesses and cannot be exclusively relied on.
4. Name: RAWLINGS OTSONU
Jamb Reg No. 29752699EF
Department: Economics
Faculty: Social Sciences
Assignment Question: Meaning of Economics and Behavioural Economics
Responses: The meaning of Economics, a derivative of the Greek word ‘economy’ has been succinctly defined by different scholars based on their own understanding of the subject. In line with the
word “economy”. Economy is a Greek word’oikovouoc meaning One who manages a household”). It is a composite word derived from oikoc, (house) and veuw (“manage, distribute”) by the way of
oikovouia, meaning household Management. And economy consist of Economic system in a certain region, comprising the production, distribution or trading and consumption of the limited goods and
services in that region or country. Therefore, economy is the total sum of product and services transactions of value between two or more economic agent in a region, whether individual(s),
organization or States.
Economics as a term can be defined as follows:
The classical economist, such as Adam Smith put Economics to be”the study of production, distribution and growth of wealth in society”. This definition of economics is based on the aspect of
wealth and concrete economic activities that are not intangible. They emphasized basically on the physical aspect of human activities, leading to utilisation of physical resources in the society,
especially in actual production, distribution and growth in a competitive economy.
That is why of of the classical economists in the person of Adam Smith defined Economics as “an inquiry into the nature and causes of the wealth of Nations”. Another school of thought, known as
the Marxist understand economics to be based on the aspect of labour influencing the development of the economy and its productivity level. Their understanding level of the subject (economics)
encompasses only the aspect of labour population and their effects.
The above points lay emphasis economics in micro aspect, not macro. For that reason, the social scientists postulated that economics studies the way in which societies solve the fundamental
problems of reconciling unlimited desires of individuals with scarce resources, likely to be affected by numerous alternative uses. This is why I would like to adopt the definition of economics
by the great economist, Professor Lord Robinson). He defined Economics as a science, which study human behaviour, as a relationship between the ends and scarce means, which have alternative. His
definition is of economics is all encompassing and it covers all the Scopes and fields of economics, being macro micro.
His definition of economics is generally recognized and used by young learners.
Behavioural Economics:
This according to a scholar Atma Jaya Rosdiana Sijabat of a Catholic University in Indonesia quoted that in the traditional economics approach, ‘an individual’s decision reflect that individual’s
best interests and made rationally ‘. For that, she viewed that Behavioural Economics as a field of study in Economics that integrates economics and psychology in analysing human behaviour, which
is important for explaining why individuals’ decisions and behaviour may not reflect their best interests”. According to findings, Behavioural Economics has advantage for its power to explain
individual’s psychological State (State of the mind) in decision making process, in both individual, group of individuals and institutions.
Some technical aspects of the behavioural economics are: pricing process and opportunity cost.
According to the view of Brzezicka and Wisniewski in 2013, Behavioural Economics is an experimental science, as it is based on experiment that combine economic deduction and psychological
induction, thereby creating a complementary means of explaining human decisions.
Another scholar, known as Beenheim and Rangel in 2007 opined that behavioural economics combines the theoretical concepts with those of the state of mind, thereby allowing it to develop various
models for explaining the difficult issues of warfare evaluation, which means that with the help of that, scholars would be able to use it in tackling technical problems involving both psychic
and physical economic challenges because it offers theoritical and methodological means of understanding human behaviour (physical exhibition or response to stimulus or stimuli); by combining the
principles of Behavioural science and micro-economics in line with the view of Kaplan et al in 2018.
MC Mahon also used the same sense to explain behavioural economics in 2015 when he said that: “The fundamental assumption of economic resources distribution is that individuals are rational
beings (rational homo oeconomus, economics humans) when making economic decisions.
Also, Alm and Bordeaux in 2013 supported that stand, he reported that that was why individuals are rational in their views and decision making processes.
Reference from:
1. Acheson, J. D. Lynch, 2017.; Implications of behavioural economics for tax policy. Retrieve from http://igees'gov.ie/wp-content/uploads/2014/01/
Behavioural-economics-and-Tax.pdf%5BAccessedMarch10, 2018].
2. Alm, J., 2010. Testing behavioural public economics theories in the Laboratory. National Tax Journal, 63:635-658.view@googlescholar|View at publisher, etc.
5. Student information
Name: UCHIN MIMI MOSES
Reg. No: 2020/242645
Department: ECONOMICS
Email: uchinmoses1@gmail.com
Economics as a science takes on scientific approaches to arrive at theories, laws and generalizations. To achieve this, economists use methods which are basically known as methods of economic
analysis. These methods are;
Deductive method
Inductive method
The Deductive method also known as the abstract, analytical or prior method involves the process of generalization that derives conclusion from general truths or phenomenal and analyses to simple
conclusions. It talks about economic issues in large aggregates and uses them to draw conclusions on smaller units. For example, it may use the general price level to tackle the problem of
individual demands. In summary, the deductive method moves from complex relations to simple phenomenal in tackling economic issues or drawing of generalizations.
The inductive method also known as the empirical method involves the process of reasoning from simple facts to general principles. This method of analysis derives economic generalizations on the
basis of experimentations, observations and statistical methods. In summary, it deals with economic relations from simple to complex. For example, the price of a particular commodity could be
used to draw conclusions on the general price level in the market.
6. NAME: Nweke Dominic Ede
Reg No:2018/243563
Dept: Public Administration and Local Government
Email Address: domnweke81@gmail.com
METHODS OF ECONOMICS ANALYSIS
Like any other science, Economics adopts two important methods in its investigations and formulation of laws and principles. The two methods are:
Deductive Methods and Inductive Methods.
Deductive Method of Economics Analysis is known as the analytical abstract a priori method. Here we start with certain formal data and assumptions. Then by logical reasoning we arrive at certain
conclusions. We start with undisputed fundamental facts and after adding some assumptions we build up a theory. For instance, it is assumed that businessmen aim at maximum profit. It follows from
this that businessmen buy the materials in the cheapest market and sell it in the dearest market.
In Deductive method of Economic Analysis we proceed from the general to the particular. This is also known as an hypothetical method for some of the assumptions may not correspond to actual
facts, but very near actual facts which may be used as premise for starting, reasoning and drawing conclusions. In economics we start with very simple premises and work up gradually or more and
more complex hypotheses.
A complete form of deductive method consists of three stages, viz.,
(ii) Deductive reasoning and
(iii) Instance and testing by means of further observations.
Deductive reasoning provides us with hypotheses or generalizations. If the hypotheses are tested and verified with relevance to facts, we have valid economic laws.
Advantages of Deductive Method of Economic Analysis:
1. Deductive method is exceedingly simple. For example, the law that the utility derived by an individual from a commodity goes on diminishing with every successive addition is a self-evident
truth from which we may draw many logical conclusions, viz., larger the stock of money, the lower shall be the utility of money; rich persons have lesser marginal utility of money than the poor
people; so taxes should not be levied on proportional basis. If taxes are levied proportionately, the sacrifice of the poor will be larger than the rich. This is against the Canon of equity, etc.
Thus the principle of progressive taxation is derived from the law of diminishing utility through deductive reasoning.
2. Deductive method obviates the necessity of experimentation. Economics being a social science, experimentation may not be available as in the case of physics or chemistry. So, the next best
alternative to experiment is deductive reasoning. According to Boulding this method of deductive reasoning is the method of intellectual experiment.
3. The deductive method results in accuracy and exactness in generalization, because of logical reasoning. The method gives a very high standard of precision in abstract economic reasoning.
Disadvantages of Deductive Method of Economic Analysis:
1. Deduction is based mainly on assumptions which are perfectly valid. If assumptions are wrong, generalizations made on the basis of wrong assumptions will be imperfect and invalid. All economic
laws are based on too many assumptions where there are more scope for committing errors through wrong hypotheses.
2. In deduction there is too much of abstraction and economists by means of their intellectual exercises produce only “intellectual toys” having little connection with reality.
3. Deductive generalizations started on wrong premises will be dangerous when such generalization claim universal validity. Then such faulty generalizations are made use of in framing government
policies, the results would be nothing but disastrous. For example, J.B.Say, claimed universal validity for his ‘Law of Markets’ in which he maintained that supply creates its own demand and
there will not be over-production in the market. But this celebrated ‘Law of Market’ was torn to pieces when critics proved that Say’s Law was wrong and overproduction would be possible.
(2) Inductive Method of Economic Analysis
In this method, economists proceed from a practical angle to problems of science to reduce the gulf between theory and practice. Induction is done by two forms, viz. experimentation and
statistical form. Facts are collected first, arranged and conclusions are drawn. Then these general conclusions are further verified with reference to actual facts.
The inductive method is generally associated with the statistical form of inductions. The statistical approach has a larger field in economic investigations than the method of experimentation.
Further, the method of statistical induction is indispensable for the formulation of economic policy. Malthus presented his famous theory of population only after studying the facts of population
in various countries; He then used statistics to support his theory. Similarly Engel, the German statistician employed inductive method and used statistics to formulate his law of consumption.
Advantages of Inductive Method of Economic Analysis:
1. It is highly practical add realistic as it describes things as they are.
2. It is helpful in verifying the conclusions of the deductive method.
3. Economic laws under this method are not universal but valid only under certain conditions.
Disadvantages of Inductive Method of Economic Analysis:
1. When the investigators lack a balanced judgement there is the risk of drawing hurried conclusions based on inadequate and irrelevant facts and data.
2. Collection of facts in the inductive process is a highly complex and complicated job warranting extraordinary understanding to alienate economic from non-economic factors.
3. Mere induction alone will not deliver goods unless it is supplemented by means of deductive reasoning. Without deduction, the inductive method would result in producing only a mass of
unrelated and unconnected facts.
Deductive or Inductive?
From the above discussion, we can infer that there is no point in pleading one method against the other. The two methods have to be made use of or blended to achieve the required objective. The
two methods, deductive and inductive, are not competitive, but complementary in nature helping the investigator.
7. NAME: OMEKE PRECIOUS OGECHI
REG. NO: 2020/243294
EMAIL: preciousomeke1@gmail.com
COURSE CODE: ECO 101
ECONOMIC ANALYSIS
Economic analysis can be seen as the study of economic system which is the study of a production process or an industry. Economic analysis is all about analysing the economic aspects of things.
METHODS OF ECONOMIC
The basic methods of economic analysis are:- Deductive method and Inductive method or reasoning.
METHOD OR REASONING
Deductive method is also known as an abstract, analytical or priori reasoning. The analysis start from unchallenged elementary or rudimentary facts or assumptions and then arrive at a conclusion
using Logical analysis or one personal analytical abilities. So in general, Deductive method consists in deriving conclusion from general truths.
STEPS IN DEDUCTIVE METHOD OR REASONING
* Identify the problem:- You need to know the problem in other to get the solution.
* Make assumptions about the problem.
* There should be a logical deduction to derive implications.
* Formulation or making of hypothesis.
* Make predictions and test the hypothesis deduced using more observation.
* Predictions should be in agreement with facts.
“Note, ‘Deductive reasoning gives us hypothesis and if the hypothesis gets verified, we will have a general economic principles of law.'”
INDUCTIVE METHOD OR REASONING
Inductive method is also known asa Empirical method. This method is a type of reasoning that flows from facts to theory. First of all, there will be a collection of information or facts and then
providing of evidence using economic theory and facts. Inductive method derives economic analysis on the basis of experience and observations. Inductive method formulate principles using
sub-methods they are:- Observations, Experimentations and Statistical methods.
STEPS IN INDUCTIVE METHODS
* Identify the problem.
* Define the technical terms and alterables related to the problem found.
* Collection of datas about the variables related to the problem.
* Procession of the data collected to find out how the variables are related.
* Make predictions or foretales on the problem and test them.
* Predictions are in agreement with facts.
8. the methods of economics analysis
inductive method is generally associated with the statistical form of inductions .the statisfical approach has lager field in economic investigations than the methods of experiemental futher. the
methods of statistical inductions is indispensible for the formulations of economic policy .mathus presented the famous theory of populations only after studing the facts of populaton in various
countries ,he then used statistics to support the theory
2,Deductive method is know as the analytical abstract a piror method .with certain formula ,data and assumptions then by logical reasoning we arrive at certain conclusions .we start with
indisputed fundamental facts and after adding some assumption we build up a theory .for instance it is assumed that bussinessmen aim at maximum profit .it follow from this that bussiness men buy
the materials in the cheapest market and sell in the dearest market
9. Favour Chinenye Amalaha
The basic methods of analysis used by Economists include,
Deductive Reasoning
Inductive Reasoning
Deductive Reasoning
Deductive Reasoning, also called a priori method, analytical, or abstract method, is an excellent definition of the best expression “moving from the known to the unknown.”
Here, economists makes conclusion from facts by applying logical reasoning. The whole process starts with identifying a problem, then deriving premises, deducing a hypothesis from the already
formed premises, and using logical reasoning to deduce and test the theory. However, this method of analysis creates room for fallacy.
Inductive Reasoning
The empirical or inductive analysis method is based purely on experience or experiments, observation, and statistical evaluation. After identifying and defining the problems, an economist will
move to gather enough data on all the possible variables. The vast data collected is then processed to construct theories. However, unlike the deductive reasoning approach, inductive reasoning
tests these new theories against existing ones. And to ensure the success of this method, economists must collect sufficient data.
10. Name: Abraham Chibuike Sunday
Reg no:20033827AF
What are the basic method of analysis used by economist.
First before I stated them let me quickly define economic analysis.
Economic analysis involves the formulations of laws and generalization through two method.
Now heat are the basic method of analysis used by economists.
1) Deductive method.
2) Inductive method.
1) Deductive method: Now this method can also be called priori reasoning.It is involves the observation of issues,making and building hypothesis using more observation and if adopted then it
becomes an economic law. This method is easy as only simple deduction is necessary and boost economic reasoning.
2). Inductive method: This type of reasoning flows from information, facts,and theory.In this type we first gather facts,information and then move towards bringing proves using economic
theory,information and facts.
Three ways of formulating economics principles and theories.
1) observation
2) Econometric method or statistical.
3) experimentation.
Name Abraham Chibuike Sunday
Course Public administration
11. Chukwu Emmanuel Chimezie
2 methods of economic analysis includes: Deductive method and Inductive method.
Deductive method also called Abstract or analytical method. The Deductive method is unique on it’s own in the sense that it does not involve empirical method. It is not based on experiments.
steps involved in Deductive method are:
1. perception of the problem: get to know what the problem entails
2. define precisely and clearly the technical terms.
3. deduce hypothesis from assumptions
4. test the hypothesis
The Inductive Method(empirical method):
It deals with experience and observations. it is in this method that data are collected with regard to a certain phenomenon and from the observations and data collected, they make
generalizations. 3 ways which can be used for deriving economic principles includes;experimentation, Observation and econometric method.
Steps involved in Inductive method
1. Get to know the problem
2. define technical terms
3. Collect data and do some preliminary thinking about the possible functional relationship between the relevant variables.
4. processing of those data collected and find out the relations between variables that actually hold good.
5. testing of the processed data through statistical method
12. Economics analysis involves deploying various methods to analyze the economy by economists.
The basic methods of economic analysis involves two methods;
1.deductive method
2. Inductive method
The two methods are based on generalization and theory.
DEDUCTIVE METHOD.
The deductive method is also called analytical or prior method.It involves deriving conclusions from known accepted truth, takes them and applies them to draw conclusion.Take for instance, if I
accept the general proposition that Nigerians are lawless. I can conclusively say that we are uncivilized. We see from above illustration that it moved from general to particular. In deductive
method, conclusions cannot of your inference cannot be false given that the premises are true.
1. Perception of the problem :
The analyst must have clear and precise idea of the problem to be inquired into.
2. Find precisely the technical terms, define them and make assumptions.
3. Deduce hypothesis :
From the assumptions made, hypothesis are deduced. The hypothesis could be null or unnull hypothesis.
4. Test the hypothesis ;
Before generalization or theories are established, hypothesis should be verified through direct observation of events and through statistical methods.
MERITS OF DEDUCTIVE METHOD
1. The deductive method is near reality, less expensive and time consuming
2. The method is simple because it is analytical
3. The method can help to derive economic theories
DEMERITS OF DEDUCTIVE METHOD
1.It is highly abstract, requires alot of care to avoid faulty economic reasoning
2. Deduction analysis is not applicable universally.
The imperfections and incorrect assumptions associated with this method that leads to faulty conclusions prompted the classical and neo- classical economists to look for alternative method of
economic analysis thus the inductive method.
THE INDUCTIVE METHOD.
The inductive method also called empirical method was adopted by Historical School of Economists in a bid to improve faulty assumptions associated with the deductive method. It derives
generalization on the basics of experiments, observation and statistical methods. It involves making inferences based on observed patterns or simple repetition, Often used in reference to predict
about what will happen or does happen, based upon what has happened. For instance,we observe all UNN students during during rainy season. We find that 90% uses umbrella. Out of the remaining 10%,
6% wear rain coat despite that it is expensive while 4% doesn’t have umbrella nor rain coat. From the above illustration,we can easily draw conclusion that UNN students uses umbrella during rainy
season unless they are devoid of common sense.
MERITS OF INDUCTIVE METHOD.
1. It’s based on facts and at such is reliable and realistic
2. Inductive method is dynamic
The changing economic phenomenon are analysed and on the basics of collected data,solution and conclusions are drawn.
3. Inductive method helps in future investigation
DEMERITS OF INDUCTIVE METHOD
1.It is time consuming and expensive
2. Data collection is not an easy task
The two methods discussed above have weakness and cannot be exclusively relied on. Modern economists believe that both methods are complimentary
They are partners and not rivals. Alfred Marshall said that”inductive and deductive methods are both needed for scientific thought,as the right and left foot needed for walking”.
13. Name: Anekwe Blessing Ifeoma.
Registration Number: 20726551IF.
Email: anekweblessing13@gmail.com.
Department: Public Administration and local Government.
WHAT ARE THE BASIC METHODS OF ANALYSIS USED BY ECONOMISTS? BRIEFLY AND CONVINCINGLY DISCUSS EACH OF THEM.
There are basically two methods of analysis used by economists, that are;
*Deductive method.
*Inductive method.
DEDUCTIVE METHOD.
Deductive method is also called abstract, analytical and a priori method and it represents an abstract approach to the derivation of economic generalizations and theories.
* Perception of the problem: He/she must have a clear idea of the problem to be enquired into.
* Defining of technical terms and making of assumption (postulates or premises): Defining precisely the various technical terms to be used in the analysis and also stating clearly the assumption
he makes to derive generalizations.
* Deducing hypothesis through logical deduction:
This is deriving relationship between the variables having a bearing on the phenomenon.
* Testing/verification of hypothesis: The hypothesis need to be verified before established as generalization or principles of economics.
INDUCTIVE METHOD.
This method also known as empirical method derives economic generalization on the basis of experience and observations. Here detailed data/information are collected with regard to economic
phenomenon and effort is made to arrive at a generalization from the observations collected.
There are 3 ways used for deriving economic principles and theories, they are;
* Experimentation.
* Observation.
* Statistical or econometric method.
STEPS IN INDUCTIVE METHOD.
* Identifying the problem.
* Defining technical terms and variables related to the problem.
* Collection of data about variables related and doing preliminary thinking about possible relationship between relevant variables.
* Consumption of economic theories.
Once the theory is developed one can make predictions on its basis as in the deductive approach. If the new theory works better than the previous ones, it replaced them.
But if the predictions are against actual facts and behaviour of the economy, they are either discarded or modified by collecting more data and processing them.
The above discussion comes to a conclusion that both deductive and inductive methods are needed because they are complementary and not competitive.
14. NAME:ADAMGBE IORWUESE AMOS
DEPT: ECONOMICS
MATRIC NO.2020/242575
COURSE CODE: ECO 101
METHODS OF ECONOMIC ANALYSIS
(1) THE DEDUCTIVE METHOD: Deductive method is essentially a top-down approach which moves from the more general to the more specific. In other words, we start with a general notion or theory,
which we then narrow down to specific hypotheses, which are then tested.
steps involved in Deductive methods are;
(1)perception of the problem
(2)postulates/making assumptions
(3)deduction of hypothesis
(4)Testing the hypothesis
INDUCTIVE METHOD:
The inductive method is more of a bottom-up approach, moving from the more specific to the more general, in which we make specific observations, detect patterns, formulate hypotheses and draw
steps involved in inductive method includes;
(1) observation
(2) experience
(3) econometrics methods
DEPARTMENT: Public Administration and Local Government
MATRIC NO: 2020/243287
The Brief explanation of the Basic analysis used economists are:
Economics like any other science, has two major methods in the creation of principles, which includes:
a) The Deductive Method of Analysis
b) The Inductive Method of Analysis
A) The Deductive Method of Analysis:
This can be know as the abstract and analytical method, which actually deals with assumptions, which are not corresponding with the actual fact and may be close to the fact, but by logical
reasoning, we arrive at a conclusion. Deductive reasoning/analysis proceed from general to particular which is know as hypothetic method.
Deductive Method consists of three stages, which includes:
i. Observation
ii. Deductive reasoning
III. Testing by further observation
a) Because of the logical reasoning involved in the Deductive Method, it is able to provide accurate prediction in abstract economic reasoning.
b) Deductive Method unlike any other science, help economists do away with the need for experiments for arriving at their final conclusion. According to Boulding, this Deductive reasoning is know
as ‘INTELLECTUAL EXPERIMENT’.
a) Deductive Method is based mainly on assumptions and not the actual facts, so therefore, if an assumption is wrong, then generalization made on the assumption is invalid.
b) In deduction, the use of the mind is too much(abstraction) , which makes them have little or no connection with reality.
B) Inductive Method of Economic Analysis:
Inductive Method unlike Deductive method include the use of experiments and statical way of gathering facts, arranging them, and then conclusions are drawn from them in reference to actual facts
and connection to reality.
i) It is helpful in the verification and cross-checking of the conclusion made through the deductive method.
ii) It deals more on reality than abstract.
i) when it comes to gathering the facts, it is complex and complicated
ii) without deductive method, inductive Method would end up creating unrelated facts because logical reasoning was not applied before arriving at the final conclusion.
16. Name: Chukwu Augustina Chicheta
Matric no: 2020/243289
Department: Public Administration and Local Government
Email: chukwuaugustinac98@gmail.com
The basic method of analysis used by economist are Deductive method and Inductive method.
1. Deductive method of reasoning is a process of reasoning from one or more statements to reach conclusions.
The deductive method also known as abstract, analytical represent abstract approach to the derivation of economic generalization and theories.
The steps in the process of deriving economic generalization through deductive method are;
i. Perception of the problem.
ii. definition of technical terms and making os assumption.
iii. deducing hypothesis through logical deduction.
iv. Verification of hypothesis.
2. Inductive method of analysis is a method of reasoning in which statements are viewed as supplying some evidence, but not full assurance, of the the the conclusion.
In inductive method of analysis, one’s experiences and observations, including what’s learned from others, ara synthesized to come up with a general truth.
Here are the steps in developing economic theories through inductive method are:
i. Identifying the problem.
ii. defining the technical terms and variables related to the problem.
iii. collection of data about the variables related to the problem.
iv. construction of economic theories etc.
17. Eze Mmesoma Benita
Public Administration and Local Govt
1, what are the basic methods of analysis used by economist? Briefly and convincingly discuss each of them
1,first and foremost it’s very vital to note that every economic has it challenges,any economic Analysis involves the formulation of laws and generatization through two method which are
1Deductive method
2Inductive method
Deductive method:This is also called a prior reasoning .we start from unchallenged elementary or rudimentary assumptions/facts and then aim at conclusions(build a hypothesis or theory)using
logiccal analysis as our own analytical abilities .In this kind of reasoning we go from general to specific .i.echanging your generalization to theories.The stages involved in deductive method
are as follows:
*Observation of a task / issue;observe and identify the problem or the issue bcause without the problem there cannot be a theory.
*Making the hypothesis;The hypothesis needs to be made in order to test it.
*Testing the hypothesis:Test the hypothesis using more observations.
Inductive method:This type of reasoning flows from facts to theory,first we collect information and facts and then move towards providing evidence using economic theory and facts.Data is
collected about a particular economic theory and then conclusion are drawn .The stages in this method include :
*Observation : observe and identify the problem or the issue
*Formulation of hypothesis:you get to formulate your hypothesis in order to test later on.
*Generalizing principle:you generalize the principle
*Verifying against actual facts:Also known testing your hypothesis because in the process of this you can actually pick the fact that are true or not.
18. NAME: CHIDUMEBI ONYEJE
REG NUMBER: 20683830DF
DEPARTMENT: ECONOMICS
Methods of Economics Analysis:
Like any other science, Economics adopts two important methods in its investigations and formulation of two laws and principles. The two methods are:
1. Deductive method
2. Inductive method
1. Deductive method of economic analysis: Deductive method is known as the analytical abstract, a prior method. Here we start with certain formal data and assumptions, then by logical reasoning
we arrive at certain conclusions. We start with undisputed fundamental facts and after adding some assumptions we build up theory. For instance, it is assumed that business men aim at maximum
profit. It follows from this that business men buy the materials in the cheapest market and sell it in the nearest market.
In deductive method of economic analysis we proved from the general to the particular. This is also known as an hypothetical method for some of the assumptions may not correspond to actual facts
which may be used as premise for starting, reasoning and drawing conclusions
2. Inductive method of economic analysis: In this method, economists proceed from a practical angle to problem of science to reduce the gulf between theory and practice. Induction is done by two
forms, viz ; experimentation and statistical form. Facts are collected first, arranged and conclusions are drawn. Then these general conclusions are further verified with reference to actual
The inductive method is generally associated with the statistical form of inductions. The statistical approach has a larger field in economic investigations than the method of statistical
induction in indispensable for the formulation of economic policy.
19. Name:Amadi Sylvia Chinwendu
Reg no:20649454GA
Matric no:2020/243138
Dept:Public administration and local government
METHODS OF ECONOMICS ANALYSIS
(1)DEDUCTIVE METHOD
(2)INDUCTIVE METHOD
(1)INDUCTIVE METHOD:This is also called abstract,analytical and prior method and represent an abstract approved to the derivation and theories
(a)Perception of the problem to be required into
(b)Defining precisely the technical terms and making appropriate assumption,often called postulate or premises
(c)Deducing hypothesis that is driving condusions from the premises through the process of logical reasoning and
(d)Testing of hypothesis deduced
INDUCTIVE METHOD:The inductive method method is also called empirical method drives economic generalization on the basic of experience and observations .ln the method details that are collected
with regards to a certain economic phenomenon and effects is then made to arrive at certain generalisations which follows from the observations collected,but is worth mentioning that the number
of observations has to be large if it can yield a valid economic generalisation one should not generalise on the basis of a very few observation .
They are three ways which can be used for driving economic principals and theories they are ;
Statistical or econometric method
Now the controversy which existed among the earlier economists as to weather deductive or inductive approach is more appropriate in developing economic theories and principals has been resolved
the modern view point in this regards is that both are needed for the proper development of scientific economic theories,indeed the two are complementary rather than competitive.
20. METHOD OF ECONOMICS ANALYSIS
We have two main method of economic analysis which includes
1.Deductive and
2.Inductive reasoning/method
Deductive method is representation of an approach to the derivation of economic analysis to a certain conclusion.it also known as analytical, abstract and prior method which derives conclusion
from the premises through the process of logical reasoning and a technical way of assumption.
Advantage of deductive method/reasoning
*It very easy to operate;it’s less expensive
*The use of mathematical method in Deductive logic helps the economist to introduce accurate estimate in economic principles and theory
*It also can draw conclusion with out detailed collection of data
Disadvantage of deductive method
*In Deductive reasoning is there is much of abstraction and economist through their intellectual exercises relating to reality.
INDUCTIVE REASONING also known as empirical method derives economic analysis through the basis of theory and practice.it is also associated with statistical form of induction where facts are
first collected and conclusion are drawn which later turn to actual facts.
Merit of inductive method
*Inductive method of economic analysis is realistic and practical
*It helps in verifying the conclusion of the deductive method
Demerit of inductive method
*Inductive method has its demerit which includes; drawing conclusion from insufficient data to obtain generalizations of economic analysis.
21. Ogbonna Innocent Victor
Dept: PALG
Methods of economical analysis
Deductive method gets it’s conclusions from fundamental assumptions or from truth established by other methods
The processes involved in this method are;
*Selecting the problem
*The formulation of assumptions on the basis of which the problem is to be explored
*The formulation of hypothesis through the process of logical reasoning
*Verifying the hypothesis
* Its a simple method: it simplifies complex problem by dividing it into component parts
* Universal: it’s more scientific which makes it more universally acceptable
* It’s efficienct
*Unrealistic assumptions: when facts refute the the theory based on the tested hypothesis the assumption are also indirectly refuted. So deduction depends upon the nature of assumptions
*Incorrect verification: the verification of theories is based on observation and right observation depends upon data which just be correct .
Inductive Method
Is the process of collecting facts, arranging them and then drawing conclusions from them.
The processes involved in this method are;
*Identifying the problem
* Collecting data
*Realistic: this method bus realistic because it’s based in facts and explains them as they are
*Statistical : this method makes use of the statistical method
*Dynamic: this method is dynamic because of its changing phenomenon which can be analysed on the basis of experiences, conclusion can be drawn
Misinterpretation: this method relies on statistical numbers for analysis that can be misused when the assumption are required
*Expensive: this inductive Method is as costly as it is time consuming. The processes of data collection is a very difficult job
* Controlled experiments are not possible in economics.
22. METHOD OF ECONOMICS ANALYSIS
the two main method of economic analysis
Which are
1.Deductive and
2.Inductive Method/Reasoning
DEDUCTIVE REASONING: this is a representation of an approach to the derivation of economic analysis to a certain conclusion.it is also known as abstract, analytical and prior method.it draw
conclusion from the premises through the process of logical reasoning and technical way of assumption.
I deductive reasoning has its merit and demerit which includes ,
Advantage of deductive method
1.its simple cause it derives important economic analysis with out detailed collection of data
2.the use of mathematical method in deductive logic helps the economist to introduce accurate estimate in economic principles and theory
Disadvantge of deductive method
*In deductive reasoning derivation of economic hypothesis and conclusion through deductive reasoning, assumption leads to a bad role
INDUCTIVE REASONING
Inductive method of economic analysis is also known as empirical method which derives economic analysis through the basis of theory and practical.it is generally associated with statistical form
of induction where facts are first collected and will turn into actual facts later.
Inductive method has three ways which can be used for derivation of economic analysis which are
2.Observation and
3.Econometric method
Merit of inductive method/reasoning
* It is realistic and practical
* It helps in verifying the conclusion of the deductive method
Demerit of inductive method
*It draws conclusion from insufficient data to obtain generalization of economic analysis.
23. METHOD OF ECONOMICS ANALYSIS
themain method of economic analysis
Which is
1.Deductive and
2.Inductive Method/Reasoning
DEDUCTIVE REASONING: this is a representation of an approach to the derivation of economic analysis to a certain conclusion.it is also known as abstract, analytical and prior method.it draw
conclusion from the premises through the process of logical reasoning and technical way of assumption.
I deductive reasoning has its merit and demerit which includes ,
Advantage of deductive method
1.its simple cause it derives important economic analysis with out detailed collection of data
2.the use of mathematical method in deductive logic helps the economist to introduce accurate estimate in economic principles and theory
Disadvantge of deductive method
*In deductive reasoning derivation of economic hypothesis and conclusion through deductive reasoning, assumption leads to a bad role
INDUCTIVE REASONING
Inductive method of economic analysis is also known as empirical method which derives economic analysis through the basis of theory and practical.it is generally associated with statistical form
of induction where facts are first collected and will turn into actual facts later.
Inductive method has three ways which can be used for derivation of economic analysis which are
2.Observation and
3.Econometric method
Merit of inductive method/reasoning
* It is realistic and practical
* It helps in verifying the conclusion of the deductive method
Demerit of inductive method
*It draws conclusion from insufficient data to obtain generalization of economic analysis.
24. METHOD OF ECONOMICS ANALYSIS
In economics we have two main method of economic analysis which are
1.deductive and
2.inductive method or Reasoning.
*DEDUCTIVE REASONING:this is a presentation of approach through the derivation of economic analysis to a certain conclusion.deductive logic also Know as analytical, abstract and prior method
draws conclusion from the premises through the process of logical reasoning and a technical way of assumption.it also has its demerit and merit which are;
Advantage of deductive method
*It is simple because through deductive reasoning important economic theories can be drawn with out detailed collection of data.
*The use of mathematical method in deductive logic helps the economist to introduce accurate estimate in economic principles and theory.
Disadvantage of deductive method
*The derivation of economic hypothesis and conclusion through deductive reasoning, assumption leads to bad role.
INDUCTIVE REASONING
Inductive method also known as empirical method derives economic conclusion through the basis of theory and practice.inductive reasoning is generally associated with statistical form of induction
where facts are first collected and conclusion are drawn which later turn to actual facts.
Inductive method has three ways which can be used for derivation of economic principles which are
*Observation and
*Econometric method.
Advantage of inductive method
*Inductive reasoning is realistic and practical.
*it help in verifying the conclusion of the deductive method
Disadvantage of inductive method
Inductive reasoning has its own disadvantage which is drawing conclusion from insufficient data to obtain generalization.
25. Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Deductive And Inductive Methods
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data
26. Reg no__20683659DF
Department__public Administration and Local Government
Two methods of economics analysis are:
Deductive and inductive method..
1.DEDUCTIVE METHOD___This is also called a priori reasoning,it will start from unchallenged elementary or rudimentary assumptions (fact and then arrive at conclusions (build a hypothesis or
theory) Using logical analysis or our own analytical abilities.In this kind of reasoning will go from general to specific..
THE STAGES INDUCTIVE method are:
a.. Observation of a fact and issues
b.. Making the hypothesis, Testing the hypothesis using more observation
__Advantage of deductive method is _
It is a simple method,it doesn’t involve the use of any complex software analysis
2 ..INDUCTIVE METHOD
This type of reasoning flows from fact to theory.first,it will collect information and facts and then move towards providing evidence using economic theory and facts ..This methods formulates
principles using the observations, experimentation, statistical methods.
ADVANTAGE of inductive method
1.Since it is based on fact,it is more realistic and reliable.
DISADVANTAGE of inductive method
1.it is a time consuming process and expensive as well.
27. ODIGIDAWU IFEANYI
PURE AND INDUSTRIAL CHEMISTRY
Any economic analysis involves the formulation of laws and generalizations through two methods- deductive and inductive
Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
28. NAME:UGOCHUKWU DAVID PRECIOUS
FACULTY:PHYSICAL SCIENCE
REG NO:2019/250069
WHAT IS THE BASIC METHODS OF
ANALYSIS USED BY
This process actually involves two basic methods which are Deductive and inductive.
THE DEDUCTIVE METHOD
This is method can also be referred to as a priori reasoning. We start from unchallenged elementary assumptions and then arrive at conclusions i.e (build a hypothesis or theory) using logical
analysis . In this kind of reasoning, we have to go from general to specific.
The stages in deductive reasoning includes:
* Observation of a task
* Making the hypothesis
* Testing the hypothesis using more observations.
This reasoning actually gives us a hypothesis and if this hypothesis gets verified we will get a general economic principles or laws.
ADVANTAGES OF A DEDUCTIVE
* It is a simple method, which doesn’t involve the use of any complex software analysis.
* Simple deductive logic is required.
* This method is really important for economists as it focuses upon economic reasoning which is importance.
THE DISADVANTAGES OF AN
This method of reasoning will start from assumptions, thus, if the assumptions happen to be logically flawed then the whole process becomes faulty which leads to wrong conclusions.
INDUCTIVE METHOD
This kind of reasoning flows from facts to theory. We have to collect informations and then move towards providing evidence using economic theory and facts.
This method formulates principles using the sub-methods which are:
*Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method includes:
* Observation
* Formulation of a hypothesis
* Generalizing principles
* Verifying against actual facts.
THE ADVANTAGES OF AN INDUCTIVE METHOD
* Since this method is based on facts it is more realistic.
* Using the statistical methods and experimentations makes the process more scientific, thus.
* Since the economic environment is dynamic,relying upon a more scientific method will always helps in reaching logical conclusions.
THE DISADVANTAGES OF AN INDUCTIVE
* The data that is been used is insufficient and faulty it would lead to faulty conclusions, thereby making the hypothesis less reliable.
* It is a time-consuming process.
* The collection of all the data is not an easy job.
* It varies from person to person. As to how they collect the data.
29. Methods of Economic Analysis
DEDUCTIVE METHOD
INDUCTIVE METHOD
DEDUCTIVE METHOD:The deductive method is also called abstractive ,analytical and apriori method and represents an abstract approach to derivation of economic generalisation and theories .
THE STAGES IN DEDUCTIVE
a. Observation of a task or issues
b. Making the hypothesis
c. Testing the hypothesis using more observation etc.
ADVANTAGES OF DEDUCTIVE
a.It is simple method doesn’t involve the use of any complex software etc.
b.Only simple deductive logic is required
a. The great demerit of deductive is that it highly sophisticated theoretical
2. INDUCTIVE METHOD:This deductive method is the type of reasoning that flows from Facts to theory ,first we collect information and facts and then move towards providing evidence using economic
theory and facts
STAGES IN INDUCTIVE
a. Observation
b. Formulation of a hypothesis
c. Generalizing principles
d. Verifying against actual facts
ADVANTAGES OF INDUCTIVE
a. Since it us based on facts it is more realistic and reliable
a. It is a time consuming process
b. The collection of all the data is not an easy job and varies from person to person
30. METHODS OF ECONOMIC ANALYSIS
There are basically two methods of economic analysis
1. Deductive method
2. Inductive method
Deductive Method
The deductive Method is also called abstract, analytical or a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a
hypothesis or theory) using logical analysis or our own analytical abilities. In this kind of reasoning, we go from general to specific.
The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method
formulates principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn.
The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person as to how they collect data.
31. The methods used by economist analysis
1. Deduction Method
2. Inductive Method
DEDUCTION METHOD- methods used in deduction by economist are..
(a). Perception of the problem to be enquired into
(b). defining precisely the technical terms and Making appreciate assumptions, often called POSTULATES OR PREMISES
(c). deduction hypothesis, that’s deriving conclusions from the premises through the process of logical reasoning
(d). testing of hypothesis deducted
PERCEPTION OF THE PROBLEM TO BE ENQUIRED
The analyst must know the significant variables regarding whose behavior and interrelationships he wants to derive generalizations and must have a clear ideas of the problem to be enquired into.
Assumptions may be behavioral pertaining to the behavior of the economic variables or they may be technological aspects relating to the state of technology and the factor endowment. the main
assumptions that has been taken in economics is that consumers try to maximize there satisfaction and producers try to maximize their risk and maximize the expected rate of their profits. the
crucial factor in building up a valid theory is whether it’s predictions are corroborated by the facts in the world. A correct scientific theory or generalizations must expressed in the form of a
HYPOTHESIS that is conceivably refutable
A hypothesis describes relationship between factor affecting a phenomenon. it establishes the cause and effect. relationship between the variables having a bearing on the phenomenon through
logical process.hypothesis is deduced from the assumption made. this logical reasoning may be carried out verbally or it may be conducted in symbolic terms using the language of what is known as
SYMBOLIC LOGIC.
It is worthwhile to note that in deriving analytically sound hypothesis,one should guard against commiting logical fallacy in the process of logical deduction.egs. it is inappropriate to conclude
that A must be the cause of B, if A happens to proceed B.
This is the final stages l of deducting method used by economist.hypothesis obtained above have to be verified before they are established as generalizations or principles of economics.
for the verification of hypothesis economist cannot make controlled experiment because they have to discover uniformities in behavioral pattern of man.
INDUCTIVE METHOD- The inductive Method which is also called empirical methods derive economic generalization on the basic of experience and observations. detailed data are collected with regards
to certain economics phenomenon and effort.
WAYS WHICH CAN BE USED FOR DERIVING ECONOMICS L AND THEORIES
a. Experimentation
b. Observations
c. Statistical or econometric methods
THE EXPERIMENTATION.
This is the use of contrived experiment is of limited applicability in economics. Experiments have been conducted to find out which law of production is valid, that is whether law of diminishing
returns operates in the real world.
STEPS IN INDUCTIVE METHODS
Various steps are gone through in developing economics theories through inductive Method
a. In the deductive approach is to identify the problem
b. Defining technical terms and variables related to problem.
c. Collection of data
d. processing of data collected and finding out what relations between the variables actually hold good
32. Economic Analysis
We have two methods of economic analysis
1.) Deductive method
2.) Inductive method
Deductive method is starting with undisputed fundamental facts and after adding some assumptions it builds up into a theory. It is also called Hypothesis.
Inductive method is based on experiences and observations to derive economic generalizations. This type of reasoning flows from facts to theory. First, we collect information and facts and then
move toward providing evidence using economic theory and facts.
33. An economic theory derives laws or generalizations through two methods:
(1) Deductive Method and (2) Inductive Method.
These two ways of deriving economic generalizations are now explained in brief:
(1) Deductive Method of Economic Analysis:
The deductive method is also named as analytical, abstract or prior method. The deductive method consists in deriving conclusions from general truths, takes few general principles and applies
them draw conclusions.
For instance, if we accept the general proposition that man is entirely motivated by self-interest. In applying the deductive method of economic analysis, we proceed from general to particular.
The classical and neo-classical school of economists notably, Ricardo, Senior, Cairnes, J.S. Mill, Malthus, Marshall, Pigou, applied the deductive method in their economic investigations.
Steps of Deductive Method:
The main steps involved in deductive logic are as under:
(i) Perception of the problem to be inquired into: In the process of deriving economic generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.
(ii) Defining of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should also be precise
(iii) Deducing hypothesis from the assumptions: The third step in deriving generalizations is deducing hypothesis from the assumptions taken.
(iv) Testing of hypothesis: Before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
(Their inverse relationship between price and quantity demanded of a good is a well established generalization)
(2) Inductive method of Economic Analysis:method which also called empirical method was adopted by the “Historical School of Economists”. It involves the process of reasoning from particular
facts to general principle.
This method derives economic generalizations on the basis of (i) Experimentations (ii) Observations and (iii) Statistical methods.
In this method, data is collected about a certain economic phenomenon. These are systematically arranged and the general conclusions are drawn from them.
For example, we observe 200 persons in the market. We find that nearly 195 persons buy from the cheapest shops, Out of the 5 which remains, 4 persons buy local products even at higher rate just
to patronize their own products, while the fifth is a fool. From this observation, we can easily draw conclusions that people like to buy from a cheaper shop unless they are guided by patriotism
or they are devoid of commonsense.
Steps of Inductive Method:
The main steps involved in the application of inductive method are:
(i) Observation.
(ii) Formation of hypothesis
(iii) Generalization.
(iv) Verification.
34. The basic economic method are
(1) Deductive and Inductive method
DEDUCTIVE METHOD
In this kind of method, we go from general to specific. The stages in deductive reasoning are:
Observation of a task
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
ADVANTAGE OF DEDUCTIVE METHOD
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
INDUCTIVE METHOD
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods. Data is collected about a particular economic theory and then conclusions are drawn. The stages in this
method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
ADVANTAGES OF INDUCTIVE METHOD
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
DEMERIT OF INDUCTIVE METHOD
(1)If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
(2)it is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
35. Obi Francisca Nwamaka
Faculty of Education
Department of Social Science Education
ECO 101- PRINCIPLE OF ECONOMICS
What are the basic methods analyses used by the Economists?
Any economic analysis involves the formulation of laws and generalizations through two methods-
1. Deductive Method
2. Inductive Method
– Briefly and convincingly discuss each of them
Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions (build a hypothesis or theory) using logical
analysis or our own analytical abilities. In this kind of reasoning, we go from general to specific.
The stages in deductive reasoning are:
• Observation of a task/ issue
• Making the hypothesis
• Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
• It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
• This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
• Observation
• Formulation of a hypothesis
• Generalizing principles
• Verifying against actual facts.
Advantages of Inductive Method
• Since it is based on facts it is more realistic and reliable.
• Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
• Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
• If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
• It is a time-consuming process and thus expensive as well.
• The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
36. Name:Ossai Benita Toochukwu
Reg no:2019/245534
Dept:Pure and Industrial Chemistry
METHODS OF ECONOMIC ANALYSIS
The generalisations of economics like the laws of other sciences, state cause and effect relationships between variables and describe those economic hypotheses which have been found consistent
with facts or, in other words, have been found to be true by empirical evidence. But a distinction may be drawn between a generalisation (law) and a theory.
Some of the most important methods of economic analysis are as follows: 1. Deductive Method 2. Inductive Method
Deductive method:Deduction Means reasoning or inference from the general to the particular or from the universal to the individual. The deductive method derives new conclusions from fundamental
assumptions or from truth established by other methods. It involves the process of reasoning from certain laws or principles, which are assumed to be true, to the analysis of facts.
Then inferences are drawn which are verified against observed facts. Bacon described deduction as a “descending process” in which we proceed from a general principle to its consequences. Mill
characterised it as a priori method, while others called it abstract and analytical.
Deduction involves four steps: (1) Selecting the problem. (2) The formulation of assumptions on the basis of which the problem is to be explored. (3) The formulation of hypothesis through the
process of logical reasoning whereby inferences are drawn. (4) Verifying the hypothesis.
Inductive method:The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are
collected with regard to a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
But, it is worth mentioning that the number of observations has to be large if it can yield a valid economic generalisation. One should not generalise on the basis of a very few observations.
There are three ways which can be used for deriving economic principles and theories.
They are:(a) Experimentation,(b) observations,(c) statistical or econometric method.
37. Name: Odeh Cynthia Chiamaka
Reg No: 2019/243333
Dept: pure and industrial chemistry
Eco 101 assignment
There are two major methods used by economists to carry out economic analysis. These involves a series of clear observations, analysis and critical thinking which will be explained below. These
include the Deductive and Inductive methods respectively.
1. Deductive method: The deductive method is also called abstract, analytical and a prior method and represents an abstract approach to the derivation of economic generalizations and theories.
The principal steps in the process of deriving economic generalizations through deductive steps are:
a. Perception of the problem: In any scientific enquiry, the analyst or theorist must have a clear idea of the problem to be enquired into. There is always the need to set a significant variables
regarding whose behavior and interrelationship will need to derive such generalizations. He must identity a certain problem and diligently derive a suitable generalizations from already observed
b. Definition of technical terms and making of assumptions: This is also an important step in the process of deriving economic generalizations is to define precisely and unambiguously the various
technical terms to be used in the analysis well as to state clearly the assumptions he wants to derive generalizations.
c. Deducing hypotheses through logical deduction: It is imperative in this step to derive generalizations through deductive logic is deducing hypotheses from the assumptions or premises taken.
d. Testing or verification of hypotheses: Hypotheses obtained above have to be verified before they are established as generalizations or principles of economics. For the verification of
hypotheses, economists cannot make controlled experiments, because they have to discover uniformities in behavior patterns of man.
2. Inductive method: The inductive method which is also called empirical method derives economic generalizations on the basis of experience and observations. This method involves the
establishment and collection of clear data with regard to a certain economic phenomenon and effort is then made to arrive at certain generalizations which follow from the observations collected.
It is worthy of note that the number of observations has to be large if it can yield a valid economic generalizations. This also entails a clear and detailed observations and collection of data
before any generalization is made.
38. The simple strategies of monetary analysis used by economists are the Deductive technique and the Inductive method. Economic
generalizations describe the laws or statements of tendencies in numerous branches of economics, along with production, intake, alternate, and distribution of income. In the view of Robbins,
economic generalizations or legal guidelines are statements of uniformity which describe human conduct within the allocation of scarce resources between alternative ends.
The generalizations of economics like the laws of different sciences, kingdoms, cause and impact relationships between variables and describe those financial hypotheses which have been found
consistent with records or, in other words, have been located to be true by using empirical evidence. But a distinction may be drawn between a generalization (regulation) and a concept.
1. Deductive method of monetary evaluation:
The deductive approach is also called the abstract, analytical, and a priori approach, and represents a summary method for the derivation of financial generalizations and theories.
The essential steps in the manner of deriving financial generalizations through deductive common sense are:
(a) belief of the problem:
In any scientific enquiry, the analyst or theorist has to have a clean idea of the problem to be enquired into. He must recognise the enormous variables concerning whose conduct and relationships
he wants to derive generalizations. The notion of trouble is by no means an easy task.
(b) Definition of Technical terms and Making of Assumptions:
The next step within the system of deriving economic generalizations is to outline exactly and unambiguously the various technical phrases for use within the evaluation, in addition to the
country without doubt, the assumptions he makes to derive generalizations.
Assumptions may be behavioral, referring to the behavior of the monetary variables, or they may be technological, referring to the kingdom of generation and the issue of endowments. The crucial
assumptions are made on the basis of observations or introspection.
(c) Deducing Hypotheses via Logical Deduction:
The next step in deriving generalizations through deductive logic is deducing hypotheses from the assumptions or premises taken. A hypothesis describes dating between elements affecting a
phenomenon; it establishes the motive and effect of dating among the variables having a bearing on the phenomenon.
Then, through logical technique, a hypothesis is deduced from the assumptions made. This logical reasoning may be accomplished verbally or it is able to be carried out in symbolic phrases through
the usage of what’s known as symbolic logic.
The geometric or picture technique is likewise typically hired to deduce hypotheses about the connection between elements. Except, the procedure of logical deduction can be completed with the
help of greater formal mathematics.
(d) testing or Verification of Hypotheses:
Hypotheses acquired above need to be demonstrated earlier than they may be set up as generalizations or principles of economics. For the verification of hypotheses, economists can not conduct
controlled experiments due to the fact that they should find out the uniformities in the conduct styles of men.
We can’t do experiments with guys below managed conditions, consisting of in laboratories, as physical scientists do experiments with inanimate gadgets of nature and biologists do those with
animals and vegetation. Consequently, economists have to depend on uncontrolled experience and observations.
The statistics regarding uncontrolled enjoyment of the behavior styles regarding variables about man and the economic system are quite amply available. The reliance by economists on uncontrolled
experiences, however, does increase the wide variety of observations required to verify the hypotheses or to establish the generalizations.
deserves and merits of deductive technique:
With the aid of rigorous mathematical judgment, monetary theories can be developed through the system of deduction, which can correctly provide an explanation for economic phenomena. Secondly,
via deductive logic, useful monetary theories can be derived without the tenuous and distinct collection and analysis of data which might be required underneath the inductive technique. Therefore
, in comparison to inductive techniques, deduction is much less time-ingesting and less expensive. Thirdly, in view of the restricted scope for managed experimentation in economics, the approach
of deduction is an extremely useful technique for building economic theories. This is due to the fact that several forces act simultaneously on an economic phenomenon and it isn’t viable to
remove a number of these with the aid of a managed experiment.
This suggests the vital significance of deductive good judgment for building up monetary principles or theories. Fourthly, the usage of sophisticated mathematical techniques within the deductive
approach permits economists to introduce accuracy and exactness into economic standards and theories. Regardless
of the above-cited merits, the shortcomings of the deductive approach should now not be unnoticed. The usage of the deductive method in deriving financial generalizations requires using a
high-level competence in logic and theoretical abstraction. Similarly
, a great demerit of the deductive technique is that with it, highly state-of-the-art theoretical models based totally on surprisingly unrealistic assumptions may be evolved which do not have any
operational importance. Indeed, such highly beside the point analytical fashions with little empirical content and incapable of being used for coverage systems have in truth been evolved by
economists. Such fashions are not any more than mere “highbrow toys”. If economics is to function as a device for social betterment, the building of such theoretical fashions having no
operational use ought to be averted. Finally
, in the derivation of financial hypotheses and conclusions via deductive common sense, assumptions play a vital function. If the assumptions made are such that when on doing away with them,
economic speculation based totally on them is refuted, then the making of these assumptions isn’t legitimate. Hence
, a person who uses a deductive approach should usually keep in mind to what extent the validity of generalizations derived depends on the assumptions made. As an instance, Keynesian
macroeconomic analysis is based totally upon the assumption of a melancholy-ridden capitalist financial system with a variety of excess effective capabilities. Consequently
, a fine harm has been done in making use of the Keynesian theories in the context of growing countries like ours in which the assumptions made by using Keynes do no longer hold good.
Consequently, mere “deductive arm-chair evaluation” should be avoided, if the clinical persona of economics is to be maintained.
2. Inductive method of economic analysis
The inductive technique, which is also called the empirical approach, derives economic generalizations on the basis of experience and observations. In this technique, precise facts are collected
in regards to a positive economic phenomenon and effort is then made to arrive at sure generalizations which follow from the observations accumulated. However
, it’s really worth citing that the variety of observations has to be huge if it may yield a valid economic generalization. One must not generalize on the premise of a few observations. There are
three approaches which may be used for deriving financial principles and theories.
(a) Experimentation,
(b) observations,
(c) statistical or econometric methods.
As has been cited above, experimentation, that is, the use of contrived experiments, is of restrained applicability in economics. First, in contrast to natural sciences, which can be concerned
with studying the behavior of both inanimate objects or obedient animals, inclusive of rats and rabbits under the influence of chloroform, economics deals with the behavior of man, who’s quite
fickle, wayward, and unmanageable. Except
, man can not tolerate the idea of being experimented upon, either individually or collectively. Secondly, a monetary phenomenon is the result of a multiplicity of factors and reasons performing
and interacting with each other. Consequently
, financial phenomena no longer repeat themselves within an equal uniform pattern. Numerous elements appearing in a monetary phenomenon ‘disturb’ it and make its precise repetition unlikely. For
that reason, compared with herbal phenomena, financial phenomena are less uniform in pattern, much less repetitive and more variable.
Thirdly, economists study the financial phenomena wherein corporations, along with employees’ associations, alternate unions, farming, political events with their distinctive ideologies, and
sports make it tough to conduct controlled experiments in the economic world. However, in spite of those problems, experimental methods can be utilized in some fields. As
an example, experiments have been conducted to find out which regulation of production is valid. That is, whether or not regulation of diminishing returns, the law of consistent returns, or
regulation of increasing returns operate within the real international. Except, public undertakings or massive commercial corporations often attempt to check the impact of the adjustments on the
fees on their products at the call for it and accordingly find out the call for elasticity of their merchandise.
various Steps in the Inductive method: Diverse
steps are gone through in growing monetary theories through an inductive approach. Step one, as in the deductive technique, is to perceive the problem. The second step is defining technical
phrases and variables associated with the trouble. It
is the next step that is unusual for the inductive approach, particularly, the gathering of facts about the variables related to the trouble and doing some preliminary consideration of the viable
practical relationships between the applicable variables. The
following important step in the production of monetary theories in this approach is the processing of statistics collected and locating out what family members between the variables surely
maintain good. From this, a principle was developed which can be subtle and examined through statistical methods. As
soon as the idea has evolved, you may make predictions on its foundation, as is executed in the deductive technique. If predictions of concepts are in settlement with the facts and actual
behavior of the economy, then a new dependable theory has evolved. If a brand new idea explains “how matters work” better than the prevailing ones, it replaces them.
assessment of Inductive technique:
As has been explained above, observations of information through series of specific records and the usage of statistical methods to arrive at monetary generalizations setting up relationships
between facts are being increasingly made. A
number of recent research in the area of macroeconomics, consisting of the nature of intake feature describing the relationship between income and consumption, and the principle of acceleration
describing the factors which determine investment within the economic system, have been acquired via the use of an inductive approach.
The inductive approach has some other issues in that there is a high-quality risk of conclusions being drawn from inadequate statistics. To achieve generalizations via inductive technique, one
must take care that a sufficient number of observations or statistics have been taken under consideration. Except
, the gathering of information itself is likewise no longer a clean venture. And a researcher who desires to use the inductive method to arrive at generalizations must have proper information
about statistical techniques. That is, he should understand the art of accumulating, processing, and interpreting records. It’s apparent that compared with the deductive technique, the inductive
approach is time-eating and expensive.
39. Name: Mpama Onyinyechi ada
Reg no: 20678320df
Education economics
Methods of Economic Analysis
Any economic analysis involves the formulation of laws and generalizations through two methods- deductive and inductive.
Methods of Economic Analysis
Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method;
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method;
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method;
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
40. ASSIGNMENT ON ECO 101
NAME: ODO PHILOMINA CHINASA
REG NO: 29803740BA
DEPT: EDUCATION AND ECONOMICS
Email address: philominachinasa54@gmail.com
The basic methods of analysis used by economists are:
1. DEDUCTIVE METHOD
2. INDUCTIVE METHOD
1. Deductive method which is also called a priori reasoning starts from unchallenged elementary or rudimentary assumptions or facts and then arrives at conclusions. It builds a hypothesis or
theory using logical analysis or their own analytical abilities. In this kind of reasoning, economists start from general to specific.
Economists have different stages in deductive reasoning.
They includes;
Observation of task / issue; making the hypothesis; treating the hypothesis using more observation. This reasoning gives economists a hypothesis and if this hypothesis gets verified, they
generate economic principles or laws.
Moreover, deductive method is a simple method, it does not involve the use of any complex software analysis. It only required simple deductive logic.
Again, deductive method is important for economists as it focuses upon economic reasoning which is of paramount importance.
2. Inductive method: inductive method is the type of reasoning that flows from fact to theory. In the first place, economists collect information and facts then move towards providing evidence
using economic theory and facts.
This method formulates principles using the sub-methods-observation, experimentations, and statistical methods. Data is collected about a particular economic theory and then conclusions are
Stages in this Method Includes:
Observation, formulation of a hypothesis, generalizing principles, and verifying against actual facts
In addition, since inductive method is based on facts, it is more realistic and reliable.
Again using statistical methods and experimentations makes the process more acceptable universally rather than just depending on your own reasoning and logic.
Finally, since the economic environment is dynamic and always changing, relying open a more scientific method always help reach logical conclusions.
41. NAME: IZUCHUKWU CHIDIMMA MARY JANE.
REG NO: 21436506IA
DEPT: SOCIAL SCIENCE ( EDUCATION AND ECONOMICS)
Methods of Economic Analysis
1. DEDUCTIVE METHOD: deductive also known as abstract or priori method which required abstract approach to the derivation of Economic generalisation and theories.The steps include
A. Perception of the problem: the theorist must have the clear knowledge of the two variables he want derive his generalisation from.
B. Define your postulates: finding the relationship between the two variables and why you think the two variables are related based on your own assumptions and observation.
C. Hypothesis: predicting the possible factors that may affect the relationship between the two variables.
D.Testing the hypothesis: verifying if the factors that are assumed to affect the relationship between the two variables are factual in nature before it is generally accepted.
2. INDUCTIVE METHOD: inductive method also known as empirical method which requires collecting many observation on a particular data using statistical method to conclude whether it is consistent
with actual fact or not.Generally It requires Econometric packages to run this method.
42. Name: Edi Kenechukwu Stanley
Reg no: 20118506CF
Dept: philosophy
Assignment: what are the basic methods of analysis used by economists? Briefly and convincingly discuss each of them.
The two basic method of economic analysis are namely; deductive and inductive methods of economic analysis.
* Deductive Method:
The deductive Method of economic analysis is a method which is analytical and abstract in its approach at arriving at a generalization, abstract in a way that mainly it works enough with logical
reasoning, ideas and observations. For one to conduct a deductive analysis to derive an economic generalization, he/she has to honour these process, which are ; firstly, the economist should be
able to significantly understand and identify the problem and it’s behavioural variables to work on and bring a solution to. Secondly, he or she has to make assumptions from a proper observation
and also clearly define or breakdown the technical terms to be used, all to simplify the process of the analysis. Thirdly, the economist has to logically deduce hypothetical description from the
assumptions made, the hypothesis could be description on relationships between factors affecting a phenomenon, however in the process of this logical deduction of hypothesis, one could be advised
to use the mathematical means than the geometric means to avoid committing a logical fallacy. This is advices because mathematical means is more exact while geometric is complicated in it means
and results.
Then lastly is the testing or verification of the deduced hypothesis. In the verification of hypothesis to derive a generalization, it is understood that due to absence of controlled experiments
like the physical scientists do, Economists have to rely on uncontrolled experiences, personally engage in an increased number of direct observation of real events, engage in a careful
interpretation of facts and economic data gathered, gathering of comparatively unprocessed materials such as files of business firms, market and locally published reports, government departments
and its like, to establish a generalization. However, a contemporary way or method of testing hypothesis has been devices and has proven very useful and meritorious because it makes it possible
to obtain more precisely, the degree of relationship between economic variables. This modern method, is termed statistical it econometric method, but then this method must be preceded by
logically developed theories before it could be used.
* Inductive Method:
The inductive Method has some similarities with deductive Method in its process of analysis and derivation of an economic generalization, but distinguishes it from deductive Method is its
empirical or statistical method of testing data or information gathered. In the steps followed to analyze and develop theories through inductive means, just like deductive, firstly is to identify
the problem, after which the economist is to define the technical terms and variables related to the problem.
The next step is collection of data about variables and the possible functional relationship between relevant variables and this could be aided by preceded reasoning or thinking. After that is
making or construction of a theory by evaluating and processing data collected and ascertaining how valid relationships between variables are. When theories has been constructed, prediction are
to be made on its basis, when the predictions of the theory come in agreement with the facts and the behaviour of the economy, then a new theory is born, but if otherwise then a new theory with a
better explanation has to take the place of the existing one, so to analyze and derive generalization or theories through inductive means, demands it requires number of observations, statistical
collection and interpretation of data to achieve.
In conclusion, both method are not competitive rather complimentary in the process of economy analysation and derivation of generalization and theories.
43. Name: OKOAZE DANIEL CHINOSO
Reg no:21366202af
METHOD OF ECONOMICS ANALYSIS
1 DEDUCTIVE REASONING:Deductive reasoning is the process of drawing a conclusion based on premises that are generally assumed to be true. Also called “deductive logic,” this act uses a logical
premise to reach a logical conclusion. Deductive reasoning is often referred to as “top-down reasoning.” If something is assumed to be true and another thing relates to the first assumption, then
the original truth must also hold true for the second thing.
E.g if a car’s trunk is large and a bike does not fit into the trunk, then you may assume the bike must also be large
INDUCTIVE REASONING:Inductive reasoning is a method of logical thinking that combines observations with experiential information to reach a conclusion. When you can look at a specific set of data
and form general conclusions based on existing knowledge from past experiences, you are using inductive reasoning.
Example, if you review the population information of a city for the past 15 years, you may observe that the population has increased at a consistent rate. If you want to predict what the
population will be in five years, you can use the evidence or information you have to make an estimate.
44. NAME: Ugwuoke Okwudilichukwu David
Department: Philosophy
Reg. No 20691721AF
TWO WAY OF ECONOMIC ANALYSIS
1.Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
(2) INDUCTIVE METHOD: This type of reasoning flows from fact you theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This
method formulates principles using the sub-methods observation,experimental, statisitical methods.
45. Okeke Juliet Kelechi
Economist dept.
The basic method of economics analysis used by economists are mainly two which are:
(a) Inductive method
(b) Deductive method
(a)Inductive method: it involves the process of reasoning from particular facts to forming a general principle i.e begins with particular observations and moves to general explanations. Inductive
method process can be illustrated as thus :
Observation of the issue——->Formulation of hypothesis——->Generalizing principles——–>Verifying principle against actual fact.
(b)Deductive method: It involves the process of reasoning from general principles to a particular fact. It derives new conclusion from existing general theories/principles. Deductive method
process can be illustrated as thus:
Observe an existing theory——-> Formulate hypothesis based on existing theory——-> collect data to verify the hypothesis——-> analyse if the collected data supports the hypothesis.
46. NAME: OKPANI BLESSING
DEPARTMENT: ECONOMICS
FACULTY: SOCIAL SCIENCES
JAMB REG: 20032285CA
MATRIC NO: 2020\242623
THE METHODS OF ECONOMIC ANALYSIS USED BY ECONOMIST
knowing that inductive and deductive methods are not just methods of economic analysis but are generalization in economics is going to help us understand that, they are the main economic method
of analysis that economist use in their economic research.
DEDUCTIVE METHOD
This method is also called abstract, analytical prior method(knowledge that comes from the power of reasoning based on self evident truth) and represents an abstract approach to the derivation of
economic generalization and theories. this method involves proper reasoning from one or more statements. for deductive method to be sound, the hypothesis must be correct.
example: all men are mortals, Desmond is a man-[true]
Principle steps in the process of deriving economic generalization through deductive logic are:
A) Perception of the problem: this is not an easy step in the deductive method because if illusion and hallucination are possible, then perceptual experience, as we ordinarily understand it, is
impossible. In any scientific inquiry, the analyst must have a clear idea of the problem to be inquired into. He must know the significant variables regarding whose behavior and interrelationship
he wants to derive generalization. The perception of the problem is by no means an easy task.
B)Definition of technical terms and making of assumptions( Postulates or premises): here the economist makes assumptions or suggests the existence, facts, or truth of the problem as basis of
reasoning. Assumptions could be behavioral pertaining to the behavior of the economic variable or technological relating to the state of technology and the factor endowments.
C) Deducing hypotheses through logical deduction: a hypothesis describes relationships between factors affecting a phenomenon; it establishes the cause and effect relationship between the
variables having a bearing on the phenomenon.
Then, through logical process, hypotheses is deduced from the assumptions made. this logical reasoning could be carried out verbally or it maybe conducted in symbolic terms using the language of
what is known as symbolic logic.
D) Testing or verification of hypotheses: hypotheses gotten must be tested or verified before they are established as principles of economics. For this verification, there are no controlled
experiments, because economist have to discover uniformities in the behavioral patterns of man.
INDUCTIVE METHOD
This method could also be called empirical method. It derives economic generalization on the basis of experience and observations.In this method, detailed data are collected with regard to a
certain economic phenomenon and effort is then made to arrive at certain generalization which follows from the observations collected
47. Below are the Answers….
Deductive Method:
In this method, We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis or our own analytical
abilities. In this kind of reasoning, we go from general to specific.
The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Deductive And Inductive Methods
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method.
It is a time-consuming process and thus expensive as well…
48. NAME: EZE SYLVIA IFEDIBA.
JAMB REGISTRATION NUMBER:20636892FA
FACULTY:SOCIAL SCIENCE.
DEPARTMENT: PHILOSOPHY.
INDUCTIVE METHOD
In this method data are collected with regard to certain economic phenomenon and effort is made to arrive at certain generalization on the basis of experience and observation.
DEDUCTIVE METHOD
Deductive method is also called abstract, analytical and a priori method represents an abstract approach to the derivation of economic generalizations and theories. It organizes the problem to be
inquired into. It also defines the technical terms and makes good assumption which is often called postulates or premises.
49. Two Methods of Economic Analysis
Economic Analysis is defined as the assessing or examining topics or issues from an economist’s perspective. Economic analysis is the study of economic systems.
The analysis aims to determine how effectively the economy or something within it is operating. Economic analyses factor in the opportunity costs that people or companies employ. They measure, in
monetary terms, what the benefits of a project are to the economy or community.
The two methods include deductive analysis and inductive analysis
1. Deductive Analysis
It is also called abstract, analytical and a priori method and represents an abstract approach to the derivation of economic generalisations and theories.
The principal steps in the process of deriving economic generalisations through deductive logic are; Perception of the problem to be enquired into, defining precisely the technical terms and
making appropriate assumptions, often called postulates or premises, deducing hypotheses, that is, deriving conclusions from the premises through the process of logical reasoning; and testing of
hypothesis deduced.
2. Inductive Analysis
The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected with regard to
a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
The Various Steps in Inductive Method
a. Identifying the problem
b. Data collection and some preliminary thinking
c. Data processing to find out how they are related
d. Make predictions and test them
e. Predictions are in agreement with facts.
50. NAME: OSUCHUKWU VIVIAN CHIAMAKA
REG NO: 21305622EF
DEPT: ECONOMICS
EMAIL: vivianosuchukwu@gmail.com
There are two major methods used by economists in analysing Economic situations, they include:
1. Deductive Method of Economic Analysis
Deductive method is known as the analytical, abstract or priori method. It starts with certain formal data and assumptions. Then by logical reasoning certain conclusions are made. It is with
these undisputed fundamental facts and after adding some assumptions that theories are arrived at. For instance, it is assumed that businessmen aim at achieving maximum profit. It follows from
this that businessmen buy the materials at the cheapest market and sell it in the most costly market.
In Deductive method of Economic Analysis we proceed from the general to the particular. This is also known as a hypothetical method because some of the assumptions may not correspond with actual
facts, but very near actual facts are to be used as a premise for starting, reasoning and drawing conclusions.
A complete form of deductive method consists of three stages,
i. Observation ot perception of the problem;
ii. Making assumptions from logical reasoning
iii. Formulation of hypothesis, and
iv. Testing the hypothesis
Deductive reasoning provides us with hypotheses or generalizations. If the hypotheses are tested and verified with relevance to facts, they become valid economic laws.
Advantages of Deductive Method of Economic Analysis
1. Deductive method is exceedingly simple.
2. Deductive method obviates the necessity of experimentation. Economics being a social science, experimentation may not be available as in the case of physics or chemistry. So, the next best
alternative to experiment is deductive reasoning.
3. The deductive method results in accuracy and exactness in generalization, because of logical reasoning. This method gives a high standard of precision in abstract economic reasoning.
Disadvantages of Deductive Method of Economic Analysis
Deductive method has its drawbacks also:
1. Deduction is based mainly on assumptions which are perfectly valid but If assumptions are wrong, generalizations made on the basis of wrong assumptions will be imperfect and invalid.
2. In deduction there is too much of abstraction and economists by means of their intellectual exercises produce only “intellectual toys” which have little connection with reality.
3. Deductive generalizations started on wrong premises will be dangerous when such generalization claim universal validity. For instance, if such faulty generalizations are made use of in framing
government policies, the results would be nothing but disastrous.
Inductive Method of Economic Analysis
In this method, economists proceed from a practical angle to problems of science to reduce the gap between theory and practice. Induction is done by two forms, viz. experimentation and
statistical form. Facts are collected first, then arranged and conclusions are drawn. Then these general conclusions are further verified with reference to actual facts.
The inductive method is generally associated with the statistical form of inductions. The statistical approach has a larger field in economic investigations than the method of experimentation.
Further, the method of statistical induction is indispensable for the formulation of economic policy. Practically, Malthus presented his famous theory of population only after studying the facts
of population in various countries; He then used statistics to support his theory. .
Advantages of Inductive Method of Economic Analysis
Inductive method has the following merits:
1. It is highly practical and realistic as it describes things as they are.
2. It is helpful in verifying the conclusions of the deductive method.
Disadvantages of Inductive Method of Economic Analysis
Inductive method has the following limitations:
1. When the investigators lack a balanced judgement there is the risk of drawing hurried conclusions based on inadequate information or data.
2. Collection of data in the inductive process is highly complex and time consuming.
3. Only induction alone will not deliver unless it is complemented by means of deductive reasoning. Without deduction, the inductive method would result in producing only a mass of unrelated and
unconnected facts.
In conclusion, the two methods have to be made use of or combined to achieve the required objective. The two methods, deductive and inductive, are not competitive, but complementary in helping
the investigator.
51. NAME: ONYEMA JANET NNEOMA
REG NUMBER: 21313973GA
MATRICULATION NUMBER: 2020/242640
DEPARTMENT: ECONOMICS
THE METHODS OF ECONOMIC ANALYSIS ARE:
1. DEDUCTIVE METHOD
The deductive method derives new conclusions from fundamental assumptions or from truth established by other methods. It observes the process of reasoning from certain laws or principles, which
are assumed to be true, to the analysis of facts, then references are drawn which are verified against facts. This is also known as hypothetical method for some of the assumptions may not
correspond to actual facts.
The principle steps in the process of deriving economic generalizations through deductive logic are:
A.Perception of the problem to be inquired into;
B. Defining precisely the technical terms and making appropriate assumptions, often called postulates or premises;
C. Deducing hypotheses, that is, deriving conclusions from the premises through the process of logic reasoning; and
D. Testing of hypothesis deduced
2. INDUCTIVE METHOD
The inductive method involves the process of reasoning from particular facts to general principles. In this method, data is collected about a certain economic phenomenon. These are systematically
arranged and the general conclusions are drawn from them.. An example of inductive logic is “the coin i pulled from the bag is a penny…. therefore all coins in the bag are pennies”. Even if all
the premises are true in a statement, inductive reasoning allows for the conclusion to be false.
52. Name: Uzodigwe Isabel Chiemerie
Department: Nursing/Nursing sciences
Regno.: 20636611ff
Faculty: Health sciences and technology.
The methods of economics analysis are: Deductive method and Inductive method.
Deductive method: In this deductive method of economics analysis we proceed from the general to the particular.
This is also known as an hypothetical method for some of the assumptions may not correspond to the actual facts but very near the actual facts which may be used as premise for starting reasoning
and drawing conclusions. Deductive method involves reasoning and a few fundamental propositions.
Inductive method: In this Inductive method of economics analysis, economists proceed from a practical angle to problems of science to reduce the difference between theory and practice. Induction
is done by two forms:
Experimental and Statistical form.
In this method facts are collected first, arranged and conclusions are drawn.
53. NAME: Okoh Chibueze Joshua
REG NUMBER:21468870EF
DEPARTMENT: ECONOMICS
COURSE CODE: ECO 101
COURSE TITLE: PRINCIPLES OF ECONOMICS
METHODS OF ECONOMIC ANALYSIS
1. DEDUCTIVE METHOD: This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory)
using logical analysis or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
1 Observation of a task/ issue
2 Making the hypothesis
3Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
2.INDUCTIVE METHOD: This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This
method formulates principles using the sub-methods- Observations, Experimentations, Statistical methods.
54. NAME:UCHEAGA BLESSING CHISOM
REG No:2019/248163
FACULTY:PHYSICAL SCIENCE
What are the basic methods of analysis used by Economists?
The economic analysis involves the formulation of laws and generalizations through two methods namely:
Deductive and Inductive.
DEDUCTIVE METHOD
This is method can also be referred to as a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory)
using logical analysis or our own analytical abilities. In this kind of reasoning, we have to go from general to specific.
The stages in deductive reasoning are:
* Observation of a task/ issue
* Making the hypothesis
* Testing the hypothesis using more observations, etc.
This reasoning actually gives us a hypothesis and if this hypothesis gets verified we will get a general economic principles or laws.
Moreover just as every thing has an advantage and disadvantage, so also those this method.
ADVANTAGES OF A DEDUCTIVE
* It is a simple method, which doesn’t involve the use of any complex software analysis, etc.
* only a simple deductive logic is required.
* This method is really important for economists as it focuses upon economic reasoning which is of paramount importance.
DISADVANTAGES OF AN DEDUCTIVE
In this method of reasoning we have to start from assumptions, thus, if the assumptions happen to be logically flawed then the whole process becomes faulty and would lead to wrong conclusions.
Thus, the logical fallacy is a disadvantage of this method.
INDUCTIVE METHOD
This kind of reasoning flows from facts to theory. First, we have to collect informations and facts and then move towards providing evidence using economic theory and facts.
This method formulates principles using the sub-methods:
*Statistical methods.
Data is as well collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
* Observation
* Formulation of a hypothesis
* Generalizing principles
* Verifying against actual facts.
ADVANTAGES OF AN INDUCTIVE
* Since this method is based on facts it is more realistic and reliable.
* Using the statistical methods and experimentations makes the process more scientific, thus, it is more acceptable universally rather than just depending on your own reasoning and logic.
* Since the economic environment is dynamic and always changing, relying upon a more scientific method will always helps in reaching logical conclusions.
DISADVANTAGES OF AN INDUCTIVE
* If the data that is been used is insufficient and faulty it would lead to faulty conclusions, thereby making the hypothesis less reliable.
* It is a time-consuming process and thus really expensive as well.
* The collection of all the data is not an easy job and it varies from person to person. As to how they collect the data.
55. Education Studies
Current Research Projects
Slippery Fish
book group
inductive or deductive approaches
inductive or deductive approaches
Approaches to data analysis are important in that they offer a theoretical orientation to practice. Three particular types of approach are often highlighted in the literature:
Induction: this is the process by which we draw a general conclusion from individual instances or observations. The benefits of an inductive approach, as seen for example in grounded theory, are
that it allows flexibility, attends closely to context and supports the generation of new theory [see the paper on social loss as example]. To its critics, however, inductive research
painstakingly works from first principles when there is no overriding need to do so given there is already a huge amount of existing literature.
Deduction: The deductive method seeks to draw valid conclusions from initial premises. It follows the logic of syllogy expressed in classical form as:
Socrates is a man (major premise )
All men are mortal (minor premise )
Therefore Socrates is mortal (conclusion)
Deduction as an approach to social research has had considerable appeal, and has been most clearly associated with a kind of classical and logical positivism. In its purest form deductive logic
has been associated with the hypothetico-deductive approach. This involves generating formulating quite specific hypotheses about phenomena generally on the basis of existing practical and
theoretical knowledge. The hypothesis is then tested under experimental conditions. If the data support the hypothesis then the hypothesis can be said to hold in this context; if not, then
assuming that the research was well designed and carried out rigorously, the hypothesis, and the theory underlying the hypothesis, is challenged or at least the limits of the theory may have been
The hypothetico-deductive approach is most associated with ‘the scientific method’ but also underpins desk based research such as large N studies, meta analysis and systematic reviews. While
powerful, deductive logic is criticised as misrepresenting the methods of natural science and, for that matter, makes an assumption that all disciplines in natural science work the same way when
they do not. Second, it carries an inbuilt logic of confirmability; if you go looking for an association you are likely to find it. Third, it focuses on association between events but fails to
provide the detailed analytical explanation which is a necessary part of establishing causality – this is why counter examples (such as the Conger and Donnellan, 2007 paper) are so important.
Abduction: The claims made for an inductive or deductive approach are contested fiercely but there is increasing recognition that this might not be a choice between one or the other. Instead
research can, and often does proceed, by taking an alternating inductive and deductive perspective – with observation leading to hypotheses which are then explored in relation to the data. In
practice whatever their explicit particular stances on research and social theory, our interviewees show the flexibility associated with an abductive approach.
56. Economics analysis entails.the evaluation of cost benefits
There are two main methods of Economic analysis
– Deductive method this is called a priopri reasoning we start from unchallenged elementary assumptions or fact and then arrive on conclusion (build a hypothesis or theory) using logical analysis
of self made analytical analysis.on this kind of reasoning we go from general to specific
Stages include:
*Observation of a task
*Making hypothesis
*Testing hypothesis using more observations
If hypothesis get verified then it is now a certified general economic principle.
*It is a simple method thus doesn’t involve the use of complex software analysis
*It is important for economist as it focuses on economics reasoning
Since the method starts from assumptions, if the assumption happens to be logically flawed the whole process will be faulty therefore give wrong conclusion
Inductive method:
This method flows from fact to theory. First, info and facts are collected which will move towards providing evidence using Economic facts and information.
Stages include:
*Formulation of hypothesis
*Generalizing principles
*Verifying against actual facts
*Since it is based on facts it is more reliable and realistic
*Making use of experimentation makes the process more scientific this it’s more acceptable generally
*If data used is insufficient and faulty it will lead to wrong conclusion
*It’s time consuming and expensive
57. Name: EKEH CHIZOBA SUCCESS.
JAMB REG NO:20682951GA.
DEPARTMENT: PHILOSOPHY.
METHODS OF ECONOMIC ANALYSIS:
Economic analysis involve two methods:
(1) DEDUCTIVE METHOD AND
(2) INDUCTIVE METHOD.
(1) DEDUCTIVE METHOD/ REASONING: Works from the more general to the more specific. It involves reasoning from a fundamental propositions, the truth of which is assumed.
For instance: When conducting deductive research, you always start with a theory ( the result of inductive research). Reasoning deductive means testing these theories. If there is no theory, you
cannot conduct deductive reasearch.
The conclusion of deductive method can only be true , if all the premises set to study are true and the terms are clear.
_ All dogs have fleas (premise)
_ Benno is a dog (premise)
_ Benno has fleas ( conclusion)
Based on the premises we have , the conclusion must be true. However, if the first premise turns out to be false, the conclusion that “Benno” has fleas cannot be relied upon.
(2) INDUCTIVE METHOD: Involves moving from specific observations to broader generalization and theories. It also involven collection of facts, datas drawing conclusions from them and testing the
conclusions by other facts.
For instance: We make observations, discern a pattern, make a generalization and infer an explanation or a theory.
Example: Is the formulation of the generalization of diminishing returns.
58. Economic analysis involves various methods. The basic methods of economic analysis are
1. deductive method and
2. Inductive method
Both methods uses generalization and theory
1. DEDUCTIVE METHOD
Also called analytical or prior method.It involves deriving conclusions from known accepted truth, takes them and applies them to draw conclusion
For instance,if I accept the general proposition that Nigerians are lawless.I can deductively infere that we are uncivilized. Deductive method moves from general to particular, conclusion of your
inference cannot be false given that the premises are true.
Generalization Steps of deductive method.
1. Perception of of the problem- a clear and precise idea of problem is needed
2. Precisely find the technical terms,define them and make assumptions
3. Deduce hypothesis– from the assumptions, made, hypothesis are deduced.The hypothesis could be null or unnull hypothesis
4. Test the hypothesis- before theory are established, hypothesis are verified through direct observation and statistical methods
MERITS OF DEDUCTIVE METHOD.
1. Less time consuming and near to reality
2. Less expensive
3. It’s simple because it’s analytical
4. It can be used to derive economic theories
1.The method is not applicable universally
2. It’s highly abstract,requires alot of care to avoid faulty economic reasoning
The imperfect nature of this method led classic and neo classic economists to employe inductive method.
2. INDUCTIVE METHOD
Also called empirical method, and was adopted by Historical School of Economists in a bid to improve faulty assumptions of deductive method.It derives generalization on the basics of experiments,
observation and statistical methods.
For example, observation of UNN students during rainy season show that 90% go with umbrella,6%wear rain coat despite it’s high cost,4%go without umbrella or rain coat.
From above,we see that UNN students uses umbrella during rainy season unless they are devoid of sense
59. Igbokwe Gloria somtoochukwu
Economics department
There’s re two types of Economics analysis
1. Deductive method: in this method of economics analysis which proceed from the general to the particular. This is also known as an hypothetical method, for some assumptions may not correspond
to actual facts, but very near , which may be be used as premise from starting, reasoning and drawing conclusion. it is also known as analytical abstract a priori method.
it consists of ;
deductive reasoning
and instance and testing by means of further observation.
This method provides us with hypothesis which re tested and verified with relevance to facts, we have as Valid economics laws.
2 . INDUCTIVE METHOD: This method aims at developing a theory unlike deductive method aims at testing an existing theory. Inductive method moves from specific observations to broad
generalizations and deductive reasoning and other way around. it is a type of method that involves drawing a general conclusion from a set of specific observations.
60. Name:Kamanu Judith Chinaza
Department : Business Education
Faculty: Vocational and Technical Education
Reg number :21676944CA
Course: Eco 101
There are two basic methods of economic analysis are :
1) Deductive method
2) Inductive method
DEDUCTIVE METHOD
This is also called abstract, analytical and priori method that represents an abstract approach to derivation of economic generalization and theories.
The ways of generalizations are:
1. Perception of the problem to be enquired into
2. Defining precisely the technical terms and making appropriate assumptions often called Postulate or premises.
3.Deducing hypothesis that is deriving conclusions from the premises through the process of logical reasoning.
4. Testing of the hypothesis deduced.
This method is near to reality, it is less consuming and expensive.it is also simple because it is analytical. It’s disadvantages are that it is highly abstract, the premise where inferences are
drawn may not hold.
INDUCTIVE METHOD
it is also called emperical method. It’s process of reasoning from practical facts to general principles. This method derives economic generalization on the basis in experimentations,
observations and statistical method. Data collected is mostly about a certain economic phenomenon.
Formation of hypothesis
This method is based on facts;it is realistic
It makes statistical techniques easy therefore its more reliable.
It is dynamic
It also helps in future investigations
But it’s disvadvantages are
Generalizations obtained may be faulty if conclusions are drawn from insufficient data.
* collection of data isn’t easy.
It is time consuming and expensive.
61. What are the basic methods of analysis used by Economists?
The economic analysis involves the formulation of laws and generalizations through two methods namely:
Deductive and Inductive.
DEDUCTIVE METHOD
This is method can also be referred to as a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory)
using logical analysis or our own analytical abilities. In this kind of reasoning, we have to go from general to specific.
The stages in deductive reasoning are:
* Observation of a task/ issue
* Making the hypothesis
* Testing the hypothesis using more observations, etc.
This reasoning actually gives us a hypothesis and if this hypothesis gets verified we will get a general economic principles or laws.
Moreover just as every thing has an advantage and disadvantage, so also those this method.
ADVANTAGES OF A DEDUCTIVE
* It is a simple method, which doesn’t involve the use of any complex software analysis, etc.
* only a simple deductive logic is required.
* This method is really important for economists as it focuses upon economic reasoning which is of paramount importance.
DISADVANTAGES OF AN DEDUCTIVE
In this method of reasoning we have to start from assumptions, thus, if the assumptions happen to be logically flawed then the whole process becomes faulty and would lead to wrong conclusions.
Thus, the logical fallacy is a disadvantage of this method.
INDUCTIVE METHOD
This kind of reasoning flows from facts to theory. First, we have to collect informations and facts and then move towards providing evidence using economic theory and facts.
This method formulates principles using the sub-methods:
*Statistical methods.
Data is as well collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
* Observation
* Formulation of a hypothesis
* Generalizing principles
* Verifying against actual facts.
ADVANTAGES OF AN INDUCTIVE
* Since this method is based on facts it is more realistic and reliable.
* Using the statistical methods and experimentations makes the process more scientific, thus, it is more acceptable universally rather than just depending on your own reasoning and logic.
* Since the economic environment is dynamic and always changing, relying upon a more scientific method will always helps in reaching logical conclusions.
DISADVANTAGES OF AN INDUCTIVE
* If the data that is been used is insufficient and faulty it would lead to faulty conclusions, thereby making the hypothesis less reliable.
* It is a time-consuming process and thus really expensive as well.
* The collection of all the data is not an easy job and it varies from person to person. As to how they collect the data.
62. Methods of Economic Analysis,.
1Deductive method,also know as abstract or priori method which required abstract approach to the derivation of Economic generalisation and theories.It implies perception of the problem which
means having clear knowledge of the two variables that you want to derive your generalisation from.Also,defining your postulate which requires finding the relationship between the two variables
and why you think the two variables are related based on your own observation which makes you think so.There also is hypothesis which requires predicting the possible factors that may affect the
relationship between the two variables.Testing the hypothesis, verifying if the factors that are assumed to affect the relationship between two variables are factual in nature before it is
generally accepted.
2.lnductive method also know as empirical method requires collecting many observation on a particular data for using statistical methods to analysis whether is consistent with actual facts or
63. In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.
Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a “top-down” approach. We might begin with thinking up a theory about our topic of
interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to
be able to test the hypotheses with specific data – a confirmation (or not) of our original theories.
Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a “bottom up” approach (please note that
it’s “bottom up” and not “bottoms up” which is the kind of thing the bartender says to customers when he’s trying to close for the night!). In inductive reasoning, we begin with specific
observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.
These two methods of reasoning have a very different “feel” to them when you’re conducting research. Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the
beginning. Deductive reasoning is more narrow in nature and is concerned with testing or confirming hypotheses. Even though a particular study may look like it’s purely deductive (e.g., an
experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the
project. In fact, it doesn’t take a rocket scientist to see that we could assemble the two graphs above into a single circular one that continually cycles from theories down to observations and
back up again to theories. Even in the most constrained experiment, the researchers may observe patterns in the data that lead them to develop new theories
64. NAME: OKORO SANDRA ADAUGO
REG NO: 2019/248481
EMAIL: adaugosandra2019@gmail.com
Economic analysis involves the formulation of laws and generalizations through two methods- deductive and inductive.
Deductive method is also known as abstract method or analytical method. This method is based on a priori reasoning and conclusions are drawn from certain fundamental assumptions
The deductive method moves from the general assumption to the specific application.
STEPS OF DEDUCTIVE METHOD:
The steps in deductive reasoning are:
i) Observation of a task/ issue
ii)Making the hypothesis
iii) Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
ADVANTAGES OF DEDUCTIVE METHOD
The deductive method is a simple method, because it doesn’t involve the use of any complex software analysis only simple deductive logic is required.
It is also real, powerful, exact, indispensable and universal.
This method is important for economists as it focuses on economic reasoning which is of utmost importance.
In this method of reasoning we start from assumptions, meaning that if the assumptions happen to be logically flawed or unrealistic the whole process becomes faulty and would give misleading
conclusions. Thus, logical fallacy is a disadvantage of this method.
The deductive method is also not applicable universally because the premises from which they are deduced may not hold good at all time and places.
INDUCTIVE METHOD
The inductive method is also called the empirical method, it involves the process of reasoning from particular facts to general principle
First, we collect information and facts and then move towards providing evidence using economic theory and facts.
The inductive method moves from specific observations to generalization.
STEPS OF INDUCTIVE METHOD:
The main steps involved in the application of inductive method are:
(i) Observation
(ii) Formulation of hypothesis.
(iii) Generalizing principles
(iv) Verifying against actual facts.
ADVANTAGES OF INDUCTIVE METHOD
(i) It is based on facts as such the method is realistic.
(ii) Induction method also helps in future investigations.
(iii) Inductive method is dynamic. The changing economic phenomenon are analyzed and on the basis of collected data, conclusions and solutions are drawn from them.
(iv) In order to test the economic principles, method makes statistical techniques. The inductive method is, therefore, more reliable.
DISADVANTAGES OF INDUCTIVE METHOD:
The main weaknesses of this method are as under:
(i) The inductive method is time-consuming and expensive.
(ii) The collection of data itself is not an easy task. The sources and methods employed in the collection of data differ from investigator to investigator. The results, therefore, may differ
even with the same problem.
(iii) If conclusions drawn from insufficient data, the generalizations obtained may be faulty
65. Methods of Economic Analysis:
There are two methods of economic analysis. They are:(1) Deductive Method and (2) Inductive Method.
(1) Deductive Method of Economic Analysis:
The deductive method is also named as analytical, abstract or prior method. The deductive method consists in deriving conclusions from general truths, takes few general principles and applies
them draw conclusions.
For instance, if we accept the general proposition that man is entirely motivated by self-interest. In applying the deductive method of economic analysis, we proceed from general to particular.
Steps of Deductive Method:
The main steps involved in deductive logic are :
(i) Perception of the problem to be inquired into: In the process of deriving economic generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.
(ii) Defining of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should also be precise.
(iii) Deducing hypothesis from the assumptions: The third step in deriving generalizations is deducing hypothesis from the assumptions taken.
(iv) Testing of hypothesis: Before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
(Their inverse relationship between price and quantity demanded of a good is a well established generalization).
Merits of Deductive Method:
The main merits of deductive method are as under:
(i) This method is near to reality. It is less time consuming and less expensive.
(ii) The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis.
(iii) There being limited scope of experimentation, the method helps in deriving economic theories.
(iv) The method is simple because it is analytical.
Demerits of Deductive Method:
It is true that deductive method is simple and precise, underlying assumptions are valid.
(i) The deductive method is simple and precise only if the underlying assumptions are valid. More often the assumptions turn out to be based on half truths or have no relation to reality. The
conclusions drawn from such assumptions will, therefore, be misleading.
(ii) Professor Learner describes the deductive method as ‘armchair’ analysis. According to him, the premises from which inferences are drawn may not
hold good at all times, and places. As such
deductive reasoning is not applicable universally.
(iii) The deductive method is highly abstract. It require; a great deal of care to avoid bad logic or faulty economic reasoning.
As the deductive method employed by the classical and neo-classical economists led to many facile conclusions due to reliance on imperfect and incorrect assumptions, therefore, under the German
Historical School of economists, a sharp reaction began against this method. They advocated a more realistic method for economic analysis known as inductive method.
(2) Inductive Method of Economic Analysis:
Inductive method which also called empirical method was adopted by the “Historical School of Economists”. It involves the process of reasoning from particular facts to general principle.
This method derives economic generalizations on the basis of (i) Experimentations (ii) Observations and (iii) Statistical methods.
In this method, data is collected about a certain economic phenomenon. These are systematically arranged and the general conclusions are drawn from them.
For example, we observe 300 persons in the market. We find that nearly 295 persons buy from the cheapest shops, Out of the 5 which remains, 4 persons buy local products even at higher rate just
to patronize their own products, while the fifth is a fool. From this observation, we can easily draw conclusions that people like to buy from a cheaper shop unless they are guided by patriotism
or they are devoid of commonsense.
Steps of Inductive Method:
The main steps involved in the application of inductive method are:
(i) Observation.
(ii) Formation of hypothesis.
(iii) Generalization.
(iv) Verification.
Merits of Inductive Method:
(i) It is based on facts as such the method is realistic.
(ii) In order to test the economic principles, method makes statistical techniques. The inductive method is, therefore, more reliable.
(iii) Inductive method is dynamic. The changing economic phenomenon are analyzed and on the basis of collected data, conclusions and solutions are drawn from them.
(iv) Induction method also helps in future investigations.
Demerits of Inductive Method:
The main weaknesses of this method are as under:
(i) If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
(ii) The collection of data itself is not an easy task. The sources and methods employed in the collection of data differ from investigator to investigator. The results, therefore, may differ
even with the same problem.
(iii) The inductive method is time-consuming and expensive.
The above analysis reveals that both the methods have weaknesses. We cannot rely exclusively on any one of them. Modern economists are of the view that both these methods are complimentary. They
partners and not rivals. Alfred Marshall has rightly remarked:
“Inductive and Deductive methods are both needed for scientific thought, as the right and left foot are both needed for walking”.
We can apply any of them or both as the situation demands.
66. The method used by economist in reasoning are inductive and deductive reasoning is that inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing
theory. Inductive reasoning moves from specific observations to broad generalizations, and deductive reasoning the other way around.
18 Apr 2019
67. Name:Ezeme Lilian ifeoma
Department: Economics
Reg no:20689942gf
The method of Economics analysis are:
A. Inductive method
B. Deductive method
Inductive method :This is a theory based on data obtained from actual experience . Basically,in induction method ,it is done in two forms: Experimental and stastistical form.In this form facts
are collected first,arranged and conclusions are drawn.Then these general conclusion are further verified with reference to actual facts.The induction method is generally associated with the
stastical form of induction. It has larger field in Economic investigation than the method of Experimentation
Deductive method:This is the scientific approach based on logical reasoning from formal data and assumption. Then by logical reasoning,we arrive at certain conclusions. The conclusions is drawn
from general to the particular which is known as hypothetical method . The argument in this hypothetical method is that some of the assumptions may not correspond to the actual facts but very
near to actual facts. It is also called abstract Analytical and prior method
68. NAME: IGWEDIBIA JUDITH CHIAMAKA
MATRIC NO: 2019/246689
DEPT: PURE AND INDUSTRIAL CHEMISTRY
EMAIL: igwedibiajudith@gmail.com
Basic Methods of Analysis used by Economists
(1) Deductive Method
(2) Inductive Method.
(1) Deductive Method of Economic Analysis:
The deductive method is also known as analytical, abstract or prior method.
Steps of Deductive Method:
The main steps involved in deductive logic are as follows:
(i) Perception of the problem to be inquired into: In the process of deriving economic generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.
(ii) Defining of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should also be precise.
(iii) Deducing hypothesis from the assumptions: The third step in deriving generalizations is deducing hypothesis from the assumptions taken.
(iv) Testing of hypothesis: Before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
(Their inverse relationship between price and quantity demanded of a good is a well established generalization).
Merits of Deductive Method:
The main merits of deductive method are as follows:
i. It is less time consuming and less expensive.
(iv) The method is simple because it is analytical.
Demerits of Deductive Method:
i. The deductive method is highly abstract. It require; a great deal of care to avoid bad logic or faulty economic reasoning.
(2) Inductive Method of Economic Analysis:
Inductive method which also called empirical method was adopted by the “Historical School of Economists”. It involves the process of reasoning from particular facts to general principle.
Steps of Inductive method:
The main steps involved in the application of inductive method are:
(i) Observation.
(ii) Formation of hypothesis.
(iii) Generalization.
(iv) Verification.
Merits of Inductive Method:
(i) It is based on facts as such the method is realistic.
(ii) In order to test the economic principles, method makes statistical techniques. The inductive method is, therefore, more reliable.
Demerits of Inductive Method:
The main weaknesses of this method are as under:
(i) If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
(iii) The inductive method is time-consuming and expensive.
69. Department of Pure and Industrial Chemistry
The basic methods of analysis used by Economists are; The Inductive reasoning and The Deductive reasoning.
The deductive method: This is also called a priori reasoning with the process of making unchallenged elementary assumptions/fact to building a hypothesis or theory using logical analysis or our
own abilities. Here, we go from general to specific. This method is of advantage in the sense that it does not involve the use of any complex software analysis , hence it is simple and it is of
disadvantage that since the method starts from assumptions, thus, if the assumptions happen to be logically flared the whole process becomes faulty and would give wrong conclusion.
The Inductive method: Here, reasoning flows from facts to theory . First, we collect information and facts and then move towards providing evidence using economic theory and facts This method
formulates principles using the sub-methods observation, experimentations, statistical methods. Data is collected about a particular economic theory and then conclusions are drawn. This method
too is of advantage that it is more realistic and reliable since it is based on facts and not just assumptions and since the economic environment is dynamic and always changing, relying upon a
more scientific method always helps reach logical conclusion. The Bad thing or the disadvantage about this method is that if the data used is insufficient it results to faulty conclusions making
the hypothesis less reliable, it’s a time consuming process and this very expensive.
70. Any economic analysis involves the formulation of laws and generalizations through two methods- deductive and inductive
Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Deductive And Inductive Methods
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
REG. NO.: 2019/SD/37705
1) What are the difference between macroeconomic and microeconomics?
2) Discuss the three different ways of computing GDP.
3) Without diagrams, clearly discuss the circular flow of income and product in a 2 – sector economy, 3 – sector economy and 4 – sector economy.
Micro-economics refers to the branch of economics which deals with smaller units or components of the economics. It is concerned with the analysis of basic decision making components of
households, individuals, firma and governments. It relates to cost, output, production, pricing and marketing activities of households, firms and governments. Microeconomics focuses on firms and
Macro-economics refers to the branch of economics which deals with larger units or aggregate of the economy. Macro-economic relates to large aggregates such as national income; inflation,
unemployment, balance of payment etc. Macro economics focuses on the sum total of economics activity, dealing with the issues of growth, inflation and unemployment.
Differences between Micro-Economics and Macro-Economics
S/N Micro-Economics Macro-Economics
1 involves supply and demand in individual markets monetary/fiscal policy. e.g. what effect does interest rates have on the whole economy.
2 involves individual consumer behaviour e.g. consumer choice theory reasons for inflation and unemployment.
3 individual labour markets e.g. demand for labour wage determination economic growth
4 externalities arising from production and consumption e.g. externalities international trade and globalisation
Formula to Calculate G.D.P
GDP is Gross Domestic product and is indicator to measure the economic health of a country. The formular to calculate GDP is of three types which include:
Expenditure Approach;
Income approach, and
production approach
Expenditure Approach: There are three main groups of expenditure household, business and government. By adding all expenses, we get below equation.
GDP = C + I + G + NX
C = All private consumption/consumer spending in the economy. It includes durable goods, nondurable goods and services
I = All of a country’s investment in capital equipment, housing etc.
G = All of the country’s government spending. It includes the salaries of a government employee, construction, maintenance, etc.
NX = Net country export – Net country import.
This can also be written as:
GDP = Consumption + Investment + government spending + Net export
Income Approach: The income approach is a way for calculation of GDP by total income generated by goods and services.
GDP = Total National Income + sales taxes + Depreciation + Net foreign factor income.
Where – Total national income = sum of rent, salaries profit.
Sales Taxes – Tax. Imposed by a government on sales of goods and services.
Depreciation – The decrease in the value of an asset.
Net foreign factor income – Income earn by a foreign factor like the amount of foreign company or foreign person earn from the country and it is also the difference between a country citizen and
country earn.
Production or Value Added Approach:
From the name, it is clear that value is added at the time of production. It is also known as the reverse of the expenditure approach. To estimate the gross value – added total cost of economic
output is reduced by the cost of intermediate goods that are used for the production of the facial goods.
Gross value added = Gross value of output – value of intermediate consumption.
GDP Formular
Expenditure Approach = C + I + G + NX
Income Approach = Total National Income + Sales taxes + Depreciation + Net foreign factor income.
Value Added Approach = Grosses value of output – Value of intermediate consumption.
CIRCULAR INCOME FLOW IN A TWO SECTOR ECONOMY
Real flow of resources, goods and services such as land, capital and entrepreneurial ability flow from households to business firms. Money flow from business firms to the households as factor
payments such as wages, rent, interest and profits.
Money flows from households to firms as consumption expenditure made by the households on the goods and services produced by the firms, while the flow of goods and services is in opposite
direction from business firms to households.
IN THREE SECTOR ECONOMY WITH GOVERNMENT
Government affects the economy in a number of ways, such as its taxing, spending and borrowing roles. Government purchase goods and services just as households and firms do. Government
expenditure takes many forms including spending on capital goods and infrastructure (highways, power, communication), on defence goods, and on education and public health etc. These add to the
money flows. Government expenditure may be financed through taxes, out of assets or by borrowing. The money flow households and business firms to the government. This money flow includes all the
tax payments made by households less transfer payments received from the government. Transfer payments are treated as negative tax payment.
This includes the foreign sector which reveals to us the transaction of the domestic economy with foreign countries. Foreigners interact with the domestic firms and households through exports and
imports of goods and services as well as through borrowing and lending operations through financial market.
CIRCULAR FLOW OF PRODUCT
Product flow is the distribution channel that is viewed as a unified system of interdependent organizations which intermediaries work together to build values as products proceed through the
channel to the consumer. It includes movement of goods from supplier to consumer (internal as well as external), as well as dealing with customer service needs such as input materials or
consumables or services like housekeeping.
72. Name: Samuel Favour Udochukwu
Reg num: 22000131df
Dept: Public Administration and Local Government
Faculty: Social Science
Methods of Economic Analysis
1. Deductive Method= The deductive method can also be called abstract method. There are principle steps in which we can derive economic generalizations through deductive method.
a) Perception of the problem. In any scientific inquiry, the analyst must have a clear idea of the problem he wants to solve.
b) He must define precisely the various technical terms to be used in the analysis.
c) Deducing hypothesis through logical deduction. A hypothesis describes relationship between factors affecting a phenomenon.
d) Hypothesis gotten above have to be verified before the are established as principles of economics.
2. Inductive Method= The inductive method is also called “Empirical method”. It obtains economic generalizations on the basis of experience and observations. In this method, detailed data are
gathered with regard to a particular economic term. Effort is now made to get at certain generalizations which follow from observations collected. Empirical studies made in inductive approach
also brings a light significant economic facts which require analytical explanation through deductive logic.
73. NAME: IFEABUNIKE ONYINYE JACINTA
REG NO: 2019/244764
FACULTY: PHYSICAL SCIENCES
DEPT: PURE AND INDUSTRIAL CHEMISTRY
ANSWERS: There are two basic methods of economic analysis which are:
1. The deductive method
2. The Inductive method
-DEDUCTIVE METHOD OF ECONOMIC ANALYSIS: The deductive method is also known as the analytical, abstract or prior method. It involves deriving conclusions from general truths, taking few general
principles and applies them in drawing conclusions.
For instance, if we accept the general proposition that man is entirely motivated by self-interest. In applying the deductive method of economic analysis, we proceed from general to particular.
STEPS INVOLVED IN DEDUCTIVE METHOD:
(i) Perception of the problem to be inquired into: In the process of deriving economic generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.
(ii) Definition of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should also be precise.
(iii) Deducing hypothesis
(iv) Testing of hypothesis: Before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
-INDUCTIVE METHOD OF ECONOMIC ANALYSIS: This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory
and facts. Here data is collected about a particular economic theory and then conclusions are drawn.
STAGES INVOLVED IN THIS METHOD ARE:
i. Observation
ii. Formulation of a hypothesis
iii. Generalizing principles
iv. Verifying against actual facts.
ADVANTAGES OF THE INDUCTIVE METHOD
i.It is based on facts therefore more realistic and reliable.
ii. Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
iii. Since the economic environment is dynamic, relying upon a more scientific method always helps reach logical conclusions.
i. Insufficient data leads to faulty conclusions, making the hypothesis less reliable.
ii. It is a time-consuming process and expensive as well.
iii.Data collected often varies from person to person.
74. NAME: CHUKWU IFEOMA RITA
REG. NO: 2019/241539
EMAIL: chukwuifeomaa@gmail.com
Methods Of Economic Analysis.
There are two basic methods of analysis used by Economists
-Deductive Method
-Inductive Method
Deductive Method.
This is also called analytical or a prior method.
Deductive Method consists in deriving conclusions from general truths, takes few general principles and applies them in drawing conclusions
Steps of Deductive Method
(I) Perception Of The Problem To Be Inquired Into:
The first step involved in deductive method of economic analysis, the analyst must have an exact and comprehensible idea of the problem to be inquired into
(II) Defining Of Terms:
In this step, you need to clearly define the technical terms used in the analysis
(III) Deducing Hypothesis from the assumptions:
Here, you need to draw conclusion on the hypothesis from the assumptions
(IV) Testing Of Hypothesis:
On the process of establishing laws, hypothesis must first be tested
➜The deductive method is less expensive and less time consuming
➜This method is simple because it is analytical
➜This method also helps in deriving economic theories
➜The method is highly abstract; it requires a good deal of care to avoid bad logic or faulty economic reasoning
➜The premises from which inferences are drawn may not hold good at all times and places.
➜The deductive method is simple and precise only when the assumptions are valid.
Inductive Method.
This is also called empirical method. It involves the process of reasoning from particular facts to general principle
Steps Of Inductive Method
(I) Observation
(II) Formation Of Hypothesis
(III) Generalization
(IV) Verification
➜Inductive method also helps in future investigation
➜It is based on facts as such, the method is realistic.
➜This method is reliable and it makes statistical techniques
➜The inductive method is time consuming and expensive.
➜The generalization may be faulty only if the conclusions are drawn from insufficient data.
➜The sources and methods employed in the collection of data differ from investigator to investigator. Therefore, the results may differ even with the same problem
75. Methods of Economic Analysis:
There are two methods of economic analysis. They are:(1) Deductive Method and (2) Inductive Method.
(1) Deductive Method of Economic Analysis:
The deductive method is also named as analytical, abstract or prior method. The deductive method consists in deriving conclusions from general truths, takes few general principles and applies
them draw conclusions.
For instance, if we accept the general proposition that man is entirely motivated by self-interest. In applying the deductive method of economic analysis, we proceed from general to particular.
Steps of Deductive Method:
The main steps involved in deductive logic are :
(i) Perception of the problem to be inquired into: In the process of deriving economic generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.
(ii) Defining of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should also be precise.
(iii) Deducing hypothesis from the assumptions: The third step in deriving generalizations is deducing hypothesis from the assumptions taken.
(iv) Testing of hypothesis: Before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
(Their inverse relationship between price and quantity demanded of a good is a well established generalization).
Merits of Deductive Method:
The main merits of deductive method are as under:
(i) This method is near to reality. It is less time consuming and less expensive.
(ii) The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis.
(iii) There being limited scope of experimentation, the method helps in deriving economic theories.
(iv) The method is simple because it is analytical.
Demerits of Deductive Method:
It is true that deductive method is simple and precise, underlying assumptions are valid.
(i) The deductive method is simple and precise only if the underlying assumptions are valid. More often the assumptions turn out to be based on half truths or have no relation to reality. The
conclusions drawn from such assumptions will, therefore, be misleading.
(ii) Professor Learner describes the deductive method as ‘armchair’ analysis. According to him, the premises from which inferences are drawn may not
hold good at all times, and places. As such
deductive reasoning is not applicable universally.
(iii) The deductive method is highly abstract. It require; a great deal of care to avoid bad logic or faulty economic reasoning.
As the deductive method employed by the classical and neo-classical economists led to many facile conclusions due to reliance on imperfect and incorrect assumptions, therefore, under the German
Historical School of economists, a sharp reaction began against this method. They advocated a more realistic method for economic analysis known as inductive method.
(2) Inductive Method of Economic Analysis:
Inductive method which also called empirical method was adopted by the “Historical School of Economists”. It involves the process of reasoning from particular facts to general principle.
This method derives economic generalizations on the basis of (i) Experimentations (ii) Observations and (iii) Statistical methods.
In this method, data is collected about a certain economic phenomenon. These are systematically arranged and the general conclusions are drawn from them.
For example, we observe 300 persons in the market. We find that nearly 295 persons buy from the cheapest shops, Out of the 5 which remains, 4 persons buy local products even at higher rate just
to patronize their own products, while the fifth is a fool. From this observation, we can easily draw conclusions that people like to buy from a cheaper shop unless they are guided by patriotism
or they are devoid of commonsense.
Steps of Inductive Method:
The main steps involved in the application of inductive method are:
(i) Observation.
(ii) Formation of hypothesis.
(iii) Generalization.
(iv) Verification.
Merits of Inductive Method:
(i) It is based on facts as such the method is realistic.
(ii) In order to test the economic principles, method makes statistical techniques. The inductive method is, therefore, more reliable.
(iii) Inductive method is dynamic. The changing economic phenomenon are analyzed and on the basis of collected data, conclusions and solutions are drawn from them.
(iv) Induction method also helps in future investigations.
Demerits of Inductive Method:
The main weaknesses of this method are as under:
(i) If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
(ii) The collection of data itself is not an easy task. The sources and methods employed in the collection of data differ from investigator to investigator. The results, therefore, may differ
even with the same problem.
(iii) The inductive method is time-consuming and expensive.
The above analysis reveals that both the methods have weaknesses. We cannot rely exclusively on any one of them. Modern economists are of the view that both these methods are complimentary. They
partners and not rivals. Alfred Marshall has rightly remarked:
“Inductive and Deductive methods are both needed for scientific thought, as the right and left foot are both needed for walking”.
We can apply any of them or both as the situation demands.
76. The economist uses two method in analysis used and they are inductive and deductive method reasoning is that inductive reasoning aims at developing a theory while deductive reasoning aims at
testing an existing theory. Inductive reasoning moves from specific observations to broad generalizations, and deductive reasoning the other way around.
77. NAME:Ugwunweze Robinson Ndubuisi
MATRIC NO: 2020/243243
DEPARTMENT: public Administration And local Government
Economic deals with the study of how the goods and services that we want for our consumption are get produced and how they are distributed among people.
INDUCTIVE reasoning takes a specific representative case or fact and then, draws generalization or conclusion from them.
Inductive reasoning must be based on a sufficient amount of reliable evidence, in other words the facts you draw in must fairly represent the larger station or population .
(a) Fair trade agreements have raised the quality of life for coffee producers, so
(b) Fair trade agreements could be used to help other farmers as well.
In this example the specific case of fair trade agreements with coffee producers us being used as the starting point for the claim because these agreements have worked the author conclude that it
could work for other farmer as well.
DEDUCTIVE reasoning begins with a generalization and then applies it to a specific case. The generalizatio you start will must have been based on a sufficient amount of evidence. Example,
Genetically modified seeds have caused poverty hunger, and a decline in bio-diversity everywhere there have been introduced, so there is no reason the same thing will not occur which genetically
modified corn seeds are introduced in Mexico.
In this example the author starts with a large claim, that genetically modified seeds have been problematic everywhere, and from this draws the more localized or special conclusion vthat Mexico
will be affected in the same way.
78. There are two main basic method of Economic Analysis, which is Deductive and Inductive reasoning
DEDUCTIVE METHOD
This is a simple logic of knowledge required based solely on experience or personal observations that comes with the power of reasoning which uses general principles to arrive at specific facts
or conclusion. It is ought to give us a hypothesis and when gets verified we get general Economic principles or laws.
But when our assumption happens to be logically flawed the whole process becomes faulty which is one disadvantage of this method.
Deductive method can also be called Priori reasoning.
INDUCTIVE METHOD
This is a method that formulates principles using the sub methods observations, experiments, statistical, Economic theory etc to collect information and flows of fact to theory, therefore
providing evidence.
This method is said to be more realistic, reliable and acceptable universally because of the statistical methods and experimentations than just depending on your own reasoning and logic, but when
the collection of all the data used is insufficient and faulty it would lead to faulty conclusions making the hypothesis less reliable.
79. Name:Ani Godlen Daberechi
Reg no:2019/246120
Email address:daberechi.ani.246120@unn.edu.ng
Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Deductive And Inductive Methods
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data
80. Name;Ngerem ugonna Samuel
Jamb reg no:20694751FF
Faculty of Health science
INDUCTIVE:This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method
formulates principles using the sub-methods- Observations, Experimentations, Statistical methods…
Advantages; Since it is based on facts it is more realistic and reliable. And also
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Disadvantages; If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable. And
It is a time-consuming process and thus expensive as well…
DEDUCTIVE METHOD:This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using
logical analysis or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
Advantages; It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages; In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions.
Thus, the logical fallacy is a disadvantage of this method.
81. Any economic analysis involves the formulation of laws and generalizations through two methods- (deductive and inductive)
*Deductive Method:
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
1. Observation of a task/ issue
2. Making the hypothesis
3. Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
*Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
*Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
*Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
1. Observation
2. Formulation of a hypothesis
3. Generalizing principles
4.Verifying against actual facts.
*Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
82. Name: Augustine Uchechukwu Sampson
Reg no:2020/243121
Department: Philosophy
What are the basic methods of analysis used by economists?
they are two basic methods:
(1) Deductive method
(2) Inductive method
Briefly and convincingly discuss each of them.
(1) Deductive method:it means drawing of inference or reasoning from universal to individual.
Steps of Deductive method
(a)formulating the assumption: the investigator forms an assumption which are the basic of hypothesis in any economic inquiry,more that one set of assumption.
(b) selecting the problem:the problem which investigates from inquiry must be stated clearly the more narrow the problem,the better it will be to conduct the inquiry.
(2) Inductive method:it means collecting information from personal research and giving it out to the universe.
Steps of Inductive method
(a)the data should be analysed using appropriate analytical statical technique.
(b)the problem should be properly stated.
(c) observation:the problem should be observed in a special way
83. Name: Otti Victoria Chiemerie
Faculty: Health science and Technology
Department: Nursing sciences
Reg No:20681839BF
Inductive method:
The inductive method was employed in economics by the German Historical School which sought to develop economics wholly from historical research. The historical or inductive method expects the
economist to be primarily an economic historian who should first collect material, draw gereralisations, and verify the conclusions by applying them to subsequent events. For this, it uses
statistical methods. The Engel’s Law of Family Expenditure and the Malthusian Theory of Population have been derived from inductive reasoning.
1. The Problem:
In order to arrive at a generalisation concerning an economic phenomenon, the problem should be properly selected and clearly stated.
2. Data:
The second step is the collection, enumeration, classification and analysis of data by using appropriate statistical techniques.
3. Observation:
Data are used to make observation about particular facts concerning the problem.
4. Generalisation:
On the basis of observation, generalisation is logically derived which establishes a general truth from particular facts.
Thus induction is the process in which we arrive at a generalisation on the basis of particular observed facts.
The best example of inductive reasoning in economics is the formulation of the generalisation of diminishing returns. When a Scottish farmer found that in the cultivation of his field an increase
in the amount of labour and capital spent on it was bringing in less than proportionate returns year after year, an economist observed such instances in the case of a number of other farms, and
then he arrived at the generalisation that is known as the Law of Diminishing Returns.
Merits of Inductive Method:
The chief merits of this method are as follows:
(1) Realistic:
The inductive method is realistic because it is based on facts and explains them as they actually are. It is concrete and synthetic because it deals with the subject as a whole and does not
divide it into component parts artificially
(2) Future Enquiries:
Induction helps in future enquiries. By discovering and providing general principles, induction helps future investigations. Once a generalisation is established, it becomes the starting point of
future enquiries.
(3) Statistical Method:
The inductive method makes use of the statistical method. This has made significant improvements in the application of induction for analysing economic problems of wide range. In particular, the
collection of data by governmental and private agencies or macro variables, like national income, general prices, consumption, saving, total employment, etc., has increased the value of this
method and helped governments to formulate economic policies pertaining to the removal of poverty, inequalities, underdevelopment, etc.
(4) Dynamic:
The inductive method is dynamic. In this, changing economic phenomena can be analysed on the basis of experiences, conclusions can be drawn, and appropriate remedial measures can be taken. Thus,
induction suggests new problems to pure theory for their solution from time to time.
Demerits of Inductive Method:
However, the inductive method is not without its weaknesses which are discussed below.
(1) Misenterpretation of Data:
Induction relies on statistical numbers for analysis that “can be misused and misinterpreted when the assumptions which are required for their use are forgotten.”
(2) Uncertain Conclusions:
Boulding points out that “statistical information can only give us propositions whose truth is more or less probable it can never give us certainty.”
(3) Lacks Concreteness:
Definitions, sources and methods used in statistical analysis differ from investigator to investigator even for the same problem, as for instance in the case of national income accounts. Thus,
statistical techniques lack concreteness.
(4) Costly Method:
The inductive method is not only time-consuming but also costly. It involves detailed and painstaking processes of collection, classification, analyses and interpretation of data on the part of
trained and expert investigators and analysts
Deductive method:
Deduction Means reasoning or inference from the general to the particular or from the universal to the individual. The deductive method derives new conclusions from fundamental assumptions or
from truth established by other methods. It involves the process of reasoning from certain laws or principles, which are assumed to be true, to the analysis of facts.
Then inferences are drawn which are verified against observed facts. Bacon described deduction as a “descending process” in which we proceed from a general principle to its consequences. Mill
characterised it as a priori method, while others called it abstract and analytical.
Deduction involves four steps: (1) Selecting the problem. (2) The formulation of assumptions on the basis of which the problem is to be explored. (3) The formulation of hypothesis through the
process of logical reasoning whereby inferences are drawn. (4) Verifying the hypothesis. These steps are discussed as under.
row relating to an industry. The narrower the problem the better it would be to conduct the enquiry.
(2) Formulating Assumptions:
The next step in deduction is the framing of assumptions which are the basis of hypothesis. To be fruitful for enquiry, the assumption must be general. In any economic enquiry, more than one set
of assumptions should be made in terms of which a hypothesis may be formulated.
Formulating Hypothesis:
The next step is to formulate a hypothesis on the basis of logical reasoning whereby conclusions are drawn from the propositions. This is done in two ways: First, through logical deduction. If
and because relationships (p) and (q) all exist, then this necessarily implies that relationship (r) exists as well. Mathematics is mostly used in these methods of logical deduction.
(4) Testing and Verifying the Hypothesis:
The final step in the deductive method is to test and verify the hypothesis. For this purpose, economists now use statistical and econometric methods. Verification consists in confirming whether
the hypothesis is in agreement with facts. A hypothesis is true or not can be verified by observation and experiment. Since economics is concerned with human behaviour, there are problems in
making observation and testing a hypothesis.
For example, the hypothesis that firms always attempt to maximise profits, rests upon the observation that some firms do behave in this way. This premise is based on a priori knowledge which will
continue to be accepted so long as conclusions deduced from it are consistent with the facts. So the hypothesis stands verified. If the hypothesis is not confirmed, it can be argued that the
hypothesis was correct but the results are contradictory due to special circumstances.
Under these conditions, the hypothesis may turn out to the wrong. In economics, most hypotheses remain unverified because of the complexity of factors involved in human behaviour which, in turn,
depend upon social, political and economic factors. Moreover, controlled experiments in a laboratory are not possible in economics. So the majority of hypotheses remain untested and unverified in
Merits of Deductive Method:
The deductive method has many advantages.
(1) Real:
It is the method of “intellectual experiment,” according to Boulding. Since the actual world is very complicated, “what we do is to postulate in our own minds economic systems which are simpler
than reality but more easy to grasp. We then work out the relationship in these simplified systems and by introducing more and more complete assumptions, finally work up to the consideration of
reality itself.” Thus, this method is nearer to reality.
(2) Simple:
The deductive method is simple because it is analytical. It involves abstraction and simplifies a complex problem by dividing it into component parts. Further, the hypothetical conditions are so
chosen as to make the problem very simple, and then inferences are deduced from them.
(3) Powerful:
It is a powerful method of analysis for deducing conclusions from certain facts. As pointed out by Cairnes, The method of deduction is incomparably, when conducted under proper checks, the most
powerful instrument of discovery ever wielded by human intelligence.
(4) Exact:
The use of statistics, mathematics and econometrics in deduction brings exactness and clarity in economic analysis. The mathematically trained economist is able to deduce inferences in a short
time and make analogies with other generalisations and theories. Further, the use of the mathematical-deductive method helps in revealing inconsistencies in economic analysis.
It is a powerful method of analysis for deducing conclusions from certain facts. As pointed out by Cairnes, The method of deduction is incomparably, when conducted under proper checks, the most
powerful instrument of discovery ever wielded by human intelligence.
Demerits of Deductive Method:
Despite these merits, much criticism has been levelled against this method by the Historical School which flourished in Germany.
1 .Unrealistic Assumption:
Every hypothesis is based on a set of assumptions. When a hypothesis is tested, assumptions are indirectly tested by comparing their implications with facts. But when facts refute the theory
based on the tested hypothesis, the assumptions are also indirectly refuted. So deduction depends upon the nature of assumptions. If they are unrealistic, in this method, economists use the
ceteris paribus assumption. But other things seldom remain the same which tend to refute theories
2. Not Universally Applicable:
Often the conclusions derived from deductive reasoning are not applicable universally because the premises from which they are deduced may not hold good at all time and places. For instance, the
classicists assumed in their reasoning that particular conditions prevailing in England of their times were valid universally. This supposition was wrong. Prof. Lerner, therefore, points out that
the deductive method is simply “armchair analysis” which cannot be regarded as universal.
3. Incorrect Verification:
The verification of theories, generalisations or laws in economics is based on observation. And right observation depends upon data which must be correct and adequate. If a hypothesis is deduced
from wrong or inadequate data, the theory will not correspond with facts and will be refuted. For instance, the generalisations of the classicists were based on inadequate data and their theories
were refuted. As pointed out by ircholson, “the great danger of the deductive method lies in the natural aversion to the labour of verification.”
The above analysis reveals that independently neither deduction nor induction is helpful in scientific enquiry. In reality, both deduction and induction are related to each other because of some
facts. They are the two forms of logic that are complementary and co-relative and help establish the truth.
Marshall also supported the complementary nature of the two methods when he quoted Schmoller: “Induction and deduction are both needed for scientific thought as the right and left foot are needed
for walking.” And then Marshall stressed the need and use of integrating these methods.
Now-a-days, economists are combining induction and deduction in their studies of economic phenomena in various fields for arriving at generalisations from observed facts and for the indirect
verification of hypotheses. They are using the two methods to confirm the conclusions drawn through deduction by inductive reasoning and vice versa. Thus true progress in economic enquiries can
be made by a wise combination of deduction and induction.
84. What are the basic methods of analysis used by Economists? Briefly and convincingly discuss each of them.
The basic methods of analysis used by economists are
1.Deductive method.
2. Inductive method.
1. Deductive method
The deductive method is also called abstract, analytical and a priori method and represents an abstract approach to the derivation of economic generalisations and theories.
The principal steps in the process of deriving economic generalisations through deductive logic are:
(a) Perception of the problem to be enquired into;
(b) Defining precisely the technical terms and making appropriate assumptions, often called postulates or premises;
(c) Deducing hypotheses, that is, deriving conclusions from the premises through the process of logical reasoning; and
(d) Testing of hypothesis deduced.
2. Inductive Method
The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected with regard to
a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
There are three ways which can be used for deriving economic principles and theories.
They are:
(a) Experimentation,
(b) observations,
(c) statistical or econometric method.
85. Uwakwe Esther Chekwube,pure and industrial chemistry,2019/242747, uwakweestherchekwube@gmail.com
The methods are inductive and Deductive method.
Deductive method/priori reasoning:here,we start from unchallenged elementary and arrive at conclusions using logical analysis or our own analytical abilities.The stages in this method are
observation of a task/issue, making the hypothesis, testing the hypothesis using more observation.also,it is a simple method , doesn’t involve the use of any complex software analysis.
Inductive method: flow from facts to theory,we collect information and facts and then move towards providing evidence using economic theory and facts.this method formulates principles using the
sub method_observation.The stages in this method are observation, formulation of a hypothesis, Generalizing principles, verifying against actual facts.Also it is more realistic and reliable.
86. METHOD OF ANNALYSIS
1. DEDUCTIVE METHOD
2. INDUCTIVE METHOD
1. DEDUCTIVE METHOD:It is also called abstract analytical and proir method and represent an abstract approach. Precisely the technical terms and making of assumptions, deducing hypothesis and
testing the hypothesis is also a process followed in deductive method .
Then by logical reason they arrive at certain conclusions
2. INDUCTIVE METHOD:It Involves observation and measures of deriving economic generalization in the basis of experience and they also use econometric method of observation. In the inductive
methods facts are collected and conclusions are drawn.
87. NAME: Okenwa Eunice Chiyere
REG NO:2020/242140
EMAIL ADDRESS: chiyereeunice@gmail.com
DEPT: Business Education
COURSE:Eco 101
TOPIC:BASIC METHOD OF ANALYSIS USED BY ECONOMIST
*Deductive method
*Indecuctive method
DEDUCTIVE METHOD
It is also abstract , analytical and prior method and represents an abstract approach to the derivation of economics generalization and theories.The staages involved are:
-observation of a task
-making the hypothesis
-testing the hypothesis using more observation.
ADVANTAGES OF DEDUCTIVE METHOD
*it is a simple method,and doesn’t involve the use of any complex software analysis ,only simple deductive logic is needed.
In this method of reasoning which started from assumption,thus if the assumptions is logically flawed the whole process become faulty and would give wrong conclusions.
INDECUCTIVE METHOD
In this method reasoning flows from fact of theory.Firstly, collecting information and facts and then moving forward to providing evidence using economic theory and facts.the stages are:
*Formation of a hypothesis
*Generalizing principles
*Verifying against actual facts
ADVANTAGES OF INDUCTIVE METHOD
-It is more realistic and reliable
-using statical method and experimentation process are scientifically more acceptable than just our own reasoning and logic
-It is time-consuming and also expensive
Collection of data is not easy and varies from person to person.As to how the data is collected.
88. Method of economic analysis
(1)Deductive method or prior reasoning it starts from unchallenged elementary or rudimentary assumption /facts and then arrive at conclusions (building a hypothesis or theory) using logical
analysis or our own analytical abilities.
Observation of a task /issues
-making the hypothesis
-testing the hypothesis using more observation.
-This reasoning gives us a hypothesis and if this hypothesis get verified we get general economics principles or law
Inductive method
This type of reasoning flows from facts of theory, first we collect information and facts and then move towards providing evidence using economic theory and facts, this method formulates
principles using the sub-method observation, experimentation,statistical method.
Stages in these inductive method
2.Formulation of hypothesis
3.Generalizing principles
2.Verifying against actual facts.
89. NAME: EGWIM CHINONSO THERESA
DEPARTMENT: ECONOMICS
LEVEL:100 LEVEL
EMAIL ADDRESS: egwimtheresa2@gmail.com
METHODS OF ECONOMICS ANALYSIS
An economic theory derives laws or generalizations through two methods namely;
1. Deductive method
2.inductive method
1.DEDUCTIVE METHOD OF ECONOMICS ANALYSIS
The deductive method is also named as analytical, abstract or prior method. The deductive method consists in deriving conclusions from general truths,takes few general principles and applies them
and draw conclusions.
For instance,if we accept the general preposition that man is entirely motivated by self interest. In applying the deductive method of economics analysis, we proceed from general to particular.
STEPS OF DEDUCTIVE METHOD
The main steps are;
1. Perception of the problem to be inquired into.
2. Clearly defining the one technical terms and analysis.
3. Deducing hypothesis from the assumptions.
4. Testing of hypothesis; before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
This is the simple and easiest way in deriving economic theories.
2. INDUCTIVE METHOD OF ECONOMIC ANALYSIS.
This is also called “empirical method” was adopted by the “historical school of economists”. It involves the process of reasoning from particular facts to general principles.
This methods derives economic generalizations on the basis of ;
i. Experimentation ii. Observations iii. Statistical methods.
In this method,data is collected about a certain economic phenomenon .These are systematically arranged and the general conclusions are drawn from them.
For example: we observe 200 persons in the market. We find that nearly 195 persons buy from the cheapest shops. Out of the 5 which remains, 4 persons buy local products at a higher rate just to
patronise their own products,while the fifth is a fool.
From the observation,we can easily draw conclusions that people like to buy from a cheaper shop unless they are guided by patriotism or they are devoid of common sense.
STEPS OF INDUCTIVE METHOD
1. Observation
2. Formation of hypothesis.
3. Generalization.
4. Verification
The above analysis reveals that both the methods have weaknesses.we cannot rely exclusively on any one of them .
Modern economists are of the view that both these methods are complimentary .They are partners and not rivals.
ALFRED MARSHALL rightly said :”inductive and deductive method are both needed for scientific thought,as the right and left foot are both needed for walking”. We can apply any of them or both as
the situation demand.
90. NAME: Abonyi Ifebuche Faith
Jamb reg no: 20691720BA
Email: ifebuchefaith51@gmail.com
Firstly, Economic analysis can be defined as a process by which economic laws, generalizations and theories are found. There are two basic methods of economic analysis, namely;
1.. DEDUCTIVE METHOD: Deductive reasoning,also known as priori, analytical or hypothetical reasoning make analysis based on assumptions and generalizations which precede from general to
particular until a theory is made and established.
EXAMPLE:All valuable goods are expensive, diamond is a valuable good, therefore,diamond is expensive. Below are the steps:
1. Observation of an issue/problem: The economist must have a clear idea of what the problem is.
2. Definition of the technical terms and making assumptions: These assumptions are made on careful observations over time. They are called POSTULATES or PREMISES.
3. Hypothesis: hypothesis are made from observations. Note that hypothesis can be either NULL or ALTERNATE.
4.Test: Lastly, you test your hypothesis using statistical method.
⚫Advantages:It is simple,precise, less expensive, less time consuming and helps in deriving economic theories.
⚫Disadvantages:It depends highly on assumptions and varies from time to time and place to place.
2.. INDUCTIVE METHOD: The inductive method which makes use of data-induced experiments, observations and statistics, involves the process of reasoning which transcends from general to particular.
BACON described it as an ascending order.
EXAMPLE:If tomatoes is a perishable goods and most tomatoes I have bought are sold cheap, then all perishable goods are sold cheap. Below is the step by step procedure;
1️⃣ perception of the problem
2️⃣collection of data/facts
3️⃣Making of observations for a period of time
4️⃣Making of Hypothesis.
5️⃣Testing and Generalization.
⚫Advantages:It is based on factual data, it is dynamic
⚫Disadvantages:It uses insufficient data for a large general purpose, its expensive to run, it’s tedious and time consuming.
91. Name: LIVINUS MURNA
Department: Economics
Reg no: 20686117JF
Email: livinusmurna7@gmail.com
TYPES OF ACCOUNTING
i.Tax accounting:is the subsector of accounting that deals with the preparation of tax returns and tax payments.Tax accounting is used by individuals, businesses, corporations and other
entities.Tax accounting for an individual focuses on income, qualifying deductions, donations and any investment gains or losses.
ii Financial accounting:is a specific branch of accounting involving a process of recording, summarizing and reporting the myriad of transactions resulting from business operations over a period
of time…work opportunities for a financial accountant can be found in both the public and private sectors.
iii.Mansgerial accounting:is the practice of identifying, measuring, analysing, interpreting and communicating financial informations to managers it helps a business Pursue it’s goals by doing
all this and communicating it to the manager.
This are the major types of accounting but we have some other ones like forensic accounting,cost accounting, project accounting, Government accounting e.t.c, with their various uses and
92. NAME:AYOGU FREDRICK CHIBUIKE
REG NO: 2019/242710
DEPT: PURE AND INDUSTRIAL CHEMISTRY
COURSE CODE:ECO 101
COURSE TITLE: PRINCIPLE OF ECONOMICS
QUESTION: TWO METHODS OF ECONOMIC ANALYSIS
There are two methods of reasoning in theoretical economics. They are the deductive and inductive methods.
As a matter of fact, deduction and induction are the two forms of logic that help to establish the truth.
The Deductive Method:
Deduction Means reasoning or inference from the general to the particular or from the universal to the individual. The deductive method derives new conclusions from fundamental assumptions or
from truth established by other methods. It involves the process of reasoning from certain laws or principles, which are assumed to be true, to the analysis of facts.
Then inferences are drawn which are verified against observed facts. Bacon described deduction as a “descending process” in which we proceed from a general principle to its consequences. Mill
characterised it as a priori method, while others called it abstract and analytical.
Deduction involves four steps: (1) Selecting the problem. (2) The formulation of assumptions on the basis of which the problem is to be explored. (3) The formulation of hypothesis through the
process of logical reasoning whereby inferences are drawn. (4) Verifying the hypothesis. These steps are discussed as under.
(1) Selecting the problem:
The problem which an investigator selects for enquiry must be stated clearly. It may be very wide like poverty, unemployment, inflation, etc. or narrow relating to an industry. The narrower the
problem the better it would be to conduct the enquiry.
(2) Formulating Assumptions:
The next step in deduction is the framing of assumptions which are the basis of hypothesis. To be fruitful for enquiry, the assumption must be general. In any economic enquiry, more than one set
of assumptions should be made in terms of which a hypothesis may be formulated.
(3) Formulating Hypothesis:
The next step is to formulate a hypothesis on the basis of logical reasoning whereby conclusions are drawn from the propositions. This is done in two ways: First, through logical deduction. If
and because relationships (p) and (q) all exist, then this necessarily implies that relationship (r) exists as well. Mathematics is mostly used in these methods of logical deduction.
(4) Testing and Verifying the Hypothesis:
The final step in the deductive method is to test and verify the hypothesis. For this purpose, economists now use statistical and econometric methods. Verification consists in confirming whether
the hypothesis is in agreement with facts. A hypothesis is true or not can be verified by observation and experiment. Since economics is concerned with human behaviour, there are problems in
making observation and testing a hypothesis.
For example, the hypothesis that firms always attempt to maximise profits, rests upon the observation that some firms do behave in this way. This premise is based on a priori knowledge which will
continue to be accepted so long as conclusions deduced from it are consistent with the facts. So the hypothesis stands verified. If the hypothesis is not confirmed, it can be argued that the
hypothesis was correct but the results are contradictory due to special circumstances.
Under these conditions, the hypothesis may turn out to the wrong. In economics, most hypotheses remain unverified because of the complexity of factors involved in human behaviour which, in turn,
depend upon social, political and economic factors. Moreover, controlled experiments in a laboratory are not possible in economics. So the majority of hypotheses remain untested and unverified in
Merits of Deductive Method:
The deductive method has many advantages.
(1) Real:
It is the method of “intellectual experiment,” according to Boulding. Since the actual world is very complicated, “what we do is to postulate in our own minds economic systems which are simpler
than reality but more easy to grasp. We then work out the relationship in these simplified systems and by introducing more and more complete assumptions, finally work up to the consideration of
reality itself.” Thus, this method is nearer to reality.
(2) Simple:
The deductive method is simple because it is analytical. It involves abstraction and simplifies a complex problem by dividing it into component parts. Further, the hypothetical conditions are so
chosen as to make the problem very simple, and then inferences are deduced from them.
(3) Powerful:
It is a powerful method of analysis for deducing conclusions from certain facts. As pointed out by Cairnes, The method of deduction is incomparably, when conducted under proper checks, the most
powerful instrument of discovery ever wielded by human intelligence.
(4) Exact:
The use of statistics, mathematics and econometrics in deduction brings exactness and clarity in economic analysis. The mathematically trained economist is able to deduce inferences in a short
time and make analogies with other generalisations and theories. Further, the use of the mathematical-deductive method helps in revealing inconsistencies in economic analysis.
(5) Indispensable:
The use of deductive method is indispensable in sciences like economics where experimentation is not possible. As pointed out by Gide and Rist, “In a science like political economy, where
experiment is practically impossible, abstraction and analysis afford the only means of escape from those other influences which complicate the problem so much.”
(6) Universal:
The deductive method helps in drawing inferences which are of universal validity because they are based on general principles, such as the law of diminishing returns.
Demerits of Deductive Method:
Despite these merits, much criticism has been levelled against this method by the Historical School which flourished in Germany.
1 .Unrealistic Assumption:
Every hypothesis is based on a set of assumptions. When a hypothesis is tested, assumptions are indirectly tested by comparing their implications with facts. But when facts refute the theory
based on the tested hypothesis, the assumptions are also indirectly refuted. So deduction depends upon the nature of assumptions. If they are unrealistic, in this method, economists use the
ceteris paribus assumption. But other things seldom remain the same which tend to refute theories.
2. Not Universally Applicable:
Often the conclusions derived from deductive reasoning are not applicable universally because the premises from which they are deduced may not hold good at all time and places. For instance, the
classicists assumed in their reasoning that particular conditions prevailing in England of their times were valid universally. This supposition was wrong. Prof. Lerner, therefore, points out that
the deductive method is simply “armchair analysis” which cannot be regarded as universal.
3. Incorrect Verification:
The verification of theories, generalisations or laws in economics is based on observation. And right observation depends upon data which must be correct and adequate. If a hypothesis is deduced
from wrong or inadequate data, the theory will not correspond with facts and will be refuted. For instance, the generalisations of the classicists were based on inadequate data and their theories
were refuted. As pointed out by ircholson, “the great danger of the deductive method lies in the natural aversion to the labour of verification.
4. Abstract Method:
The deductive method is highly abstract and requires great skill in drawing inferences for various premises. Due to the complexity of certain economic problems, it becomes difficult to apply this
method even at the hands of an expert researcher. More so, when he uses mathematics or econometrics.
5. Static Method:
This method of analysis is based on the assumption that economic conditions remain constant. But economic conditions are continuously changing. Thus this is a static method which fails to make
correct analysis.
6. Intellectually:
The chief defect of the deductive method “lies in the fact that those who follow this method may be absorbed in the framing of intellectual toys and the real world may be forgotten in the
intellectual gymnastics and mathematical treatment.
The Inductive Method:
Induction “is the process of reasoning from a part to the whole, from particulars to generals or from the individual to the universal.” Bacon described it as “an ascending process” in which facts
are collected, arranged and then general conclusions are drawn.
The inductive method was employed in economics by the German Historical School which sought to develop economics wholly from historical research. The historical or inductive method expects the
economist to be primarily an economic historian who should first collect material, draw gereralisations, and verify the conclusions by applying them to subsequent events. For this, it uses
statistical methods. The Engel’s Law of Family Expenditure and the Malthusian Theory of Population have been derived from inductive reasoning.
The inductive method involves the following steps:
1. The Problem:
In order to arrive at a generalisation concerning an economic phenomenon, the problem should be properly selected and clearly stated.
2. Data:
The second step is the collection, enumeration, classification and analysis of data by using appropriate statistical techniques.
3. Observation:
Data are used to make observation about particular facts concerning the problem.
4. Generalisation:
On the basis of observation, generalisation is logically derived which establishes a general truth from particular facts.
Thus induction is the process in which we arrive at a generalisation on the basis of particular observed facts.
The best example of inductive reasoning in economics is the formulation of the generalisation of diminishing returns. When a Scottish farmer found that in the cultivation of his field an increase
in the amount of labour and capital spent on it was bringing in less than proportionate returns year after year, an economist observed such instances in the case of a number of other farms, and
then he arrived at the generalisation that is known as the Law of Diminishing Returns.
Merits of Inductive Method:
The chief merits of this method are as follows:
(1) Realistic:
The inductive method is realistic because it is based on facts and explains them as they actually are. It is concrete and synthetic because it deals with the subject as a whole and does not
divide it into component parts artificially
(2) Future Enquiries:
Induction helps in future enquiries. By discovering and providing general principles, induction helps future investigations. Once a generalisation is established, it becomes the starting point of
future enquiries.
(3) Statistical Method:
The inductive method makes use of the statistical method. This has made significant improvements in the application of induction for analysing economic problems of wide range. In particular, the
collection of data by governmental and private agencies or macro variables, like national income, general prices, consumption, saving, total employment, etc., has increased the value of this
method and helped governments to formulate economic policies pertaining to the removal of poverty, inequalities, underdevelopment, etc.
(4) Dynamic:
The inductive method is dynamic. In this, changing economic phenomena can be analysed on the basis of experiences, conclusions can be drawn, and appropriate remedial measures can be taken. Thus,
induction suggests new problems to pure theory for their solution from time to time.
(5) Histrico-Relative:
A generalisation drawn under the inductive method is often histrico-relative in economics. Since it is drawn from a particular historical situation, it cannot be applied to all situations unless
they are exactly similar. For instance, India and America differ in their factor endowments. Therefore, it would be wrong to apply the industrial policy which was followed in America in the late
nineteenth century to present day India. Thus, the inductive method has the merit of applying generalisations only to related situations or phenomena.
Demerits of Inductive Method:
However, the inductive method is not without its weaknesses which are discussed below.
(1) Misenterpretation of Data:
Induction relies on statistical numbers for analysis that “can be misused and misinterpreted when the assumptions which are required for their use are forgotten.”
(2) Uncertain Conclusions:
Boulding points out that “statistical information can only give us propositions whose truth is more or less probable it can never give us certainty.”
(3) Lacks Concreteness:
Definitions, sources and methods used in statistical analysis differ from investigator to investigator even for the same problem, as for instance in the case of national income accounts. Thus,
statistical techniques lack concreteness.
(4) Costly Method:
The inductive method is not only time-consuming but also costly. It involves detailed and painstaking processes of collection, classification, analyses and interpretation of data on the part of
trained and expert investigators and analysts
(5) Difficult to Prove Hypothesis:
Again the use of statistics in induction cannot prove a hypothesis. It can only show that the hypothesis is not inconsistent with the known facts. In reality, collection of data is not
illuminating unless it is related to a hypothesis.
(6) Controlled Experimentation not Possible in Economics:
Besides the statistical method, the other method used in induction is of controlled experimentation. This method is extremely useful in natural and physical sciences which deal with matter. But
unlike the natural sciences, there is little scope for experimentation in economics because economics deals with human behaviour which differs from person to person and from place to place.
Further, economic phenomena are very complex as they relate to man who does not act rationally. Some of his actions are also bound by the legal and social institutions of the society in which he
lives. Thus, the scope for controlled experiments in inductive economics is very little. As pointed Out by Friendman, “The absence of controlled experiments in economics renders the weeding out
of unsuccessful hypo-these slow and difficult.”
The above analysis reveals that independently neither deduction nor induction is helpful in scientific enquiry. In reality, both deduction and induction are related to each other because of some
facts. They are the two forms of logic that are complementary and co-relative and help establish the truth.
Marshall also supported the complementary nature of the two methods when he quoted Schmoller: “Induction and deduction are both needed for scientific thought as the right and left foot are needed
for walking.” And then Marshall stressed the need and use of integrating these methods.
Now-a-days, economists are combining induction and deduction in their studies of economic phenomena in various fields for arriving at generalisations from observed facts and for the indirect
verification of hypotheses. They are using the two methods to confirm the conclusions drawn through deduction by inductive reasoning and vice versa. Thus true progress in economic enquiries can
be made by a wise combination of deduction and induction.
93. Methods of Economic Analysis:
An economic theory derives laws or generalizations through two methods:
(1) Deductive Method and (2) Inductive Method.
These two ways of deriving economic generalizations are now explained in brief:
(1) Deductive Method of Economic Analysis:
The deductive method is also named as analytical, abstract or prior method. The deductive method consists in deriving conclusions from general truths, takes few general principles and applies
them draw conclusions.
For instance, if we accept the general proposition that man is entirely motivated by self-interest. In applying the deductive method of economic analysis, we proceed from general to particular.
The classical and neo-classical school of economists notably, Ricardo, Senior, Cairnes, J.S. Mill, Malthus, Marshall, Pigou, applied the deductive method in their economic investigations.
Steps of Deductive Method:
The main steps involved in deductive logic are as under:
(i) Perception of the problem to be inquired into: In the process of deriving economic generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.
(ii) Defining of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should also be precise.
(iii) Deducing hypothesis from the assumptions: The third step in deriving generalizations is deducing hypothesis from the assumptions taken.
(iv) Testing of hypothesis: Before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
(Their inverse relationship between price and quantity demanded of a good is a well established generalization).
Merits of Deductive Method:
The main merits of deductive method are as under:
(i) This method is near to reality. It is less time consuming and less expensive.
(ii) The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis.
(iii) There being limited scope of experimentation, the method helps in deriving economic theories.
(iv) The method is simple because it is analytical.
Demerits of Deductive Method:
It is true that deductive method is simple and precise, underlying assumptions are valid.
(i) The deductive method is simple and precise only if the underlying assumptions are valid. More often the assumptions turn out to be based on half truths or have no relation to reality. The
conclusions drawn from such assumptions will, therefore, be misleading.
(ii) Professor Learner describes the deductive method as ‘armchair’ analysis. According to him, the premises from which inferences are drawn may not
hold good at all times, and places. As such deductive reasoning is not applicable universally.
(iii) The deductive method is highly abstract. It require; a great deal of care to avoid bad logic or faulty economic reasoning.
As the deductive method employed by the classical and neo-classical economists led to many facile conclusions due to reliance on imperfect and incorrect assumptions, therefore, under the German
Historical School of economists, a sharp reaction began against this method. They advocated a more realistic method for economic analysis known as inductive method.
(2) Inductive Method of Economic Analysis:
Inductive method which also called empirical method was adopted by the “Historical School of Economists”. It involves the process of reasoning from particular facts to general principle.
This method derives economic generalizations on the basis of (i) Experimentations (ii) Observations and (iii) Statistical methods.
In this method, data is collected about a certain economic phenomenon. These are systematically arranged and the general conclusions are drawn from them.
For example, we observe 200 persons in the market. We find that nearly 195 persons buy from the cheapest shops, Out of the 5 which remains, 4 persons buy local products even at higher rate just
to patronize their own products, while the fifth is a fool. From this observation, we can easily draw conclusions that people like to buy from a cheaper shop unless they are guided by patriotism
or they are devoid of commonsense.
Steps of Inductive Method:
The main steps involved in the application of inductive method are:
(i) Observation.
(ii) Formation of hypothesis.
(iii) Generalization.
(iv) Verification.
Merits of Inductive Method:
(i) It is based on facts as such the method is realistic.
(ii) In order to test the economic principles, method makes statistical techniques. The inductive method is, therefore, more reliable.
(iii) Inductive method is dynamic. The changing economic phenomenon are analyzed and on the basis of collected data, conclusions and solutions are drawn from them.
(iv) Induction method also helps in future investigations.
Demerits of Inductive Method:
The main weaknesses of this method are as under:
(i) If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
(ii) The collection of data itself is not an easy task. The sources and methods employed in the collection of data differ from investigator to investigator. The results, therefore, may differ
even with the same problem.
(iii) The inductive method is time-consuming and expensive
94. Department: public administration and LG
Reg. No. 20683659ED
Economics analysis in most cases involves the formation of laws and this can be achieved by the methods
1.Deductive Reasoning
2.inductive Reasoning
Deductive reasoning_also known as priori reasoning,involves the observation of issues, making and testing hypothesis using more observation and if generally acceptable becomes an economic law…
Inductive Reasoning_it is a fact, information and theories are gathered and tested on through observation result and experiment and obtained result may or may not be verified.this method is more
reliable since it is based on fact and statistical methods are used in this approach,it is time consuming and expensive and can be affected by limited data sources.
95. Economic analysis involves the formulation of laws and generalizations through two methods:
1) Deductive and
2) Inductive.
Methods of Economic Analysis
DEDUCTIVE METHOD
This is also called an abstract, analytical and a priori reasoning/method and represents an abstract approach to the derivation of economic generalisations and theories. We start from
unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis or our own analytical abilities. In this kind of
reasoning, we go from general to specific. The stages in deductive reasoning are:
i) Observation of a task/ issue
ii) Making the hypothesis
iii) Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
The principal steps in the process of deriving economic generalisations through deductive logic are:
a) Perception of the Problem:
b) Definition of technical terms and making of assumptions
c) Deducing hypotheses and through logical deduction
d) Testing or verification of hypotheses.
Advantages of Deductive Method
1) It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
2) This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
1) In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the
logical fallacy is a disadvantage of this method.
INDUCTIVE METHOD
The Inductive method is also called empirical method derives economic generalisation on the basis of experience and observations.This type of reasoning flows from facts to theory.
First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates principles using the sub-methods:
i) Observations
ii) Experimentations
iii) Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
i) Observation
ii) Formulation of a hypothesis
iii) Generalizing principles
iv) Verifying against actual facts.
Advantages of Inductive Method
1) Since it is based on facts it is more realistic and reliable.
2) Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
3) Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
1) If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
2) It is a time-consuming process and thus expensive as well.
3) The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
96. Methods of economic analysis
We have two most important methods of economic analysis they are ;
1.) Deductive reasoning : This is a fundamental structure of valid reasoning. It initiates with a general statement or hypothesis and examines the possibilities to reach a specific, logical
conclusion. Deductive reasoning works from the more specific. We might begin with thinking up a theory about our topic of interest . We then narrow that down into more specific hypothesis that we
can test . We narrow down even further when we collect observations to address the hypothesis. This ultimately leads us to be able to test the hypothesis with specific data , a confirmation of
our original theories.
Let there be 360 degrees in circle – (A general assumption)
There are four right angles in circle – (A logical argument)
Therefore this right angle has 90 degrees – (A particular conclusion)
2.) Inductive reasoning : this seeks lane generalization from specific observations. In essence there is data and then conclusions are drawn from the data. We begin with specific observations and
measures, begin to detect patterns and regularities , formulate some tentative hypothesis that we can explore, and finally end up developing some general conclusions or theories.
This apple falls to the ground. (A particular observation)
All apples fall to the ground. (More observations)
All objects attract each other. (A general explanation)
97. Name: Igboji Divinegift Onyinyechi
Reg. No.: 20006946IA
Email address: igbojidivinegift@gmail.com
There are two basic methods of analysis used by economists. They are:
(1) The Deductive method
(2) The Inductive method
The Deductive method: This method is also known as analytical, abstract or prior method. Deductive method of deriving economic generalizations consists in deriving conclusions from general
truths. The principle steps in deriving economic generalizations includes: (a) Perception of the problem to be inquired into. (b) Definition of technical terms and making of realistic assumptions
that is verifyable and precise. (c) Deducing hypothesis from the assumption or premises taken. (d) Testing or verification of the above deduced hypothesis.
The Inductive method: This method derives economic generalizations on the basis of experience and observations. It is also known as empirical method, which involves the process of reasoning from
particular facts to general principles. The steps of Inductive method includes: (a) observation (b) formation of hypothesis (c) generalization (d) verification.
98. There are two methods of economic analysis:
A. Deductive Method
The deductive method, also known as analytical or abstract method, consists of deriving conclusions from general truths and principles. This type of approach is concerned with developing an
hypothesis based on existing theory and then designing a research strategy to test the hypothesis. It explores a known theory or phenomenon and verifies if that theory is valid in certain
A deductive method follows the following steps:
1. There must be a precise or clear idea of the problem
2. Defining the technical terms used in the analysis and making logical assumptions.
3. Making or deducing hypothesis from the assumptions taken.
4. Lastly, testing or verifying the hypothesis through direct observations of areas and statistical methods.
1. The method is less time consuming and less expensive.
2. It is a simple and analytical method.
3. It uses mathematical techniques in developing theories which brings exactness and clarity in economic analysis.
1. This method is precise only if the assumptions are valid. Sometimes, the assumptions turn out to be based on half truths or have no relation to reality. Therefore, the conclusions from the
assumptions will be misleading.
2. It is highly abstract. It needs a lot of care to avoid bad logic or faulty economic reasoning.
B. Inductive Method
The inductive method, also known as empirical method, involves the process of reasoning from particular facts to general principles. It derives generalizations from experiments, observations and
statistical methods. Here, data is collected on a particular economic phenomenon. They are systematically arranged and general conclusions are drawn from them. For instance, we observe 50 people
in the market. We find out that 45 persons buy foreign product’s irrespective of it’s high rate just to patronize them while the remaining 5 persons settle for local product’s because they are
cheaper. From this observation, we conclude that people like to buy foreign product’s as long as their income rate is above their purchasing power. There are steps to conducting this method:
1. Making Observations
2. Forming hypothesis
3. Generalizations
4. Making verifications
1. It is based on facts which makes it realistic
2. It makes use of statistical techniques which makes it more reliable.
3. The method is dynamic. As economic phenomenon changes, they are analyzed and on the basis of collected data, conclusions and solutions are drawn from them.
1. It is time consuming and expensive.
2. Collection of data is not easy.
3. If the conclusions are gotten from sufficient data, the generalizations obtained may be faulty.
Reg no: 22244035DA
99. Name: Livinus Murna
Department: Economics
Reg no: 20686117JF
Email: livinusmurna7@gmail.com
METHODS OF ECONOMIC ANALYSIS:
Deductive reasoning: Deductive reasoning is a basic form of valid reasoning.Deductive reasoning or deduction,starts out with a general statement,or hypothesis,and examines the possibilities to
reach a specific, logical conclusion.
The deductive methods are:
Observation of a tasks/issue
Making the hypothesis
Testing the hypothesis using more observations.
Advantages of Deductive reasoning
It is a simple method, and doesn’t include the use of any complex software analysis, only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is kind of paramount importance.
Disadvantages of Deductive reasoning
In this method of reasoning, we start from assumptions, thus, if the assumptions happen to be logically failed, the whole process becomes faulty and would give wrong conclusions.
INDCTIVE REASONING: Inductive reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you’ve experienced, observations you’ve made,or facts you
know to be true or false.
Examples of inductive reasoning:
*: Jennifer always leaves for school at 7:00am, Jennifer is always on time
*:The cost of goods was $1.00
*:Every windstorm in this area comes from the north
Advantages of inductive reasoning
Since it is based on facts, it is more reclufia and reliable using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusion
Disadvantages of inductive reasoning
If the data used is insufficient and faulty, it would lead to faulty conclusions, making the hypothesis less reliable
It is time consuming and thus expensive as well
The collection of all the data is not easy and varies individually.
100. Uguwuonah joy Ifunaya
Reg no:2019/244617
Methods of Economic Analysis: Deductive Method and Inductive Method Some of the most important methods of economic analysis are as follows: 1. Deductive Method 2. Inductive Method.
Economic generalisations describe the laws or statements of tendencies in various branches of economics such as production, consumption, exchange and distribution of income. In the view of
Robbins, economic generalisations or laws are statements of uniformities which describe human behaviour in the allocation of scarce resources between alternative ends.
The generalisations of economics like the laws of other sciences, state cause and effect relationships between variables and describe those economic hypotheses which have been found consistent
with facts or, in other words, have been found to be true by empirical evidence. But a distinction may be drawn between a generalisation (law) and a theory. A law or generalisation just describes
the relationship between variables; it does not provide any explanation of the described relation. On the other hand, a theory provides an explanation of the stated relation between the
variables, that is, it brings out the logical basis of the generalisation. An economic theory or a model derives a generalisation through process of logical reasoning and explains the conditions
under which the stated generalisation will hold true.
1. Deductive Method:
Generalisations in economics have been derived in two ways:
(1) Deductive Method,
(2) Inductive Method. The principal steps in the process of deriving economic generalisations through deductive logic are:
(a) Perception of the problem to be enquired into;
(b) Defining precisely the technical terms and making appropriate assumptions, often called postulates or premises; The principal steps in the process of deriving economic generalisations through
deductive logic are:
(a) Perception of the problem to be enquired into;
(b) Defining precisely the technical terms and making appropriate assumptions, often called postulates or premises; 2. Inductive Method:
The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected with regard to
a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
But, it is worth mentioning that the number of observations has to be large if it can yield a valid economic generalisation. One should not generalise on the basis of a very few observations.
There are three ways which can be used for deriving economic principles and theories.
They are:
(a) Experimentation,
(b) observations,
(c) statistical or econometric method.
As has been mentioned above, the experimentation, that is, the use of contrived experiments is of limited applicability in economics. First, unlike natural sciences which are concerned with
analysing the behaviour of either inanimate objects or obedient animals such as rats and rabbits under the influence of chloroform, economics deals with the behaviour of man who is quite fickle,
wayward and unmanageable.
Besides, man cannot tolerate the idea of being experimented upon, either individually or collectively. Secondly, an economic phenomenon is the result of multiplicity of factors and causes acting
and interacting upon each other.
Therefore, economic phenomenon does not repeat itself in the same uniform pattern. Numerous factors acting on an economic phenomenon ‘disturb’ it and make its exact repetition unlikely. Thus, as
compared with the natural phenomena, economic phenomena are of less uniform pattern, less repetitive and more variable.
Thirdly, economists study the economic phenomena in which pressure groups such as employers’ associations, trade unions, farming lobby, political parties with their different ideologies play a
crucial part and their activities render it difficult to make controlled experiments in the economic world. However, in spite of these difficulties, experimental method can be used in some
For instance, experiments have been conducted to find out which law of production is valid, that is, whether law of diminishing returns, law of constant returns or law of increasing returns
operates in the real world. Besides, public undertakings or big industrial firms often try to assess the effect of the changes in the prices of their products on the demand for it and thus find
out the demand elasticity of their products Evaluation of Inductive Method:
As has been explained above, observations of facts through collection of detailed data and the use of statistical methods to arrive at economic generalisations establishing relationship between
facts are being increasingly made.
Some of the recent researches in the field of macroeconomics, such as the nature of consumption function describing the relation between income and consumption, the principle of acceleration
describing the factors which determine investment in the economy have been obtained through the use of mainly inductive method.
However, it needs to be emphasised again that the use of induction or empirical method is not of much value if it is not supported by the economic hypothesis or theory developed by deductive
logic. The inductive method can at best be used to empirically test the theory or hypothesis as to whether it is consistent with or refuted by facts.
The inductive method has another limitation in that there is a great risk of conclusions being drawn from insufficient data. To obtain generalisations through inductive method, one should take
care that sufficient number of observations or data has been taken into account.
Besides, the collection of data itself is also not an easy task. And a researcher who wants to employ the inductive method to arrive at generalisations must have good knowledge of statistical
methods, that is, he must know the art of collecting, processing and interpreting data. It is obvious that as compared with the deductive method, the inductive method is time-consuming and
101. NAME: AMAEFULE RAPHEAL IZUCHUKWU
REG NO:21353407EF
EMAIL: amaefuleraphael2002@gmail.com
METHODS OF ECONOMIC ANALYSIS
There are basic methods of reasoning in Theoretical Economics which are the Deductive and Inductive methods.As a matter of fact, these forms of logic are complementary and co-relative which help
to establish the truth. The two methods will be briefly and convincingly discussed in the subsequent paragraphs below.
-Deductive Methods:This is a method of economic analysis which involves reasoning that moves from the general to the specific ,a descending process,in which a conclusion follows necessarily from
the inferences presented ,so that the conclusion cannot be false if the inferences are true. The inferences drawn are verified against observed facts. It sole aims at testing an existing theory.
It involves;
*Selecting the problem because the narrower it is the more the study,
*Formulating assumptions which serves as a basis of forming hypothesis,
*Formulating hypothesis,
*Testing and verifying the hypothesis.
-Inductive Methods:This is a method of economic analysis termed to be an “ascending process” which involves the derivation of general principles or theories from specific instances or
observations. It aims at developing a theory. It involves;
*Collection, classification and analysing data using statistics techniques,
*Data are then used to make observations about particular facts concerning the problem,
*On the basis of observations, generalisation is logically derived which establishes a general truth from particular facts.
This method brings about exactness and clarity in economic analysis with the use of Mathematics, Statistics and Econometrics.
Economics can be a very “deductive subject” as Economists are used to constructing complicated models of human behaviour which will begin with a number of assumptions. However,Economics is also
an “empirical subject”,using deductive and Inductive methods to explain observed facts. However,In practice,it can be very difficult to say where deduction ends, induction begins as one cannot
leave his study in order to formulate theories because if the study is being left the success of analysing the problem cannot be possible.
The deductive method of economic analysis is static in nature i.e assumption that economic conditions remain constant,while the Inductive methods seems to be dynamic as it suggests new problems
to pure theory for their solution time to time. The deductive method is a simple one because it is analytical as it divides complex problems to component parts while the Inductive method is
costly and time consuming.
The world’s best Deducers are also keen observers of human behaviour and so, Economists need to use both deduction and induction in their work
102. ABAMUCHE LINDA C.
REG. NO.: 2019/SD/37674
1) What are the difference between macroeconomic and microeconomics?
2) Discuss the three different ways of computing GDP.
3) Without diagrams, clearly discuss the circular flow of income and product in a 2 – sector economy, 3 – sector economy and 4 – sector economy.
Macroeconomics is the branch of economics dealing with the performance, structure, behaviour and decision making of an economy as a whole. For example, using interest rates, taxes and the
government spending to regulate an economy’s growth and stability. While micro economics is a branch of economics that studies the behaviour of individual unit such as households, individuals and
enterprises within the economy.
Differences between Macro Economics and Micro Economics
S/N Macro economics Micro economics
1 Macro economics is the study of the whole economy Micro economics is the study of particular market
2 it loose at aggregate variables such as aggregate demand national output It looks at issues such as consumer behaviour, individual labour markets and the theory of firm.
3 macro economics is complex due to the study of large group micro economics analysis is simple
4 problems related to whole economy like employment public finance national income are included in its scope law related to marginal analysis are included in its scope.
5 it provides the information relating to national income, total output, total consumption and general price level it provides the information relating to the individual prices, individual
consumption and production.
2. DISCUSS THE THREE DIFFERENT WAYS OF COMPUTING GDP.
1. Expenditure approach
2. Income approach
3. Output approach
1) Expenditure approach: This is the most widely used approach for estimating GDP, which is a measure of the economy’s output produced within a country’s borders irrespective of who owns the
means of production. The GDP under this method is calculated by summing up all of the expenditures made on final goods and services.
2) Income Approach: This method comprise of the income generated from the basic factors of production or is been calculated by adding up all the factor incomes to the factors of production in the
society, which includes land, labour, capital entrepreneurship or organisation. The production unit are divided into different sectors, income is calculated for each sector and summed up to
arrive at net domestic product.
3) The output approach focuses on finding the total output of a nation by directly finding the total value of all goods and services a nation produces. Because of the complication of the multiple
stages in the production of a good or service, only the final value of a goods or services is included in the total output.
CIRCULAR FLOW IN A SIMPLE 2 – SECTOR ECONOMY
2 – sectors flow in circular economy flow in its basic form, looking at a simple economy which is made up of only households and firms. This is a two sector economy with no government. The
factors owns (households) in turn spend all of their income on goods which leads to a circular flow of income and also it is assumed that all production is done by firms and the firms sell all
their entire output to consumer as soon as it produced.
3 – SECTOR (CIRCULAR WITH SAVING AND INVESTMENT)
In the flow diagram, the clockwise arrows showing the flow of goods and services have been removed just to simplify the diagram, they are new 2 parts ways along which expenditures travel on their
way from household to product market. Some household income is use for consumption expenditure and reaches the product market directly; other household income is directed to savings.
4 – SECTOR FLOW WITH GOVERNMENT
They are now 2 new channels along which funds can flows from households to product market. The government take in revenue from taxes they made from household, some of the revenue immediately
returns to the household in form of transfer payment. Funds flow household to government as net taxes and then from government to product market as government purchase.
103. Name: John okechukwu james
REG no: 21445019hf
DEPT: Social Science Education ( Education Economics)
Email: sponkybrown3@gmail.com
Title : Method of Economics Analysis
An Economics theory derives laws or generalization through this method (I) Deductive method and (II) Inductive method.
1) Deductive method of Economics analysis : the deductive method consist in deriving conclusion from general truth, takes few general principles and applies them draw conclusion. Deductive method
is also named as analytical , abstract or prior method.
Steps of deductive methods;
* perception of the problem
* Defining of terms
* Deducing hypothesis from the assumptions
* Testing of hypothesis
Merits of Deductive method
1. the method is near to reality ,it is less time consuming and less expensive
2. the use of mathematical techniques in deductive theories of economics brings exactness and clarity in economics analysis
3. there is been limited scope of experimentation, the method helps in deriving economics theories.
Demerit of economics method;
* the deductive method is highly abstract. it require a great deal of care to avoid bad logic or faulty economics reasoning
* the deductive method is simply and precise only if thr underlying assumption are valid.
Inductive method of Economics analysis
This method derives economics generalization on the basic of
1) Experimentation 2) Observation and 3) Statistical method
Steps of Inductive method
* Observation
* Formation of hypothesis
* Generalization
* Verification
Merit of Inductive method;
1) is based on facts as such the method is realistic
(ii) In order to test the economic principles, method makes statistical techniques. The inductive method is, therefore, more reliable.
(iii) Inductive method is dynamic.
(iv) Induction method also helps in future investigations.
Demerit of Inductive method;
i) If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
(ii) The collection of data itself is not an easy task.
(iii) The inductive method is time-consuming and expensive.
104. OKAFOR CHIOMA NANCY
REG. NO : 2020/242649
DEPARTMENT: ECONOMICS
Email : nancyokafor2000@gmail.com
METHODS OF ECONOMIC ANALYSIS
Economic analysis is simply the study of economic systems.The analysis aims to determine how effectively the economy or something within it is operating.
There are two major methods of economic analysis and they are – DEDUCTIVE AND INDUCTIVE method-
1. INDUCTIVE METHOD: This method is also known as empirical method. in this method, observations are combined with experiential information to reach a conclusion, meaning that when faced with
specific sets of data we make reasonable conclusions based on existing knowledge we’ve had from previous experience.
2. DEDUCTIVE METHOD: This method is also known as priori method. In this method,we start from raw facts or assumptions and build a hypothesis or theory using basic analytical tools in order to
arrive at a conclusion. This method focuses on economic reasoning as hypothesis will have to be deduced and tested before any assumption can become a theory.
105. NAME: OMEKE PRECIOUS OGECHI
REG. NO: 2020/243294
LOCAL GOVERNMENT
FACULTY: SOCIAL SCIENCE
COURSE CODE: ECO 101
ECONOMIC ANALYSIS
Economic analysis is the study of economic system which is the study of a production process or an industry.
Economic analysis is all about analysing the economic aspects of things.
METHODS OF ECONOMIC ANALYSIS
There are two basic methods of economic analysis they are:- Deductive and Inductive reasonings or methods.
DEDUCTIVE METHOD
Deductive method is also called an abstract, analytical and prior reasonings. The analysis start from unchallenged elementary or rudimentary facts or assumption and then arrive at a conclusion
using logical analysis or one personal analytical truths.
STEPS OF DEDUCTIVE METHOD/ REASONING
1) Identify the problem: You need to know the problem in other to get the solution.
2) Make assumptions.
3) Logical deduction to derive implications
4) Formulation or making of hypothesis.
5) Make predictions and test the hypothesis deduced using more observation.
6) Predictions are in agreement with facts.
“Deductive reasoning gives us hypothesis and if the hypothesis gets verified we have general economic principles of law.”
This method also has advantages and disadvantages.
INDUCTIVE METHOD
Inductive method is also known as empirical method. This method is a type of reasoning that flows from facts to theory. First of all, there will be a collection of information or facts and then
providing of evidence using economic theory and facts. Inductive method derives economic analysis on the basis of experience and observation. Inductive method formulates principles using sub –
methods. they are:- Observation, Experimentations and statistical methods.
STEPS IN INDUCTIVE METHODS
1) Identify the problem.
2) Define the technical terms and alterables related to the problem found.
3) Collection of datas about the variables related to the problem.
4) Procession of the data collected to find out how the variables are related.
5) Make predictions or foretale and test them.
6) Predictions are in agreement with facts.
There are also advantages and disadvantages of Inductive method.
106. Name: NNADI MARYANN AMARACHI
Reg. No: 20684723DF
Dpet: Nursing Sciences
What are the basic methods of analysis used by Economists?
An economist is a person or an expect in the study of the reasoning behind people decisions-making and have interest in data usage to conduct research that leads to boost profits or create a
better public policy. In order to achieve its purpose, an economist apply some basic methods of analysis. These include the following;
1. Deductive method of analysis and
2. Inductive method of analysis
Briefly and convincingly discuss each of them
Deductive method of analysis
This is the method of analysis applying a kind of reasoning that goes from general to specific. It refers to priori reasoning. In this method, one observes a particular task or issue at hand,
makes hypothesis and test the hypothesis using more observations. This analysis do not involve using any complex computer software analysis but only simple deductive logic is required to complete
the task. However, as this method of reasoning begins from assumptions, when such assumptions are logically flawed, a wrong conclusions will be given.
Inductive method of analysis
This analysis uses data collected about a specific theory in economic to draw a conclusion. That is, inductive type of reasoning flows from some facts to a theory. The process involves
observation, formulation of a hypothesis, generalizing principles and verifying against actual facts. This method of analysis by economist is more realistic and reliable because it is based on
facts. However, when such analysis use insufficient and faulty data, it will result to a faulty conclusions.
107. Okechi Francis Uche
Method of Economic Analysis
Economics analysis are done major by;
1. Deductive method
2. Inductive method
Deductive method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
1. Observation of a task/ issue
2. Making the hypothesis
3. Testing the hypothesis using more observations, etc.
Advantages of Deductive Method
1. It is a simple method
2. It doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
3. This method is important for economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical fallacy is a
disadvantage of this method.
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods. We make use of econometerc ackages in this method.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
1. Observation
2. Formulation of a hypothesis
3. Generalizing principles
4. Verifying against actual facts.
Advantages of Inductive Method
1. Since it is based on facts it is more realistic and reliable.
2. Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
3. Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
1. If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
2. It is a time consuming process and thus expensive as well.
3. The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
108. Name:Magbo Chidimma Joy
Matric/Reg no: 2020/242674
Department: Economics Education
Course Code: Eco 101
Course title: principles of Economic
Email joychidimma961@gmail.com
Basic method of Analysis used by Economics are:
Deductive Method
Inductive Method
1 Deductive Method: This is also called a prior reasoning. It starts from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusion ( building hypothesis using
logical analyze or out own analysis or ablities. In this kind of reasoning we go from general to specific.
Stage in deductive Method are
1 observations on a task/ issue
2 making the hypothesis
3 Testing the hypothesis using more observation
Advantages of Deductive Method
1 it is a simple method, it doesn’t involve the uses of any complex software analysis.
2 This methods focuses more on Economic reasoning which is of paramount importance to Economists
Disadvantages of Deductive Method
i the method of reasoning start from assumptions thus if the assumptions is logical flawed the whole process becomes Faulty and would give wrong conclusion.
2 Inductive Method: This methods of reasoning flows from facts to theory. This method formulates principles using this sub-method: observations, Experimations, statistical method.
The stages in this method are:
i Observation
ii Formulation of hypothesis.
iii Generalising principles
iv Verifying against actual facts
Advantages of inductive Method
i since it is based on facts it is more realiable
ii using statistica methods and experimentation makes the process more scientific this making it more universally acceptable
Disadvantages of inductive Method
i The collection of all the data is not an easy Job and varies from person. As to how they collect data
ii it is time consuming and thus expensive as well
109. Name : Charles ThankGod Ekenedilichukwu
Reg Number : 2020/242137
Email : thankgodcharles65@yahoo.com
Course code : Eco 101
Department : Business Education.
Basic method of economic analysis :
Deductive reasoning simply mean logical thinking that starts with a general idea (premises) from general to specific and reaches a specific conclusion . An example using deductive reasoning :
1) all human being can breath
2) Mr emeka can breath
3) therefore , Mr emeka is a human being .
Inductive reasoning is a method that involves drawing one’s experience , observation, conclusion from specific observation to general . Further more, inductive reasoning involves the following
steps :
First ,observe the figures , look for similarities and difference.
2) Generalise these observation.
3) predict the figures .
110. ABAMUCHE AGATHA NKIRU
REG. NO.: 2019/SD/37673
1) What are the difference between macroeconomic and microeconomics?
2) Discuss the three different ways of computing GDP.
3) Without diagrams, clearly discuss the circular flow of income and product in a 2 – sector economy, 3 – sector economy and 4 – sector economy.
Micro economics is the study of indivisible units of an economy. It is also the study of an economy in a disaggregated form while macro economics is the branch of economics concerned with
large-scale or general economic factors, such as interest rates and national productivity.
S/N Micro Macro
1 micro economics studies the income of an individual macro economics studies about the national income
2 micro economics concerns itself decisions of individuals and business decision macro analyzes the decisions that are made by countries and government.
3 micro economics adopts a bottom-up approach. It focuses on the demand and the supply and other forces that play out in the price levels macro economics adopts a top down approach. It looks into
the policies and decisions that influence the direction taken by other players in the economy
4 micro economics engages in the study of the behaviours of individuals forms, and households in a given with regards to how they make both ends meet macro economics looks at the economy in its
entirely. It examines how the various forces interact and engage at a larger level like the region, the nation and the entire globe.
5 investors can use micro economics in the investment decision macro economics is an analytical tool mainly used to craft economic and fiscal policy
The expenditure approach
The output approach or production
The income approach
The expenditure approach also known as spending approach calculates spending by eth different groups that participate in the economy. The U.S. is primarily measured based on the expenditure
The approach can be calculated using the following formula
GDP = C + G + I + NX
C = consumption
G = government spending
I = Investment
NX = net exports
The output or production Approach: The production approach is essentially the reverse of the expenditure approach. Instead of measuring the input costs that contribute to economic activity, the
production approach estimates the total value of economic output and deducts the cost of intermediate goods that are consumed in the process.
The Income Approach: The income approach represents a kind of middle ground between the two other approaches to calculate GDP. The income approach calculates the income earned by all the factors
of production in an economy.
THE CIRCULAR FLOW IN A SIMPLE (2 SECTOR) ECONOMY
In this type of economy, it is assumed that household spend all their incomes on consumer’s goods as soon as the income is received. All consumption is assured to take place in the household.
This means that the business sector does not consume finished goods. It is also assumed that all production is done by firms and the firms sell all their entire output to consumers as soon as it
is produced.
CIRCULAR FLOW WITH SAVINGS AND INVESTMENT (3 – SECTOR) ECONOMY
Some household income is use for consumption expenditure and reaches the product market directly, other household income is indirected to savings and this is a source of funds for firms to use in
making investment expenditure. The income reaches product market directly. On the way from household to firms, the flow of savings pass through a set of financial market.
CIRCULAR FLOW WITH GOVERNMENT (4 – SECTOR)
The government take in revenue from taxes they made from households, some of the revenue immediately returns to the household in the form of transfer payment. The government collect tax as
revenue and pay out as transfer payment and it is called net taxes. Funds flows from household to government as net taxes and then from government to product market as government purchases.
111. Name: ogbonna chinecherem Rita
Reg no: 20155373IF
Dept: social science education
Unit: economics education
Course code: Eco 101
Email: ogbonnachinecheremrita@gmail.com
Economics analysis involves the formulation of law and generalisations through two methods thus: DEDUCTIVE AND INDUCTIVE REASONING.
1. Deductive method: it is a process of drawing conclusions based on the premises genaraly accepted and assumed to be true,it uses only information assumed to be correct and accurate not based on
feelings and emotions,it is also called abstract, analytical and a prior method.steps to take before drawing conclusions, there are four steps in drawing conclusion through deductive method 1.
Perception of the problem: the Economist must have a clear and vivid idea of the problem to be solved 2. Defining technical terms and making assumptions: you have to define terms to be used and
make some clear assumptions concerning to the problem to be solved 3. Deducing hypothesis: the Economist have to draw hypothesis gotten from the assumption made 4. Testing hypothesis: the
hypothesis gotten from the assumption made must be verified tested and undergo series of experiments before generalizing or going into conclusion
Example of deductive method/reasoning thus: all birds have feathers,all robins are bird therefore,robins have feathers.
2. Inductive method: it is a method of reasoning in which the premises are viewed as supplying evidence with no full assurance but drawing conclusion from a state a set of specific observation
example 1. All black dogs I have seen are wicked therefore all black dogs are wicked this is a weak arguments because they are also black dogs that are not wicked, so we make it stronger by
putting it under probability thus all black dogs I have seen are wicked therefore most black dogs are probably wicked. inductive reasoning is used everyday to build an understanding of the world,
inductive reasoning is also known as historical methods in economics analysis.
112. What are the basic methods of analysis used by Economists?
An economist is a person or an expect in the study of the reasoning behind people decisions-making and have interest in data usage to conduct research that leads to boost profits or create a
better public policy. In order to achieve its purpose, an economist apply some basic methods of analysis. These include the following;
1. Deductive method of analysis and
2. Inductive method of analysis
Briefly and convincingly discuss each of them
Deductive method of analysis
This is the method of analysis applying a kind of reasoning that goes from general to specific. It refers to priori reasoning. In this method, one observes a particular task or issue at hand,
makes hypothesis and test the hypothesis using more observations. This analysis do not involve using any complex computer software analysis but only simple deductive logic is required to complete
the task. However, as this method of reasoning begins from assumptions, when such assumptions are logically flawed, a wrong conclusions will be given.
Inductive method of analysis
This analysis uses data collected about a specific theory in economic to draw a conclusion. That is, inductive type of reasoning flows from some facts to a theory. The process involves
observation, formulation of a hypothesis, generalizing principles and verifying against actual facts. This method of analysis by economist is more realistic and reliable because it is based on
facts. However, when such analysis use insufficient and faulty data, it will result to a faulty conclusions.
113. Economic Analysis
Any economic analysis involves the formulation of laws and generalizations through two methods- deductive and inductive.
Methods of Economic Analysis
Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis
or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Deductive And Inductive Methods
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
114. NAME-Edeh loveth ifeoma
Department- combined social science
( economic/political science)
MATRIC Number- 2020/242988
Email- ifeomaloveth33@gmail.com
METHOD OF ECONOMIC ANALYSIS
1; DEDUCTIVE METHOD- we shall first explain the Deductive method of deriving economic generalisation. The Deductive method is also called abstract, analytical and a prior method and represent an
abstract approach to the derivation of economic generalisation and theories. With the aid of rigorous mathematical logic, economic theories can be developed through the process of deduction which
can successfully explain economic phenomena.through Deductive logic useful economic theories can be derived without collection and analysis of data which are required under inductive method,this
as compared to inductive method deduction is less time consuming and less expensive. The sophisticated mathematical method in the Deductive approach enables the economist to introduce accuracy
and exactness in economic principle and theories.
2; INDUCTIVE METHOD- This inductive method which is also called empirical method derived economic generalisation on the basic of experience observation.
In this method detailed data are collected with regard to a certain economic phenomenon and effort is then made to arrive at certain generalisation which follow from the observation collected.
The main step involved in the application of inductive method are
Formation of hypothesis
Inductive method is based on fact as such the method is realistic and this method is dynamic, the changing economic phenomenon are analyzed and on the collected data.conclusion and solution are
drawn from them and this method also help in future investigation.
115. NAME:MAMAH FAITH OKWUKWE
REG NO:20644865BF
EMAIL ADDRESS: http://www.mamahokwukwe24@gmail.com
METHODS OF ECONOMIC ANALYSIS:
The methods used in analyzing the relationship between two variables with the use of economic research are:
*Deductive method
*Inductive method
*DEDUCTIVE METHOD:
This is an abstract approach to the derivation of economic generalizations and theories.
STEPS INVOLVED IN DEDUCTIVE METHOD
*The analyst or theorist should perceive and observe the problem to be enquired into, have a clear understanding of it and try to present it in such a way that it awakens people’s curiosity.
*The theorist should define clearly,precisely and unambiguously the technical terms as well as make appropriate and indisputable postulates through the observations.
*The analyst should deduce a hypothesis, deriving conclusions from the postulate through the process of logical reasoning.
*The economist should test the deduced hypothesis by uncontrolled experience so as to know if the hypothesis is an alternate or nol hypothesis.
The merit of this method is that it facilitates economic reasoning and does not involve complex software analysis. The demerit is that if it’s assumption is logically flawed, the whole process
becomes faulty.
INDUCTIVE METHOD:
This is a method that encomprises of collecting data and facts about the significant variables whose interrelationship and behaviour he wants to derive generalization, provide evidence and back
up using economic theories.
STEPS INVOLVED IN INDUCTIVE METHOD ARE:
*The theorist should perceive and observe the problem to be enquired into.
*The theorist should define the technical terms clearly.
*The theorist should collect all data about the particular economic theory and make assumptions.
*The analyst should form a hypothesis.
*The analyst should draw conclusions and verify them with reference to actual facts and the behaviour of the economy.
The merit is that it is more reliable since it is based on fact, it is highly practical, it is helpful in verifying the conclusion of deductive logic etc.
The demerit is that it consumes time, data collection is not easy since it varies from person to person, mere Inductive method cannot do the job alone (it also needs deductive method).
116. NAME: Ugwuanyi Sunday Chetachi
REG. NO: 20686711HA
DEPARTMENT: Public Administration And Local Government
COURSE CODE: Eco.101
COURSE TITLE: Principles of Economics
Question: What are the basic methods of analysis used by Economists? Briefly and convincingly discuss each of them.
Basically, in Economic analysis theories obtain generalizations or laws through two methods;
A. Deductive method or Analytical Abstract method
B. Inductive method or Empirical method
DEDUCTIVE METHOD
This method of economic of Economic Analysis reach conclusion by taking and applying general or wildly accepted principles. it consists of gaining conclusions from general truth;
there are several steps involved in deductive Analysis. they include:
I. perception of the problem to be inquired into.
II. defining of terms
III. deducing hypothesis from the assumption.
iv. testing of hypothesis
This method is less time consuming and less expensive. it brings exactness and clarity in economic analysis due to the use of mathematical techniques.
On the other hand, the deductive method is highly abstract. it requires a great deal of care to avoid bad logic or faulty economic reasoning.
This method entails the process of reasoning from particular facts to general principles. it was adopted by the historical school of Economists.
In this method of Economic Analysis, Economic generalization is gained on the basis of the following;
i. experimentation
iii.statistical methods.
There are four main steps involved in this method, which include; observation, formation of hypothesis, Generalization and verification.
this method is realistic due to the fact that it is based on facts. it is also dynamic and reliable. On the other hand, this method is time-consuming and expensive. Generalization obtained
through this method may be faulty if the conclusion is drawn from insufficient data.
117. Name:Eze Immaculeta Ebubechi
Dept:public administration and local government
Reg number:20679439EF
1)Inductive method:This method flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principle using the sub-method-observation, experiments, statistical methods. Data is collected about a particular economic theory and then conclusions are drawn. The stages in the method are:
Formulation of hypothesis
Generalizing principles
Verifying against actual facts.
2:Deductive methods: This is also called prior reasoning. We start from unchallengeably elementary or rudimentary assumptions/facts and then arrive at conclusion( build a hypothesis or theory)
using logical analysis or own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task or issue
Making hypothesis
Testing the hypothesis using more observations..
118. Name: Okoloaja Vanessa Mmerichukwu
Reg no:21320516FF
Email: Mmerichukwunessa77@gmail.com
1. Deductive method: The deductive of economic analysis also known deductive logic entails the movement from general to particular reasoning,it is also known as an hypothetical method . The
deductive reasoning provides generalisation that must have been tested and verified in order to have relevance to the facts. There are various steps in deductive logic (identify the
problem,defining the technical terms, deducing hypotheses and testing or verification of hypotheses )
1. Deductive method is easy to comprehend : Looking at the law of utility, law of demand and other theories,it is a self evident that we can easily draw conclusions from the theories
2. It gives accruacy and exactness: In generalisation, deductive logic gives a very high standard of precision in abstract economic reasoning.
1. The deductive logic has its own drawback because of its too much abstraction, thereby having little or no connection to real
2. Inductive: The method moves from particular to general reasoning, it is carried out in two forms, experimentation and statistical forms. The statistical branch of inductive reasoning plays a
greater role on economic investigation, looking at the Malthusian theory of population (Rev. Thomas Malthus) he used statistics to show relationship between (food to population and population to
1. It is highly practical and realistic
2. It is helpful in verifying conclusions
1. Collection of facts in the inductive logic is difficult and complicated.
In conclusion, the two methods should not be used for competition but should be used to complement each other in the discipline of economics.
119. Name: Ogenyi Deborah Oluchi
Reg no: 20645428FA
Email: debbyluchi01@gmail .com
There are two basic method of analysing used by economist and dey are ;
1) Deductive method: This is also a priori reasoning we start from unchallenged elementary or rudimentary assumptions or fact and then arrive at conclusions using logical analysis orourvown
analytical abilities in the kind of reasoning, we go from general to specific.
2) Inductive method: This type of reasoning flows from fact to theory. first, we collect information and fact and then move towards providing evidence using economic theory and facts. This method
formulates principles using the sub-method Observation, experiments, statistical methods.
120. NAME:ONYEFULU CHIAMAKA LILIAN
MATRICULATION NUMBER: 2018/250299
DEPARTMENT: NURSING SCIENCES
FACULTY: HEALTH SCIENCES AND TECHNOLOGY
QUESTIONS: METHODS OF ECONOMICS ANALYSIS
Economic analysis: can be defined as an economic operation that involves the formulation of laws
There are basically two methods of economics analysis
1. Deductive method
2. Inductive method
DEDUCTIVE METHOD: Is also called abstract, analytical and prior method and represents an abstract approach to derivation of economics generalization through deductive logic
1. Perception of the problem: In any scientific research, the analyst must have a clear idea of the problem to be researched on. There must be liable variables in which his generalization will
depend on.
2. Precise definition of technical terms and making assumptions: This involves simple definition of various technical terms related and to be used in the analysis and this clearly states the
assumptions. Assumptions maybe behavioral pertaining to the behavior of the economics variables.
3. Deduction of hypotheses: Hypotheses are deduced from the assumptions or premises taken, Hypothesis explains relationships between factors affecting a phenomenon.
4. Testing of deduced d hypotheses: This means checking, analyzing and lastly verification of the hypothesis, when verified it can be established as generalization.
INDUCTIVE METHOD OF ECONOMICS ANALYSIS:- It can also be called empirical method, it serves economics generalization based on experiences and observations. It does not accommodate few
observations, It can only be done when large observations has been made, it uses statistical or econometric methods.
1. Perception of the problem: In any scientific research, the economist must have a clear idea of the problem-to be researched on. There must be liable variables in which his generalization will
depend on.
2. Precise definition of technical terms and making assumptions: This involves simple definition of various technical terms related and to be used in the analysis and this clearly states the
assumptions. Assumptions can also be called postulate
3. Collection of data: There will be collection of data about the variables related to the problems, as to gather large observations for the analysis.
4. Processing of data collected: Finding out the relations between variables and doing some preliminary thinking ways to relate and the variables.
5. Deduction of hypotheses: Hypotheses are deduced from the assumptions or premises taken, Hypothesis explains relationships between factors affecting a phenomenon, it shows clearly the
relationship that correlates.
6. Testing of deduced d hypotheses: This means checking, analyzing and lastly verification of the hypothesis, when verified it can be established as generalization.
121. METHODS OF ANALYSIS USED BY ECONOMISTS.
These are the deductive and inductive method.
1.Deductive method: is also called priori method, aimed at testing theories and it represents an abstract approach to the derivation of economics generalizations. Sometimes this approach is
informally called a top down. it is associated with quantitative research. Deductive involves;
1. Selection or perception of the problem
2. The formulation of assumptions on the basis of which the problem is to be explored.
3. The formulation of hypothesis through the process of logical reasoning, whereby influences are drawn.
4. Verifying the hypothesis.
Deductive method has its negative and positive sides; the positive: it is real, simple, Powerful, exact, indispensable and universal.The negative side: it is an unrealistic assumption, incorrect
verifications, abstracts method. The supply and demand analysis is an example of deductive reasoning because it comprises of generally accepted principles about supply and demand. In conclusion,
deductive method starts with a generally accepted principle and proceeds to the specific.
2. Inductive method: this concept is normally based on claims that knowledge is built primarily from an observer’s experiences and interactions with phenomena. Inductive research begin with a
research question and the collection of empirical data which are used to generate hypothesis and theory. In inductive method we use econometrics packages to run experiments such as E-views,
STdata etc.
The method of processing the data collected and finding out what relates between the variables that actually holds.This will result in the development of a further refined and tested method known
as statistical method. Inductive reasoning begins with specific observations, patterns are drawn from the observations and then generalized, the generalization are then combined to form a general
122. NAME. OGUANYA CHIDERA FAITH
DEP ECONOMICS
REG NO.21462736DA
BASIC METHODS OF ECONOMIC ANALYSIS
1. Deductive method.
2. Inductive method.
Deductive- also known as the abstract method, analytical approach and a priori method. It represents an abstract approach to the derivation of economic generalization and theories. The principles
of deriving economic generalizations through deductive logic are (a) defining precisely the technical terms and making approapiate assumptions often called postulates or premites.then the
deducing hypothesis, that is deriving conclusion from the premises through the process of logical reasoning and finally the testing of hypothesis deduced.
2. Inductive- this is also called empirical method. This method derives economic generalizations on the basis of experience and observations. In this method, dedailed data are collected with
regard to a certain economic phenomenon and effort is then made to arrive at certain generalizations which follows from the observations collected. The steps here are (a) Experimentation….(b)
observation and statistical or econometric method.
123. DEPARTMENT :PHILOSOPHY.
1) Deductive method it also called a priori reasoning.it can be unchallenged elementary or rudimentary assumption or facts that arrive at a conclusions using a logical analysis or our own
analytical reasoning.in this kind of abilities, we go from general to specific stages of deductive reasoning which are observation of issue,Making the theory,testing the hypothesis using more
observation.The advantages of these method is that it doesn’t involve the use of complex 2)Indeductive method :it flows from facts to theory.We first collect information and facts then move
towards providing evidence using economic theory and facts .this method formulates principles using the sub -methods. Advantages of Indeductive method is that,it based on facts and realistic and
reliable theories.
124. Methods of Economic Analysis
Some of the most important methods of economic analysis are as follows:
1. Deductive Method
2. Inductive Method.
Economic generalizations describe the laws or statements of tendencies in various branches of economics such as production, consumption, exchange and distribution of income. In the view of
Robbins, economic generalizations or laws are statements of uniformities which describe human behavior in the allocation of scarce resources between alternative ends.
The generalizations of economics like the laws of other sciences, state cause and effect relationships between variables and describe those economic hypotheses which have been found consistent
with facts or, in other words, have been found to be true by empirical evidence. But a distinction may be drawn between a generalization (law) and a theory.
A law or generalization just describes the relationship between variables; it does not provide any explanation of the described relation. On the other hand, a theory provides an explanation of
the stated relation between the variables, that is, it brings out the logical basis of the generalization. An economic theory or a model derives a generalization through process of logical
reasoning and explains the conditions under which the stated generalization will hold true.
1. Deductive Method:
We shall first explain the deductive method of deriving economic generalizations. The deductive method is also called abstract, analytical and a priori method and represents an abstract approach
to the derivation of economic generalizations and theories.
In any scientific enquiry, the analyst or theorist must have a clear idea of the problem to be enquired into. He must know the significant variables regarding whose behavior and interrelationship
he wants to derive generalizations. The perception of the problem is by no means an easy task.
(a) Definition of Technical Terms and Making of Assumptions:
The next step in the process of deriving economic generalizations is to define precisely and unambiguously the various technical terms to be used in the analysis as well as to state clearly the
assumptions he makes to derive generalizations.
As mentioned above, assumptions may be behavioral pertaining to the behavior of the economic variables or they may be technological relating to the state of technology and the factor endowments.
The crucial assumptions are made on the basis of observations or introspection.
A crucial assumption that has been taken in economics is that consumers try to maximize their satisfaction and producers try to maximize their profits. Likewise, it is assumed that investors try
to minimize their risk and maximize the expected rate of their profits. Some of the assumptions are made merely to simplify the analysis and may not be quite realistic.
The actual economic world is quite complex and full of details in which numerous factors play a part and act and interact on each other. The introduction of simplifying assumptions is quite
necessary in order to bring out the importance of really significant factors having a bearing on the problem under investigation.
It, therefore, follows that each and every assumption made by a theory may not be realistic. The crucial factor in building up a valid theory is whether its predictions are corroborated by the
facts in the world. A correct scientific theory or generalization must be expressed in the form of a hypothesis that is conceivably refutable.
(b) Deducing Hypotheses through Logical Deduction:
The next step in deriving generalizations through deductive logic is deducing hypotheses from the assumptions or premises taken. A hypothesis describes relationship between factors affecting a
phenomenon; it establishes the cause and effect relationship between the variables having a bearing on the phenomenon.
Then, through logical process, hypothesis is deduced from the assumptions made. This logical reasoning may be carried out verbally or it may be conducted in symbolic terms using the language of
what is known as symbolic logic.
The geometric or graphic technique is also usually employed to deduce the hypotheses about the relationship between factors. Besides, the process of logical deduction may be done with the help of
more formal mathematics.
These days in almost all branches of modern economics, mathematics as tool of analysis for deriving economic theories and generalisations is being increasingly used. The use of mathematics in
economic analysis proves extremely useful where geometrical methods make the analysis more complicated to comprehend. Besides, the use of mathematical method makes the derivation of economic
hypotheses more rigorous and exact.
It is worthwhile to note that in deriving analytically sound hypotheses, one should guard against committing logical fallacy in the process of logical deduction. For instance, it is inappropriate
to conclude that A must be the cause of B, if A happens to precede B.
Further, it is logically fallacious to argue that since there exists a high degree of correlation between the two factors, say between the supply of money and the general price level, the former
must be the cause of the latter, unless the causation must be logically developed.
(c) Testing or Verification of Hypotheses:
Hypotheses obtained above have to be verified before they are established as generalizations or principles of economics. For the verification of hypotheses, economists cannot make controlled
experiments, because they have to discover uniformities in behavior patterns of man.
We cannot make experiments with man under controlled conditions, such as in laboratories as physical scientists make experiments with inanimate objects of nature and biologists make these with
animals and plants. Therefore, economists have to rely on uncontrolled experience and observations.
The information regarding uncontrolled experience about the behaviour patterns concerning variables about man and the economy are quite amply available. The reliance by economists on uncontrolled
experiences, however, does increase the number of observations required to verify the hypotheses or to establish the generalizations.
Besides, the need to rely on uncontrolled experiences complicates the analysis and requires that facts must be carefully interpreted to discover successfully the significant relationship between
relevant economic variables.
It may, however, be pointed out that in spite of the complexities and difficulties involved in verifying economic hypotheses through successful analysis and proper interpretation of uncontrolled
experiences and observations, several useful and significant generalizations have been established in economics.
In the field of microeconomics, the well-established generalizations relate to the inverse relationship between price and quantity demanded, the direct relation between price and quantity
supplied, the tendency of the price of the product to be equal to the marginal cost under conditions of perfect competition, and the tendency for the wages to be equal to the value of marginal
product under conditions of perfect competition and several others.
In the field of macro-economics, established generalizations relate to the determination of the level of national income by aggregate demand and aggregate supply in a capitalist economy, the
multiple increase in income and employment as a result of a given initial increase in investment depending upon the size of marginal propensity to consume, the dependence of the amount of
investment on the marginal efficiency of capital and the rate of interest and several others.
It is worth noting that the absence of controlled experiments in economics affects the exactness of economic laws and generalizations.’ This means that the generalizations in economics are not as
exact as those of physical sciences and they are therefore not universally applicable under all circumstances. Because of the absence of controlled experiments economic generalizations lack in
firmness, they are not easily accepted by all and even generalizations that are refuted by empirical evidence are not abandoned for good by all.
In regard to flaming and testing of economic generalizations, two related distinctions must be borne in mind. First, functional relationship between economic variables and a historically
sequence of events must be distinguished.
For instance, the law of demand stating inverse relationship between price and quantity demanded does not become invalid in view of the fact that both prices and quantities sold of many
commodities increase during boom periods. This is because certain other forces such as a rise in aggregate investment demand operates which causes increase in both the price and quantity sold
during a boom period.
Second, prediction of a generalization to show its validity must be carefully differentiated from the forecasting of future events; actual events may not exactly come about as predicted by a
generalization and yet that generalization may be correct. This is because, as mentioned above, the actual course of events is governed by several other factors assumed by a generalization which
remains constant under the qualification “other things remaining the same.
In the absence of controlled experiments, for the verification of their theories economists have to rely on the direct observations of events in the real world. By direct observations we mean.
gathering of information personally or reliance on comparatively unprocessed material such as files of business firms and government departments, locally published reports, proceedings of
representative assemblies, newspapers, advertisements, market reports, auction notices and the like.
In order to prove the validity of hypotheses and therefore to establish laws or generalizations, importance of direct observations cannot be underrated.
Testing of Economic Hypotheses through Statistical Methods:
In recent years a very useful method to test economic hypothesis has been developed. This is the statistical method or what is now popularly called econometric method. The statistical or
econometric method to verify and establish the theoretical generalizations occupies an important place because of the limited applicability of controlled experimentation in economics.
The various statistical methods such as regression analysis have been developed to empirically test the economic hypotheses on the basis of collected economic data. The merit of econometrics is
that the degree of functional relationship between relevant economic variables in precise quantitative terms is obtained by it and also the level of significance of the results can also be
Recently, econometric method has been used to establish the precise relationships between money supply and the price level, quantity of money and the national income, consumption and income,
capital accumulation and rate of economic growth and so forth.
It may, however, be pointed out that statistical analysis or econometrics alone cannot be used to derive and establish economic principles and theories. Economic hypotheses or theories must be
developed logically before we can meaningfully use statistical analysis to test and verify them.
Indeed, a theory or hypothesis is needed beforehand for selecting the relevant facts and data regarding relevant variables which can be subjected to empirical testing through the methods of
Facts come to mean something only as ascertained and organized in the frame of a theory. Indeed, facts as part of scientific knowledge have no existence outside such a frame Questions must be
asked before answers can be obtained and, in order to make sense, the questions must be part of a logical coordinated attempt to understand social reality as a whole. A non- theoretical approach
is, in strict logic, unthinkable. Principal steps followed in formulation of economic theories and generalizations through deductive method can be summarized as given below.
Merits and Demerits of Deductive Method:
The deductive approach to establish economic generalizations was extensively used by Classical and Neo-Classical economists such as Ricardo, Malthus, Senior, J. S. Mill, Marx, Marshall and
Pigou. It still remains popular with modem economists as it has several merits. First, useful mathematical techniques can be employed to derive laws and theories of economics.
With the aid of rigorous mathematical logic, economic theories can be developed through the process of deduction which can successfully explain economic phenomena. Secondly, through deductive
logic useful economic theories can be derived without the tenuous and detailed collection and analysis of data which are required under the inductive method.
Thus, as compared to inductive method, deduction is less time-consuming and less expensive. Thirdly, in view of the limited scope for controlled experimentation in economics, the method of
deduction is extremely useful method of constructing economic theories. This is because several forces act simultaneously on an economic phenomenon and it is not possible to eliminate some of
these by means of a controlled experiment.
This indicates the crucial importance of deductive logic for building up economic principles or theories. Fourthly, the use of sophisticated mathematical methods in the deductive approach enables
the economists to introduce accuracy and exactness in economic principles and theories.
In spite of the above-mentioned merits, shortcomings of the deductive approach should not be overlooked. The use of deductive method in deriving economic generalizations requires the use of a
high-level competence in logic and theoretical abstraction.
Besides, most economists have preconceived notions or biases on several economic issues. If sound and valid economic generalizations are to be established, economists must dissociate themselves
from normative preconceptions and biases in their logical process of deducing economic generalizations.
Further, a great demerit of deductive approach is that with it highly sophisticated theoretical models based on highly unrealistic assumptions may be developed which do not have any operational
significance. Indeed, such highly irrelevant analytical models with little empirical content and incapable of being used for policy formulation have in fact been developed by economists. Such
models are no more than mere “intellectual toys”. If economics is to serve as an instrument of social betterment, building of such theoretical models having no operational use should be avoided.
Lastly, in the derivation of economic hypotheses and conclusions through deductive logic, assumptions play a crucial role. If the assumptions made are such that when on removing them, economic
hypothesis based on them is refuted, then making of these assumptions is not valid.
Thus, one who uses deductive approach should always keep in mind to what extent the validity of generalizations derived depends on the assumptions made. For instance, the Keynesian macroeconomic
analysis is based upon the assumption of a depression-ridden capitalist economy with a lot of excess productive capacity.
Therefore, a positive harm has been done in applying the Keynesian theories in the context of developing countries such as ours where the assumptions made by Keynes do not hold good. Hence, mere
“deductive arm-chair analysis” should be avoided, if the scientific character of economics is to be maintained.
2. Inductive Method:
The inductive method which is also called empirical method derives economic generalizations on the basis of experience and observations. In this method detailed data are collected with regard to
a certain economic phenomenon and effort is then made to arrive at certain generalizations which follow from the observations collected.
But, it is worth mentioning that the number of observations has to be large if it can yield a valid economic generalization. One should not generalize on the basis of a very few observations.
There are three ways which can be used for deriving economic principles and theories.
They are:
• Experimentation,
• Observations,
• statistical or econometric method.
As has been mentioned above, the experimentation, that is, the use of contrived experiments is of limited applicability in economics. First, unlike natural sciences which are concerned with
analyzing the behavior of either inanimate objects or obedient animals such as rats and rabbits under the influence of chloroform, economics deals with the behavior of man who is quite fickle,
wayward and unmanageable.
Besides, man cannot tolerate the idea of being experimented upon, either individually or collectively. Secondly, an economic phenomenon is the result of multiplicity of factors and causes acting
and interacting upon each other.
Therefore, economic phenomenon does not repeat itself in the same uniform pattern. Numerous factors acting on an economic phenomenon ‘disturb’ it and make its exact repetition unlikely. Thus, as
compared with the natural phenomena, economic phenomena are of less uniform pattern, less repetitive and more variable.
Thirdly, economists study the economic phenomena in which pressure groups such as employers’ associations, trade unions, farming lobby, political parties with their different ideologies play a
crucial part and their activities render it difficult to make controlled experiments in the economic world. However, in spite of these difficulties, experimental method can be used in some
For instance, experiments have been conducted to find out which law of production is valid, that is, whether law of diminishing returns, law of constant returns or law of increasing returns
operates in the real world. Besides, public undertakings or big industrial firms often try to assess the effect of the changes in the prices of their products on the demand for it and thus find
out the demand elasticity of their products.
Various Steps in Inductive Method:
Various steps are gone through in developing economic theories through inductive method. The first step, as in the deductive approach, is to identify the problem. The second step is defining
technical terms and variables related to the problem.
It is the next step which is peculiar to the inductive method, namely, the collection of data about the variables related to the problem and doing some preliminary thinking about the possible
functional relationships between the relevant variables.
The next important step in the construction of economic theories in this method is the processing of data collected and finding out what relations between the variables actually hold good. From
this, a theory is developed which can be further refined and tested through statistical methods.
Once the theory has been developed one can make predictions on its basis, as is done in the deductive approach. If predictions of theory are in agreement with the facts and actual behavior of the
economy, then a new reliable theory has been developed. If a new theory explains “how things work” better than the existing ones, it replaces them.
However, if predictions are in conflict with actual facts and behavior of the economy, either the theory is discarded or fresh efforts are made to modify and refine it by collecting more data and
processing them. The various steps in the construction and development of economic theories through inductive method are illustrated in Figure.
Evaluation of Inductive Method:
As has been explained above, observations of facts through collection of detailed data and the use of statistical methods to arrive at economic generalizations establishing relationship between
facts are being increasingly made.
Some of the recent researches in the field of macroeconomics, such as the nature of consumption function describing the relation between income and consumption, the principle of acceleration
describing the factors which determine investment in the economy have been obtained through the use of mainly inductive method.
However, it needs to be emphasized again that the use of induction or empirical method is not of much value if it is not supported by the economic hypothesis or theory developed by deductive
logic. The inductive method can at best be used to empirically test the theory or hypothesis as to whether it is consistent with or refuted by facts.
The inductive method has another limitation in that there is a great risk of conclusions being drawn from insufficient data. To obtain generalizations through inductive method, one should take
care that sufficient number of observations or data has been taken into account.
Besides, the collection of data itself is also not an easy task. And a researcher who wants to employ the inductive method to arrive at generalizations must have good knowledge of statistical
methods, that is, he must know the art of collecting, processing and interpreting data. It is obvious that as compared with the deductive method, the inductive method is time-consuming and
Conclusion: Integration of Two Methods:
Now, the controversy which existed among the earlier economists as to whether deductive or inductive approach is more appropriate in developing economic theories and principles has been resolved.
The modem viewpoint in this regard is that both are needed for the proper development of scientific economic theories. Indeed, the two are complementary rather than competitive.
The modern economists first derive economic hypotheses through the process of logical deduction and then empirically test them through statistical or econometric methods. Marshall rightly pointed
out, “induction and deduction are both needed for scientific thought as the right and left foot are both needed for walking.
Empirical studies made through statistical or inductive method without a theoretical hypothesis to serve as a guide for the selection of data are quite useless. The derivation of economic
generalisations through the approach of deductive logic without empirically testing them through inductive method is also not quite proper.
Empirical studies made in inductive approach also bring to light significant economic facts or phenomena which require analytical explanation through deductive logic. For instance. Farm
Management Studies in India in the mid- fifties led to the discovery of a fact that output per acre on the small-sized farms is higher than that on large farms.
This led to the various theoretical explanations of the phenomenon observed in the empirical studies. On the other hand, a theory or hypothesis is first developed through deductive logic from
some assumptions and then predictions based on the hypothesis are tested through inductive or statistical method. If the predictions are found to be constant with facts, the hypothesis or theory
stands proved and if the predictions of the theory are found to be inconsistent with facts, it stands rejected.
125. NAME: REMIGIUS CHIDEBERE RICHARD
REG NUMBER: 21410757AF
EMAIL: bcrichardremigius@gmail.com
FACULTY: SOCIAL SCIENCE
DEPARTMENT: ECONOMICS
METHODS OF ECONOMICS ANALYSIS
Basically Economic Analysis involves the formulation of laws and generalizations through Two {2} Methods:
{1} Deductive Method
{2} Inductive Method
Deductive Method
This is also called a priori or top-down reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions (build a hypothesis or theory) using
logical analysis or our own analytical abilities. In this kind of reasoning, we go from general to specific.
The Stages in Deductive Method are listed and explained belove:
1. Formulation of the Problem:
In any scientific study, the analyst must have a clear idea of the nature of the problem to be investigated (or enquired into). It is absolutely essential for the analyst or theorist to acquire
knowledge of the relevant variables; the variables about whose behaviour and interrelationship he wants to make generalisations. The perception of the problem is in most cases a complex exercise.
2. Definition of Terms and Formulation of Assumptions:
Since every subject has its own language, it is necessary to define certain technical terms associated with the analysis as the second step. It is also necessary to make assumptions.
The assumptions maybe of different types, viz., technological, relating to the state of technology and factor endowments, or behavioural, relating to the actions of economic agents like
consumers, factor owners, and producers.
It is not at all necessary for every assumption to be realistic. The most crucial factor in theorising is whether the predictions made by the theory are supported by the facts or observations. In
the words of R. G. Lipsey: “The scientific approach to any issue consists in setting up a theory that will explain it and then seeing if that theory can be refuted by evidence.” The same point
has been made by the Nobel Laureate economist Milton Friedman. He has explained the view that one should not give undue importance to the ‘realism’ of assumptions. What is most important, from
the viewpoint of scientific theory, is whether it enables us to make accurate predictions.
3. Formation of Hypothesis:
The third step in making generalisations through process of logical deduction is to form a hypothesis on the basis of the assumptions made. A hypothesis is a provisional statement the truth of
which is not known to us. A hypothesis just describes the relationship among factors affecting a particular phenomenon. Differently put, it establishes the cause-and-effect relationship among
those variables (dependent and independent) having direct bearing on the
4. Hypothesis Testing:
The final step involved in the deductive method is hypothesis testing. Hypothesis testing refers to the development and use of statistical criteria to aid decision making about the validity of a
hypothesis in uncertain conditions. In any decision about the validity of a hypothesis there is always a chance of making a correct choice and a risk of making a wrong choice.
Hypothesis testing is concerned with evaluating these chances and suggesting criteria that minimise the likelihood of making wrong decisions. Therefore, hypotheses deduced through a process of
logical reasoning have to be verified. Otherwise, it is not possible to establish them as generalisations or principles of economic science.
For the testing or verifications of hypothesis economists cannot carry out controlled experiments. Therefore, economists are forced to carry out uncontrolled experiments or rely on past
observations. The economic system itself generates necessary information about the behaviour pattern of human beings. Two major problems crop up as a result of uncontrolled experiments.
Advantages of Deductive Method
It is a simple method and it does not involve the use of any complex software analysis, etc. only simple deductive logic is required. This method is important for economists as it focuses upon
economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
Basically, in this method of reasoning we start from assumptions, and, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions.
{2} Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods: Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn.
The stages in this method are:
{1} Observation
{2} Formulation of a hypothesis
{3} Generalizing principles
{4} Verifying against actual facts.
Advantages of Inductive Method
{1} Since it is based on facts it is more realistic and reliable.
{2} Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
{3} Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
{1} If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
{2} It is a time-consuming process and thus expensive as well.
{3} The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
126. NAME: Orji Harrison Chukwuemeka
REG NUMBER: 21841174FA
EMAIL: emekavalentine20@gmail.com
METHODS OF ECONOMICS ANALYSIS
Deductive Method
This is can also be defined as priori reasoning. It start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical
analysis or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
Inductive Methods
Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates
principles using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
127. Name:Ani Chinenye Christianah
Department: Philosophy
Reg no.:21347085CA
Email: chinenyeani122@yahoo.com
Economic analysis is the evaluation of costs and benefits,it is the ranking of projects based on economic viability to aid a better allocation of resources.
They are two basic methods of economic analysis, namely Deductive and Inductive methods of analysis.
1).Deductive Method; Deductive reasoning means being able to get information from two or more statements and draw a logical conclusion.Deductive reasoning moved from generalities to specific
There are principal steps used in the derivation of economic analysis through deductive method and they are;
A). perception of the problem to be inquired into
B). Refining of the technical terms and making appropriate assumptions
C). Deducing hypothensis which is deriving conclusions from the premises through logical reasoning
D). Testing of the hypothensis that has been deduced.
2). Inductive Methods of Analysis
Inductive Reasoning is a logical thinking process in which multiple premises that are believed to be true are combined to draw a conclusion .It works in the opposite of deductive
reasoning.Inductive method unlike deductive is based on Observations.
There are three ways that can be used for deriving economics principles and they are; Experiments, Observations and Econometric methods.
128. WHAT ARE THE BASIC METHODS OF ANALYSIS USED BY ECONOMIST? BRIEFLY AND CONVINCING DISCUSS EACH OF THEM
The basic method of analysis used by economists are;
1-Deductive method
it can also be known as the analytical abstract,a prior method or hypothetical method,its derives the conclusion From fundamental assumption or from the truth.establish by other methods;its
involves the process of reasoning from certain law or Principe which are assumed to be true to the analysis of the facts.The inference are drawn which are verified against observe facts.
2- Inductive Method
In this method the specific observation and measure,its bring to detect patterns and regulations formulate some tentative hypotheses that we can explore and finally end up developing some general
conclusion or theories.in this case also the gulf can be reduce by economists that proceed from a practical angle to problem of science between practice and it’s done by two forms,
experimentation and statiscal forms.
129. Name:Ani Chinenye Christianah
Department: Philosophy
Reg no.:21347085CA
Email: chinenyeani122@yahoo.com
Economic analysis is the evaluation of costs and benefits,it is the ranking of projects based on economic viability to aid a better allocation of resources.
The deductive method is also known as abstract, analytical and priori method and it represents an abstract approach to the derivation of economic generations.
They are two basic methods of economic analysis, namely Deductive and Inductive methods of analysis.
1).Deductive Method; Deductive reasoning means being able to get information from two or more statements and draw a logical conclusion.Deductive reasoning moved from generalities to specific
There are principal steps used in the derivation of economic analysis through deductive method and they are;
A). perception of the problem to be inquired into
B). Refining of the technical terms and making appropriate assumptions
C). Deducing hypothensis which is deriving conclusions from the premises through logical reasoning
D). Testing of the hypothensis that has been deduced.
2). Inductive Methods of Analysis
Inductive Reasoning is a logical thinking process in which multiple premises that are believed to be true are combined to draw a conclusion .It works in the opposite of deductive
reasoning.Inductive method unlike deductive is based on Observations.
There are three ways that can be used for deriving economics principles and they are; Experiments, Observations and Econometric methods.
130. Name: uzodiegwu Deborah chinelo
Reg no: 20874513EA
Dep: sociology and anthropology
Email: duzodiegwu@gmail.com
Methods of economic Analysis
1. Deductive method
2. Inductive method
Deductive method: deductive method is the theoretical deduction that is considered to be true without being based on observations and experience .it is also know as analytical, abstracts and
priori methods
Steps used in deriving generalisation in deductive method
1. Perception of the problem to be enquired into
2. Finding precisely the technical terms
3. Deduction of hypothesis
4. Testing the hypothesis
Inductive methods: inductive methods derives economic generalisation on the basis of experience and observations. Inductive methods is also know as empirical methods and it makes use of
econometric packages to run their experiment.
Theories used in generalisation of inductive methods
1. Experimentation
3. Statistical or econometric methods
131. Name. Chukwuma Ogochukwu susan
Course. Eco 101
Department. Combined social science
Reg number. 2020/242910
The method of Economics analysis
Deductive method
Inductive method
Deductive method is the analytical abstract or prior method, it derives conclusion from general truth, takes few general principles and applies conclusions.
Steps in deductive method
1perception of the problem to be inquired into
2 Defining of terms
3 Deducing hypothesis
4 Testing of hypothesis
Inductive method involves the process of reasoning from particular fact to general principle, it derives economic generalization on the basis of experimentations, observations and statistical
Steps in inductive method
2Formation of hypothesis
132. Anelechukwu precious kelechi
Reg number: 21268671CF
Email: preciousanelechukwu@gmail.com
Methods of economics Analysis are;
1)Deductive analysis
2)Inductive analysis
1) Deductive analysis: This is concerned with ” developing hypothesis (or hypotheses) based in existing theory and then designing a research strategy to test the hypothesis
It has been stated that Deductive means reasoning from the particular to the general. If a casual relationship or link did obtain on more general circumstances
Deductive approach can be explained by the means of hypothesis,which can be derived from the prepositions of the theory .In other words Deductive approach is concerned with deducting conclusions
from premises or prepositions. Deductive begins with an expected pattern ” that is tested against observations whereas induction begins with observations and seeks to find a pattern within them”.
2) Inductive analysis: This refers to approaches that primarily use detailed readings of raw data to derive concepts,themes or a model through interpretations made from the raw data by a
researcher. The general Inductive approach provides an easily used and systematic set of procedures for analyzing qualitative data that can produce reliable and valid findings. Although the
general Inductive approach is not strong as some analytic strategies for theory or model development,it does provide a simple, straight forward approach for deriving findings in the context of
focused evaluation questions. Many evaluation are likely to find using a general Inductive approach less complicated than using other approaches to qualitative data analysis.
133. Name: ANIH FORTUNE KENECHUKWU
Reg no:20631084EF
Faculty: Vocational and Technical Education
Department: Business Education
Email: fortunekenny111@gmail.com
METHODS OF ECONOMIC ANALYSIS
1. Inductive Method of Economic Analysis
Inductive method which also called empirical method was adopted by the “Historical School of Economists” It involves the process of reasoning from particular facts to general principle,This
method derives economic generalizations on the basis of (i) Experimentations (ii) Observations and (iii) Statistical methods
In this method data is collected about a certain economic phenomenon These are systematically arranged and the general conclusions are drawn from them,For example, we observe 200 persons in the
market We find that nearly 195 persons buy from the cheapest shops Out of the 5 which remains 4 persons buy local products even at higher rate just to patronize their own products while the fifth
is a nonentity From this observation, we can easily draw conclusions that people like to buy from a cheaper shop unless they are guided by patriotism or they are devoid of common sense.
Steps of Inductive Method
i. Observation
ii. Formation of hypothesis
iii. Generalization
iv. Verification
Merits of Inductive Method
i. It is based on facts as such the method is realistic.
ii. In order to test the economic principles, method makes statistical techniques.
iii. Induction method also helps in future investigation.
Demerits of Inductive Method
i. If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
ii. The inductive method is time-consuming and expensive.
2. Deductive Method of Economic Analysis
The deductive method is also named as analytical, abstract or prior method. The deductive method consists in deriving conclusions from general truths, takes few general principles and applies
them draw conclusions.
Steps of Deductive Method
*Perception of the problem to be inquired into
*Defining of terms
*Deducing hypothesis from the assumptions
*Testing of hypothesis
Merits of Deductive Method
i. This method is near to reality. It is less time consuming and less expensive
ii. The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis
iii. The method is simple because it is analytical
Demerits of Deductive Method
i. The deductive method is simple and precise only if the underlying assumptions are valid
ii. The deductive method is highly abstract. It require; a great deal of care to avoid bad logic or faulty economic reasoning
134. Economic analysis involves the formulation of laws and generalization and it is achieved through the methods of Deductive Analysis and Inductive Analysis. The Deductive method also referred to
as priori starts from unchallenged elementary or rudimentary assumptions and then arrives at conclusions using logical analysis or our analytical abilities. This is achieved through different
stages which includes; (I) Observation of task, (ii) Making the hypothesis, and (iii) Testing the hypothesis using more observation. It is a simple method that doesn’t involve the use of any
complex software analysis. Inductive method of analysis is the type that flows from facts to theory. Informations and facts are first collected and then evidence are provided using economic
theory and facts. It involves other methods , namely ; observations, experimentation, and statisticalmethods in formulation of principles. Since it is based on facts, it is more realistic and
135. The Basic Methods of Economic Analysis used by economists are the Deductive Method and the Inductive Method.
Economic generalizations describe the laws or statements of tendencies in various branches of economics, such as production, consumption, exchange, and distribution of income. In the view of
Robbins, monetary generalizations or laws are statements of uniformity which describe human behavior in the allocation of scarce resources between alternative ends.
The generalizations of economics, like the legal guidelines of other sciences, state cause and effect relationships between variables and describe these economic hypotheses which have been found
consistent with facts or, in different words, have been found to be true by empirical evidence. But a distinction may also be drawn between a generalization (law) and a theory.
1. Deductive Method of Economic Analysis:
The deductive method is also called the abstract, analytical, and a priori method, and represents a summary approach to the derivation of economic generalizations and theories.
The principal steps in the process of deriving monetary generalizations through deductive logic are:
(a) Perception of the Problem:
In any scientific enquiry, the analyst or theorist must have a clear idea of the hassle to be enquired into. He must know the significant variables regarding whose conduct and interrelationship
he wants to derive generalizations. The perception of the problem is by no means an easy task.
(b) Definition of Technical Terms and Making of Assumptions:
The next step in the process of deriving economic generalizations is to outline precisely and unambiguously the various technical terms to be used in the analysis, as well as to state clearly the
assumptions he makes to derive generalizations.
Assumptions may be behavioral pertaining to the behavior of the financial variables or they may be technological relating to the state of technology and the endowments. The crucial assumptions
are made on the basis of observations or introspection.
(c) Deducing Hypotheses through Logical Deduction:
The next step in deriving generalizations via deductive logic is deducing hypotheses from the assumptions or premises taken. A hypothesis describes the relationship between factors affecting a
phenomenon; it establishes the cause and impact relationship between the variables having a bearing on the phenomenon.
Then, through a logical process, a hypothesis is deduced from the assumptions made. This logical reasoning may be carried out verbally or it may be performed in symbolic terms using the language
of what is known as symbolic logic.
The geometric or graphic approach is also usually employed to deduce hypotheses about the relationship between factors. Besides, the process of logical deduction may be performed with the help of
more formal mathematics.
(d) Testing or Verification of Hypotheses:
Hypotheses obtained above have to be verified earlier than they are established as generalizations or principles of economics. For the verification of hypotheses, economists can not conduct
controlled experiments due to the fact that they have to discover uniformities in the behavior patterns of man.
We can not do experiments with man under controlled conditions, such as in laboratories, as physical scientists do experiments with inanimate objects of nature and biologists do them with animals
and plants. Therefore, economists have to rely on uncontrolled experience and observations.
The information involving uncontrolled experience about the behavior patterns concerning variables of man and the economy is pretty amply available. The reliance by economists on uncontrolled
experiences, however, does increase the number of observations required to verify the hypotheses or to set up the generalizations.
Merits and Demerits of the Deductive Method:
With the aid of rigorous mathematical logic, economic theories can be developed through the process of deduction, which can efficiently explain economic phenomena. Secondly, through deductive
logic, beneficial economic theories can be derived without the tenuous and detailed collection and evaluation of data which is required under the inductive method.
Thus, as compared to the inductive method, deduction is less time-consuming and less expensive. Thirdly, in view of the limited scope for controlled experimentation in economics, the method of
deduction is an extremely beneficial method of constructing economic theories. This is because a number of forces act simultaneously on an economic phenomenon and it is not possible to dispose
of some of these by means of a controlled experiment.
This indicates the vital importance of deductive logic for building up economic ideas or theories. Fourthly, the use of sophisticated mathematical methods in the deductive approach enables
economists to introduce accuracy and exactness into monetary principles and theories.
In spite of the above-mentioned merits, the shortcomings of the deductive approach should not be overlooked. The use of deductive techniques in deriving economic generalizations requires the use
of high-level competence in logic and theoretical abstraction.
Further, a great demerit of the deductive approach is that, with it, tremendously sophisticated theoretical models based on highly unrealistic assumptions may additionally be developed which do
not have any operational significance. Indeed, such highly irrelevant analytical models with little empirical content and incapable of being used for policy formulation have in fact been
developed by economists. Such fashions are no more than mere “intellectual toys”. If economics is to serve as an instrument of social betterment, the building of such theoretical models having no
operational use should be avoided.
Lastly, in the derivation of monetary hypotheses and conclusions through deductive logic, assumptions play a crucial role. If the assumptions made are such that when removing them,
economic speculation based on them is refuted, then the making of these assumptions is not valid.
Thus, one who uses a deductive approach must always keep in mind to what extent the validity of generalizations derived depends on the assumptions made. For instance, the Keynesian
macroeconomic evaluation is based upon the assumption of a depression-ridden capitalist economy with a lot of excess productive capacity.
Therefore, positive damage has been done in applying the Keynesian theories in the context of developing countries such as ours, where the assumptions made by Keynes do not hold well. Hence, mere
“deductive arm-chair analysis” should be avoided, if the scientific personality of economics is to be maintained.
2. Inductive Method of Economic Analysis
The inductive method, which is also called the empirical method, derives monetary generalizations on the basis of experience and observations. In this method, detailed facts are collected with
regard to a certain economic phenomenon and an effort is then made to arrive at certain generalizations which are observed from the observations collected.
But, it is worth mentioning that the number of observations has to be large if it can yield a legitimate economic generalization. One should not generalize on the basis of very few observations.
There are three approaches which can be used for deriving economic principles and theories.
They are:
(a) Experimentation,
(b) observations,
(c) statistical or econometric methods.
As has been mentioned above, experimentation, that is, the use of contrived experiments, is of limited applicability in economics. First, unlike herbal sciences, which are concerned with
analyzing the behavior of either inanimate objects or obedient animals such as rats and rabbits under the influence of chloroform, economics deals with the behavior of man, who is quite fickle,
wayward, and unmanageable.
Besides, men can’t tolerate the idea of being experimented upon, either individually or collectively. Secondly, an economic phenomenon is the end result of a multiplicity of factors and causes
acting and interacting with each other.
Therefore, financial phenomena do not repeat themselves in the same uniform pattern. Numerous factors acting on a monetary phenomenon ‘disturb’ it and make its exact repetition unlikely. Thus,
as compared with natural phenomena, economic phenomena are of a much less uniform pattern, less repetitive and more variable.
Thirdly, economists study the economic phenomena in which strain groups such as employers’ associations, trade unions, farming lobby, and political parties with their different ideologies play
an indispensable part. Their activities make it difficult to conduct controlled experiments in the financial world. However, in spite of these difficulties, experimental methods can be used in
some fields.
For instance, experiments have been conducted to find out which law of manufacturing is valid, that is, whether the law of diminishing returns, the law of constant returns or the regulation of
increasing returns operate in the real world. Besides, public undertakings or big industrial firms frequently try to assess the effect of the changes in the prices of their products on the demand
for them and thus find out the demand elasticity of their products.
Various Steps in the Inductive Method:
Various steps are taken in developing economic theories through the inductive method. The first step, as in the deductive approach, is to identify the problem. The 2nd step is defining technical
terms and variables related to the problem.
It is the next step which is peculiar to the inductive method, namely, the series of data about the variables related to the problem and doing some preliminary thinking about
the viable functional relationships between the relevant variables.
The next important step in the development of economic theories in this method is the processing of data collected and discovering what relations between the variables actually hold. From this, a
theory is developed which can be refined and tested through statistical methods.
Once the theory has been developed, one can make predictions on its basis, as is completed in the deductive approach. If predictions of the theory are in agreement with the facts and
actual conduct of the economy, then a new reliable theory has been developed. If a new theory explains “how things work” better than the existing ones, it replaces them.
Evaluation of the Inductive Method:
As has been explained above, observations of facts through series of detailed data and the use of statistical methods to arrive at economic generalizations organising relationships between facts
are being increasingly made.
Some of the recent research in the field of macroeconomics, such as the nature of consumption feature describing the relationship between income and consumption, and the principle of acceleration
describing the factors which determine funding in the economy, have been obtained through the use of mainly inductive methods.
The inductive technique has another limitation in that there is a great risk of conclusions being drawn from inadequate data. To obtain generalizations through the inductive method, one should
take care that a sufficient range of observations or data has been taken into account.
Besides, the collection of data itself is also no longer an easy task. And a researcher who wants to employ the inductive method to arrive at generalizations has to have good knowledge of
statistical methods. That is, he must know the art of collecting, processing, and interpreting data. It is obvious that, as compared with the deductive method, the inductive method is
time-consuming and expensive.
136. Economic analysis involves the formulation of laws and generalization and it is achieved through the methods of Deductive Analysis and Inductive Analysis.
The Deductive method also referred to as priori starts from unchallenged elementary or rudimentary assumptions and then arrives at conclusions using logical analysis or our analytical abilities.
This is achieved through different stages which includes; (I) Observation of task, (ii) Making the hypothesis, and (iii) Testing the hypothesis using more observation. It is a simple method that
doesn’t involve the use of any complex software analysis.
Inductive method of analysis is the type that flows from facts to theory. Informations and facts are first collected and then evidence are provided using economic theory and facts. It involves
other methods , namely ; observations, experimentation, and statisticalmethods in formulation of principles. Since it is based on facts, it is more realistic and reliable.
137. Methods of economics analysis
1, deductive method :it is also called abstract analytical and priori method and it represents an abstract approach to the derivation of economics generalization and theories , here, we start
with fundamental fact and after adding some assumptions ,we build a theory , in the method we proceed from general to particular
Deductive methods comprises of three stages 1, observation 2,deductive reasoning 3,instance and testing by means of further observation
Merits of deductive methods 1,it’s simple ,2,it obviates the necessity of experimentation ,3,it results in accuracy and exactness
Demerits 1,it is based mainly on assumptions ,2,there’s too much abstraction .,3,it’s generalisation started on wrong presumptions will be dangerous when such generalization claims universal
2, inductive method :in this method, economists proceed from a practical angle to problem of science to reduce the gulf between theory and practice . It is done in two ways, 1,experimentation and
2,statistical form . Facts are collected first , arranged and conclusions are drawn , then these general conclusion are further verified with reference to actual fact
Merits of inductive method 1, it is highly practical , it describes things as they are 2, it is helpful in verifying the conclusion of the deductive methods
Demerits of inductive methods 1, when the investigators lack a balances judgement 2,collection of facts in inductive process is highly complex and complicated job warranting extraordinary
understanding to differentiate economic from non- economic factor ,3,mere induction alone will not deliver goods unless , it it supplemented by means of deductive reasoning .
In summary the two methods have to be made use of or blended to achieve the required objective . The two methods are not competitive but complementary in nature helping invigilator
138. WHAT ARE THE BASIC METHODS OF ANALYSIS USED BY ECONOMIST? BRIEFLY AND CONVINCING DISCUSS EACH OF THEM
The basic method of analysis used by economists are;
1-Deductive method
it can also be known as the analytical abstract,a prior method or hypothetical method,its derives the conclusion From fundamental assumption or from the truth.establish by other methods;its
involves the process of reasoning from certain law or Principe which are assumed to be true to the analysis of the facts.The inference are drawn which are verified against observe facts.
2- Inductive Method
In this method the specific observation and measure,its bring to detect patterns and regulations formulate some tentative hypotheses that we can explore and finally end up developing some general
conclusion or theories.in this case also the gulf can be reduce by economists that proceed from a practical angle to problem of science between practice and it’s done by two forms,
experimentation and statiscal forms.
139. Name: Sylvanus favour chinagorom
Matric no:2020/242141
Email address :sylvanusfavourchi7@gmail.com
METHODS OF ECONOMIC ANALYSIS
Any economic analysis involves the formulation of laws and generalization.Economist use two methods in the analysis. The include:
*DEDUCTIVE METHODS.
*Inductive method involves the use of reasoning from particular fact to general principle. The process for this method are,observation, formulation of hypothesis, general principle, verifying
against actual facts.
Deductive method of economic analysis ,we proceed from general to the particular or main facts.that is drawing conclusions for the observation made so far.
140. Name: ANIH FORTUNE KENECHUKWU
Reg no: 20631084EF
Faculty: Vocational and Technical Education
Department: Business Education
Email: fortunekenny111@gmail.com
METHODS OF ECONOMIC ANALYSIS
1. Inductive Method
Inductive method which also called empirical method was adopted by the “Historical School of Economists” It involves the process of reasoning from particular facts to general principle,This
method derives economic generalizations on the basis of
*Statistical methods
In this method data is collected about a certain economic phenomenon These are systematically arranged and the general conclusions are drawn from them,For example, we observe 200 persons in the
market We find that nearly 195 persons buy from the cheapest shops Out of the 5 which remains 4 persons buy local products even at higher rate just to patronize their own products while the fifth
is a nonentity From this observation, we can easily draw conclusions that people like to buy from a cheaper shop unless they are guided by patriotism or they are devoid of common sense.
Steps of Inductive Method
i. Observation
ii. Formation of hypothesis
iii. Generalization
iv. Verification
Merits of Inductive Method
i. It is based on facts as such the method is realistic.
ii. In order to test the economic principles, method makes statistical techniques.
iii. Induction method also helps in future investigation.
Demerits of Inductive Method
i. If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
ii. The inductive method is time-consuming and expensive.
2. Deductive Method
The deductive method is also named as analytical, abstract or prior method. The deductive method consists in deriving conclusions from general truths, takes few general principles and applies
them draw conclusions.
Steps of Deductive Method
*Perception of the problem to be inquired into
*Defining of terms
*Deducing hypothesis from the assumptions
*Testing of hypothesis
Merits of Deductive Method
i. This method is near to reality. It is less time consuming and less expensive
ii. The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis
iii. The method is simple because it is analytical
Demerits of Deductive Method
i. The deductive method is simple and precise only if the underlying assumptions are valid
ii. The deductive method is highly abstract. It require; a great deal of care to avoid bad logic or faulty economic reasoning
141. Name: Chukwu Augustina Chicheta
Martic no: 2020/243289
Department: Public Administration And Local Government
Email: chukwuaugustinac98@gmail.com
The basic method of analysis used by economist are; Deductive method and Inductive method.
1.Deductive method is a process of reasoning from one or more statement to reach conclusions.
In deductive method also known as abstract, analytical represent abstract approach to the derivation of economic generalization and theories.
The steps in the process of deriving economic generalization through deductive method are:
i. perception of the problem.
ii. definition of technical terms and making if assumption.
iii. deducing hypothesis through logical deduction.
iv. verification of hypothesis.
2. Inductive method of analysis is a method of reasoning in which statements are viewed as supplying some evidence, but not full assurance of the truth of the conclusion.
In this method of reasoning, one’s experiences and observations, including what is learned from others, are synthesized to come up with a general truth.
The followings are the steps in developing economic theories through inductive method:
i. Identifying the problem.
ii. defining technical terms and variables related to the problem.
iii. Collection of data.
iv. construction of economic theories.
142. Method of economics analysis:
An economic analysis involves the formulation of laws and generations through two method deductiveand inductive method
1:Deductivemethod.: known as abstract or analytical method.the deductive method consist in deriving conclusion from general all truth only few principle applies them conclusion for instance: if
we accept the general proposition that man is entirely motivated by self interest in applying the deductive method of economic analysis ,we proceed from general to particular.step involves in
deductive method (a). testing of hypothesis (b) defining of terms etc.
2: inductive method: which is also called empirical method was adopted by the historical school of economist it involves the process of reasoning from particular facts to general principle .this
method derives economics generalization on the basis. 1) experimentation 2) observation and statistical method in this method data is collected about a certain economic phenomenon these
systematically arranged and the general conclusion are drawn from them step involved are observation:
*Generaralization and formation of hypothesis
143. NAME: ONUIGBO ADAEZE JENNIFER
MATRIC NUMBER: 2020/242608
METHODS OF ECONOMIC ANALYSIS
Any economic analysis involves the formulation of laws and generalizations through two methods;
1. Deductive Method
2. Inducive Method
1. DEDUCTIVE METHOD: Here, economist observea and form certain assumptions ( elementary) or facts and then arrive at buildings hypothesis or theory using logical analysis or our own analytical
abilities. They go from general to specific reasoning. It is a simple method and doesn’t require complex software analysis etc. The stages in deductive reasoning are;
1. Observation
2. Hypothesis
3. Testing hypothesis
If the hypothesis gets verified it becomes economic principles/laws and if it fails, the economist returns and look for another or an alternate hypothesis for the observation.
PATTERN FOR DEDUCTIVE METHOD;
OBSERVATION ( INFORMATION AND PATTERN)
TENTATIVE HYPOTHESIS
2. INDUCIVE METHOD: This type of reasoning flows from facts to theory. First, we collect information and facts and then more towards providing evidence using economic theory and facts. This
method formulates principle using sub-methods; observations, experimentations, statistical methods. Data is collected about a particular economic theory and then conclusions are drawn. The stages
here include;
1. Observation
2. Formulation of hypothesis
3. Generalization of principles
4. Verifying against actual facts.
PATTERN FOR INDUCIVE METHOD:
144. Okelekwe Chiamaka Mediatrix
Department of Economics
Qs: Briefly discuss on the basic method of economic analysis
There mainly two basic method of economic analysis
1. Deductive analysis
2. Inductive analysis
1. Deductive analysis: also called prori reasoning. It starts from unchallenged elementary or rudimentary assumptions or facts and then arrive at conclusions using logical analysis. It usually
goes from general to specific. The stages involved are:
a. Observation of a task
b. Making hypothesis
c. Testing the hypothesis using more observations
There are advantages and disadvantages using this method
Advantages: it is a simple method that doesn’t involve the use of a complex software analysis. It is also good for economists as it only involves the use of economic reasoning.
Disadvantages: This method of reasoning starts from mere assumptions which can be logically flawed which then makes it unreliable for use.
2. Inductive method: this type of reasoning flows from facts to thoery. First of all, there is collection of information and facts and then moving towards providing evidence using economic theory
and facts. The stages are:
a. Observation
b. Formulation
c. Generalizing principle
d. Verifying against actual fact.
There are also advantages and disaOkelekwe Chiamaka Mediatrixdvantages of using this method
Advantages: since it based in facts is more reliable and realistic. More so, seeing that it uses statistical method of experiment, the process is scientific.
Disadvantages: if the data collected is insufficient and faulty then the conclusion cannot be trusted. It is also expensive and time consuming.
145. Chukwu Emmanuel Ugonna
What are the basic methods of analysis used by economists? Briefly and convincingly discuss each of them.
Deductive Method;
This is also called “priori reasoning”. A deductive approach to research and observation is the one that people typically liaise with scientific investigation. The researcher studies and take
note of what others have done, reads existing theories/archives of whatever phenomenon he or she is studying and then tests the hypothesis that come forth from those theories, in brief this
method aims at testing existing theories.
Inductive Method;
This method objective or prime goal is to generate theories based on specific instances of experimental observations. It refers to approaches that primarily use detailed list of data to bring out
concepts. In brief inductive method aims at developing a theory.
146. NAME: OKORAFOR CHINONYEREM MGBO
MATRIC NUMBER:2020/242636
DEPARTMENT: ECONOMICS
COURSE CODE: ECO 101
COURSE TITLE: PRINCIPLES OF ECONOMICS
Deductive method a way of reasoning whereby a new true statement is formulated from several true statements (assumptions) following the rules of logic. Deductive reasoning has a status of proof.
In the wide sense, deductive method is a cognitive operation in which new knowledge is logically obtained from a system of available certified knowledge. Deductive method is the main method of
investigation in economics.
Inductive method is method of reasoning based on empirical observations. It allows for conclusions about the whole to be drawn based on evidence to given by samples(certain economic phenomenon).
Simply put, it allows one to reason from the parts to establish the whole.
147. Name:Nwosu Uchenna E.
Reg number:20011956BF
Dept.Business Education
Faculty:Vocational Technical education
Methods of Economic Analysis
Like any other science, Economics adopts two important methods in its investigations and formulation of laws and principles. The two methods are:
Deductive Methods and
Inductive Methods
1.Deductive method:Here we start with certain formal data and assumptions. Then by logical reasoning we arrive at certain conclusions. We start with undisputed fundamental facts and after adding
some assumptions we build up a theory. For instance, it is assumed that businessmen aim at maximum profit. It follows from this that businessmen buy the materials in the cheapest market and sell
it in the dearest market.
In Deductive method of Economic Analysis we proceed from the general to the particular. This is also known as an an hypothetical for some of the assumptions may not correspond to actual facts,
but very near actual facts which may be used as premise for starting, reasoning and drawing conclusions. In economics we start with very simple premises and work up gradually or more and more
complex hypotheses.
A complete form of deductive method consists of three stages and they are;
deductive reasoning and
instance and testing by means of further observations.
2.Inductive method:In this method, economists proceed from a practical angle to problems of science to reduce the gulf between theory and practice. Induction is done by two forms, viz.
experimentation and statistical form. Facts are collected first, arranged and conclusions are drawn. Then these general conclusions are further verified with reference to actual facts.
The inductive method is generally associated with the statistical form of inductions. The statistical approach has a larger field in economic investigations than the method of experimentation.
Further, the method of statistical induction is indispensable for the formulation of economic policy. Malthus presented his famous theory of population only after studying the facts of population
in various countries; He then used statistics to support his theory. Similarly Engel, the German statistician employed inductive method and used statistics to formulate his law of consumption.
148. THE BASIC METHOD OF ECONOMIC ANALYSIS
The basic method of analysis used by economists are classified into the deductive reasoning and inductive reasoning.
1.) The deductive reasoning: it is also called analytical, abstract or prior method. the deductive method consists in deriving conclusions from general truths, takes few general principles and
applies them then draw conclusion.
Steps of Deductive Method:
The main steps involved in deductive logic are as under:
(i) Perception of the problem to be inquired into: In the process of deriving economic generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.
(ii) Defining of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should also be precise.
(iii) Deducing hypothesis from the assumptions: The third step in deriving generalizations is deducing hypothesis from the assumptions taken.
The merits are:
(i) This method is near to reality. It is less time consuming and less expensive.
(ii) The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis.
(iii) There being limited scope of experimentation, the method helps in deriving economic theories.
(iv) The method is simple because it is analytical.
(iv) Testing of hypothesis: Before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
(Their inverse relationship between price and quantity demanded of a good is a well established generalization).
The demerits are:
(i) The deductive method is highly abstract. It require; a great deal of care to avoid bad logic or faulty economic reasoning.
(i) The deductive method is simple and precise only if underlying assumptions are valid.
2.) The inductive reasoning: it is also called empirical method and was adopted by the historical school of economists. it involves the process of reasoning from particular facts to general
This method derives economic generalization on the basics of (i) Experiment (ii) Observation (iii)Statistical methods.
Steps of Inductive Method: the main steps are
(i) Observation.
(ii) Formation of hypothesis.
(iii) Generalization.
(iv) Verification.
Merits of Inductive Method:
(i) It is based on facts as such the method is realistic.
(ii) It is dynamic and also helps in future investigation
Demerits of Inductive Method:
The main weaknesses of this method are as under:
(i) If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
(ii) The collection of data itself is not an easy task. The sources and methods employed in the collection of data differ from investigator to investigator. The results, therefore, may differ
even with the same problem.
(iii) The inductive method is time-consuming and expensive.
□ THE BASIC METHOD OF ECONOMIC ANALYSIS
The basic method of analysis used by economists are classified into the deductive reasoning and inductive reasoning.
1.) The deductive reasoning: it is also called analytical, abstract or prior method. the deductive method consists in deriving conclusions from general truths, takes few general principles
and applies them then draw conclusion.
Steps of Deductive Method:
The main steps involved in deductive logic are as under:
(i) Perception of the problem to be inquired into: In the process of deriving economic generalizations, the analyst must have a clear and precise idea of the problem to be inquired into.
(ii) Defining of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should also be precise.
(iii) Deducing hypothesis from the assumptions: The third step in deriving generalizations is deducing hypothesis from the assumptions taken.
The merits are:
(i) This method is near to reality. It is less time consuming and less expensive.
(ii) The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis.
(iii) There being limited scope of experimentation, the method helps in deriving economic theories.
(iv) The method is simple because it is analytical.
(iv) Testing of hypothesis: Before establishing laws or generalizations, hypothesis should be verified through direct observations of events in the rear world and through statistical methods.
(Their inverse relationship between price and quantity demanded of a good is a well established generalization).
The demerits are:
(i) The deductive method is highly abstract. It require; a great deal of care to avoid bad logic or faulty economic reasoning.
(i) The deductive method is simple and precise only if underlying assumptions are valid.
2.) The inductive reasoning: it is also called empirical method and was adopted by the historical school of economists. it involves the process of reasoning from particular facts to general
This method derives economic generalization on the basics of (i) Experiment (ii) Observation (iii)Statistical methods.
Steps of Inductive Method: the main steps are
(i) Observation.
(ii) Formation of hypothesis.
(iii) Generalization.
(iv) Verification.
Merits of Inductive Method:
(i) It is based on facts as such the method is realistic.
(ii) It is dynamic and also helps in future investigation
Demerits of Inductive Method:
The main weaknesses of this method are as under:
(i) If conclusions drawn from insufficient data, the generalizations obtained may be faulty.
(ii) The collection of data itself is not an easy task. The sources and methods employed in the collection of data differ from investigator to investigator. The results, therefore, may differ
even with the same problem.
(iii) The inductive method is time-consuming and expensive.
149. Name: Nweze Kingsley Ifeanyi
Jamb reg: 20679046BF
Faculty: Vocational and Technical Education
Department: Business Education
Email: nwezeikechukwujohnmartin@gmail.com
There are two types of Economist Analysis
1. Deductive method
2. Inductive method
Deductive method is also known analytical abstract a priori method.Deductive method make use of a certain data and assumption and by logical reasoning it will arrive at certain conclusions.For
instance,it is assumed that businessmen aim at maximum profit.it says that businessmen buy the materials in the cheapest market and sell it in the dearest market where they will make profit.In
Deductive method of Economist Analysis we proceed from the general to the particular.This is also known as an hypothetical method for some of some of the assumptions may not correspond to actual
facts,but very near actual facts which may be used as premise for starting, reasoning and drawing conclusions.
A complete form of deductive method consists of these stages;
ii.deductive reasoning
iii.Instance and testing by means of further observation.
Inductive method.
In this method,economists proceed from a practical angle to problems of science to reduce the gulf between theory and practice. Inductive is done by two form; Experimentation and Statistical
form.Here facts are collected first,arranged and conclusions are drawn.
The Inductive method is generally associated with the statistical form of induction. The statistical approach has larger field in economic investigations than the experimentation method.
In conclusion,the two methods, Inductive and Deductive are very important in economics analysis.Both of them are complementary to each other.
150. Name: Ezeka ChiNaza Bella
Department:Eco 101
Reg. Number: 20167946BF
Faculty: VTE
1.Deductive method :in deductive method of economic analysis we proceed from the general to the particular. Tips is also known as an hypothetical method for some of the assumptions may not
correspond to actual facts which may be used as premise for starting, reasoning and drawing conclusions.
The methods are as follows:
A.perception of the problem to inquire into.
B.define precisely the technical term.
2. Inductive Method:
The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected with regard to
a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
But, it is worth mentioning that the number of observations has to be large if it can yield a valid economic generalisation. One should not generalise on the basis of a very few observations.
There are three ways which can be used for deriving economic principles and theories.
They are:
(a) Experimentation,
(b) observations,
(c) statistical or econometric method.
As has been mentioned above, the experimentation, that is, the use of contrived experiments is of limited applicability in economics. First, unlike natural sciences which are concerned with
analysing the behaviour of either inanimate objects or obedient animals such as rats and rabbits under the influence of chloroform, economics deals with the behaviour of man who is quite fickle,
wayward and unmanageable.
Besides, man cannot tolerate the idea of being experimented upon, either individually or collectively. Secondly, an economic phenomenon is the result of multiplicity of factors and causes acting
and interacting upon each other.
Therefore, economic phenomenon does not repeat itself in the same uniform pattern. Numerous factors acting on an economic phenomenon ‘disturb’ it and make its exact repetition unlikely. Thus, as
compared with the natural phenomena, economic phenomena are of less uniform pattern, less repetitive and more variable.
Thirdly, economists study the economic phenomena in which pressure groups such as employers’ associations, trade unions, farming lobby, political parties with their different ideologies play a
crucial part and their activities render it difficult to make controlled experiments in the economic world. However, in spite of these difficulties, experimental method can be used in some
For instance, experiments have been conducted to find out which law of production is valid, that is, whether law of diminishing returns, law of constant returns or law of increasing returns
operates in the real world. Besides, public undertakings or big industrial firms often try to assess the effect of the changes in the prices of their products on the demand for it and thus find
out the demand elasticity of their products.
151. Okechukwu prosper
Matric no:2020/242139
Basic methods of economics analysis are:
1.Inductive method
2.Deductive method
1.Inductive method which is also known as empirical method.it involves logical thinking that combines observations with experiented information to reach a conclusion.It is aimed at developing a
2.Deductive method which is also called abstract, analytical,or priori method represent an abstract approach to the derivative of economic generalization and theories.It is aims at testing an
existing theory.it can also be called hypothetical method for some of the actions may not correspond to actual fact, but very near actual facts which may be used as premises for starting,
reasoning and drawing conclusions.
152. METHOD OF ECONOMICS ANALYSIS
Economics analysis involves formulation of laws and generalizations
(1)Deductive Method
This is also called priori reasoning. It’s start from unchallenged elementary or rudimentary assumption /facts and when arrive at conclusions (build a hypothesis or theory) using logical analysis
or own analytical abilities.in these kind of reasoning we go from general to specific.
-observation of a task/issue
-making the hypothesis
-testing the hypothesis using more observation.
Advantage of deductive method
(1)It doesn’t involve the use of any complex software analysis.
(2)This method is important for economists as it focuses upon economics reasoning which is of paramount importance.
Disadvantages of deductive method
(1) it starts from assumptions,thus if the assumption happen to be logically flawed the whole process become faulty and would give wrong conclusions.
INDUCTIVE METHOD
This type of reasoning flows from facts of theory. First we collect information and facts then move towards providing evidence using economic theory and facts. This method formulates principles
using the sub-method -observation, Experimentation, Statistical method
Stages in Inductive method
(2)Formulation of hypothesis
(3)Generalizing principles
(4)Verifying against actual facts
Advantages of Inductive method
-since it is based on facts it is more realistic and reliable.
-Using statistical method and experimentations makes the process more scientific thus, more acceptable universally rather than just depending on your own reasoning and logic.
-Since the economic environment is dynamic and always changing, relying upon a more scientific method always help reach logical conclusion.
Disadvantages of inductive method
(1)if data used is insufficient and faulty, it will lead to faulty conclusions, making the hypothesis less reliable.
(2) it is a time -consuming process and thus expensive as well.
(3) the collection of the data is not an easy job and varies from person to person, as how they collect data.
Two types of economic analysis
Deduction Means reasoning or inference from the general to the particular or from the universal to the individual. The deductive method derives new conclusions from fundamental assumptions or from
truth established by other methods. It involves the process of reasoning from certain laws or principles, which are assumed to be true, to the analysis of facts.
Then inferences are drawn which are verified against observed facts. Bacon described deduction as a “descending process” in which we proceed from a general principle to its consequences. Mill
characterised it as a priori method, while others called it abstract and analytical.
Deduction involves four steps: (1) Selecting the problem. (2) The formulation of assumptions on the basis of which the problem is to be explored. (3) The formulation of hypothesis through the process
of logical reasoning whereby inferences are drawn. (4) Verifying the hypothesis. These steps are discussed as under.
(1) Selecting the problem:
The problem which an investigator selects for enquiry must be stated clearly. It may be very wide like poverty, unemployment, inflation, etc. or narrow relating to an industry. The narrower the
problem the better it would be to conduct the enquiry.
(2) Formulating Assumptions:
The next step in deduction is the framing of assumptions which are the basis of hypothesis. To be fruitful for enquiry, the assumption must be general. In any economic enquiry, more than one set of
assumptions should be made in terms of which a hypothesis may be formulated.
(3) Formulating Hypothesis:
The next step is to formulate a hypothesis on the basis of logical reasoning whereby conclusions are drawn from the propositions. This is done in two ways: First, through logical deduction. If and
because relationships (p) and (q) all exist, then this necessarily implies that relationship (r) exists as well. Mathematics is mostly used in these methods of logical deduction.
(4) Testing and Verifying the Hypothesis:
The final step in the deductive method is to test and verify the hypothesis. For this purpose, economists now use statistical and econometric methods. Verification consists in confirming whether the
hypothesis is in agreement with facts. A hypothesis is true or not can be verified by observation and experiment. Since economics is concerned with human behaviour, there are problems in making
observation and testing a hypothesis.
For example, the hypothesis that firms always attempt to maximise profits, rests upon the observation that some firms do behave in this way. This premise is based on a priori knowledge which will
continue to be accepted so long as conclusions deduced from it are consistent with the facts. So the hypothesis stands verified. If the hypothesis is not confirmed, it can be argued that the
hypothesis was correct but the results are contradictory due to special circumstances.
Under these conditions, the hypothesis may turn out to the wrong. In economics, most hypotheses remain unverified because of the complexity of factors involved in human behaviour which, in turn,
depend upon social, political and economic factors. Moreover, controlled experiments in a laboratory are not possible in economics. So the majority of hypotheses remain untested and unverified in
Merits of Deductive Method:
The deductive method has many advantages.
(1) Real:
It is the method of “intellectual experiment,” according to Boulding. Since the actual world is very complicated, “what we do is to postulate in our own minds economic systems which are simpler than
reality but more easy to grasp. We then work out the relationship in these simplified systems and by introducing more and more complete assumptions, finally work up to the consideration of reality
itself.” Thus, this method is nearer to reality.
(2) Simple:
The deductive method is simple because it is analytical. It involves abstraction and simplifies a complex problem by dividing it into component parts. Further, the hypothetical conditions are so
chosen as to make the problem very simple, and then inferences are deduced from them.
(3) Powerful:
It is a powerful method of analysis for deducing conclusions from certain facts. As pointed out by Cairnes, The method of deduction is incomparably, when conducted under proper checks, the most
powerful instrument of discovery ever wielded by human intelligence.
(4) Exact:
The use of statistics, mathematics and econometrics in deduction brings exactness and clarity in economic analysis. The mathematically trained economist is able to deduce inferences in a short time
and make analogies with other generalisations and theories. Further, the use of the mathematical-deductive method helps in revealing inconsistencies in economic analysis.
(5) Indispensable:
The use of deductive method is indispensable in sciences like economics where experimentation is not possible. As pointed out by Gide and Rist, “In a science like political economy, where experiment
is practically impossible, abstraction and analysis afford the only means of escape from those other influences which complicate the problem so much.”
(6) Universal:
The deductive method helps in drawing inferences which are of universal validity because they are based on general principles, such as the law of diminishing returns.
Demerits of Deductive Method:
Despite these merits, much criticism has been levelled against this method by the Historical School which flourished in Germany.
1 .Unrealistic Assumption:
Every hypothesis is based on a set of assumptions. When a hypothesis is tested, assumptions are indirectly tested by comparing their implications with facts. But when facts refute the theory based on
the tested hypothesis, the assumptions are also indirectly refuted. So deduction depends upon the nature of assumptions. If they are unrealistic, in this method, economists use the ceteris paribus
assumption. But other things seldom remain the same which tend to refute theories.
2. Not Universally Applicable:
Often the conclusions derived from deductive reasoning are not applicable universally because the premises from which they are deduced may not hold good at all time and places. For instance, the
classicists assumed in their reasoning that particular conditions prevailing in England of their times were valid universally. This supposition was wrong. Prof. Lerner, therefore, points out that the
deductive method is simply “armchair analysis” which cannot be regarded as universal.
3. Incorrect Verification:
The verification of theories, generalisations or laws in economics is based on observation. And right observation depends upon data which must be correct and adequate. If a hypothesis is deduced from
wrong or inadequate data, the theory will not correspond with facts and will be refuted. For instance, the generalisations of the classicists were based on inadequate data and their theories were
refuted. As pointed out by ircholson, “the great danger of the deductive method lies in the natural aversion to the labour of verification.”
4. Abstract Method:
The deductive method is highly abstract and requires great skill in drawing inferences for various premises. Due to the complexity of certain economic problems, it becomes difficult to apply this
method even at the hands of an expert researcher. More so, when he uses mathematics or econometrics.
5. Static Method:
This method of analysis is based on the assumption that economic conditions remain constant. But economic conditions are continuously changing. Thus this is a static method which fails to make
correct analysis.
6. Intellectually:
The chief defect of the deductive method “lies in the fact that those who follow this method may be absorbed in the framing of intellectual toys and the real world may be forgotten in the
intellectual gymnastics and mathematical treatment.”
The Inductive Method:
Induction “is the process of reasoning from a part to the whole, from particulars to generals or from the individual to the universal.” Bacon described it as “an ascending process” in which facts are
collected, arranged and then general conclusions are drawn.
The inductive method was employed in economics by the German Historical School which sought to develop economics wholly from historical research. The historical or inductive method expects the
economist to be primarily an economic historian who should first collect material, draw gereralisations, and verify the conclusions by applying them to subsequent events. For this, it uses
statistical methods. The Engel’s Law of Family Expenditure and the Malthusian Theory of Population have been derived from inductive reasoning.
The inductive method involves the following steps:
1. The Problem:
In order to arrive at a generalisation concerning an economic phenomenon, the problem should be properly selected and clearly stated.
2. Data:
The second step is the collection, enumeration, classification and analysis of data by using appropriate statistical techniques.
3. Observation:
Data are used to make observation about particular facts concerning the problem.
4. Generalisation:
On the basis of observation, generalisation is logically derived which establishes a general truth from particular facts.
Thus induction is the process in which we arrive at a generalisation on the basis of particular observed facts.
The best example of inductive reasoning in economics is the formulation of the generalisation of diminishing returns. When a Scottish farmer found that in the cultivation of his field an increase in
the amount of labour and capital spent on it was bringing in less than proportionate returns year after year, an economist observed such instances in the case of a number of other farms, and then he
arrived at the generalisation that is known as the Law of Diminishing Returns.
Merits of Inductive Method:
The chief merits of this method are as follows:
(1) Realistic:
The inductive method is realistic because it is based on facts and explains them as they actually are. It is concrete and synthetic because it deals with the subject as a whole and does not divide it
into component parts artificially
(2) Future Enquiries:
Induction helps in future enquiries. By discovering and providing general principles, induction helps future investigations. Once a generalisation is established, it becomes the starting point of
future enquiries.
(3) Statistical Method:
The inductive method makes use of the statistical method. This has made significant improvements in the application of induction for analysing economic problems of wide range. In particular, the
collection of data by governmental and private agencies or macro variables, like national income, general prices, consumption, saving, total employment, etc., has increased the value of this method
and helped governments to formulate economic policies pertaining to the removal of poverty, inequalities, underdevelopment, etc.
(4) Dynamic:
The inductive method is dynamic. In this, changing economic phenomena can be analysed on the basis of experiences, conclusions can be drawn, and appropriate remedial measures can be taken. Thus,
induction suggests new problems to pure theory for their solution from time to time.
(5) Histrico-Relative:
A generalisation drawn under the inductive method is often histrico-relative in economics. Since it is drawn from a particular historical situation, it cannot be applied to all situations unless they
are exactly similar. For instance, India and America differ in their factor endowments. Therefore, it would be wrong to apply the industrial policy which was followed in America in the late
nineteenth century to present day India. Thus, the inductive method has the merit of applying generalisations only to related situations or phenomena.
Demerits of Inductive Method:
However, the inductive method is not without its weaknesses which are discussed below.
(1) Misenterpretation of Data:
Induction relies on statistical numbers for analysis that “can be misused and misinterpreted when the assumptions which are required for their use are forgotten.”
(2) Uncertain Conclusions:
Boulding points out that “statistical information can only give us propositions whose truth is more or less probable it can never give us certainty.”
(3) Lacks Concreteness:
Definitions, sources and methods used in statistical analysis differ from investigator to investigator even for the same problem, as for instance in the case of national income accounts. Thus,
statistical techniques lack concreteness.
(4) Costly Method:
The inductive method is not only time-consuming but also costly. It involves detailed and painstaking processes of collection, classification, analyses and interpretation of data on the part of
trained and expert investigators and analysts
(5) Difficult to Prove Hypothesis:
Again the use of statistics in induction cannot prove a hypothesis. It can only show that the hypothesis is not inconsistent with the known facts. In reality, collection of data is not illuminating
unless it is related to a hypothesis.
(6) Controlled Experimentation not Possible in Economics:
Besides the statistical method, the other method used in induction is of controlled experimentation. This method is extremely useful in natural and physical sciences which deal with matter. But
unlike the natural sciences, there is little scope for experimentation in economics because economics deals with human behaviour which differs from person to person and from place to place.
Further, economic phenomena are very complex as they relate to man who does not act rationally. Some of his actions are also bound by the legal and social institutions of the society in which he
lives. Thus, the scope for controlled experiments in inductive economics is very little. As pointed Out by Friendman, “The absence of controlled experiments in economics renders the weeding out of
unsuccessful hypo-these slow and difficult.”
The above analysis reveals that independently neither deduction nor induction is helpful in scientific enquiry. In reality, both deduction and induction are related to each other because of some
facts. They are the two forms of logic that are complementary and co-relative and help establish the truth.
Marshall also supported the complementary nature of the two methods when he quoted Schmoller: “Induction and deduction are both needed for scientific thought as the right and left foot are needed for
walking.” And then Marshall stressed the need and use of integrating these methods.
Name:Ani Emmanuella Ngozi
Reg no : 20633789BA
Dep: Business Education
The methods use in economics analysis are
Deductive and Inductive method
1)Deductive /abstract method : we start with certain formal data and assumption , but by logical reason we arrive at certain conclusion,we start with undisputed fundermental fact and after adding
some assumption,we build up a theory and in this method assumptions may not correspond to actual fact, when this happens it is HYPOTHETICAL method .
2)Inductive /empirical method :in this method detailed data are collected with regard to a certain economic phenomenon and effort is then made to arrive at certain generalization which follow from
the observation collected ,one should not generalize on the basis of a very few but in large way .
In this method we make use of econometric package to run the experiment
Name: Benjamin Revelation Chiemerie.
Reg number:20690724FA
Department: Nursing Sciences
Email: revelationchiemerie0@mail.com.
Generalisation in economic analysis have been derived in two ways.
1. Deductive Mettod: The deductive Mettod of generalisation is also called the abstract, analytical and a priori Mettod and represent an abstract approach to the derivation of economic generalisation
and theories, this is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions facts and then arrive at conclusion building a hypothesis and theory using our
logical analysis or our own analytical abilities.there are stages in deductive reasoning which are;
1. Observation of a task issue
2. Making the hypothesis
3. Testing the hypothesis using more observation.
1. It doesn’t involve the use of any complex software analysis
2. This Mettod is important for economist as it focuses upon economic reasoning which is Paramount importance.
1. Logical Fallacy.
INDUCTIVE METTOD: This is also called Emperical Mettod derives economic generalisation on the basis of experience and observation in this Mettod detailed data are called with regard to a certain
economic phenomenon and effort is then made arrive at certain fact. this type of reasoning flows from facts to theory,we collect information and facts and then move towards providing evidence using
economic theory and facts. This Mettod fumulate principles using the sub-mettods which are:
1. Observation
3. Statistical Mettod.
1. It is based on facts
2. It is dynamic and always change.
1. It makes data insufficient.
2. It has faulty conclusion
NAME: Ndufuechi Oluchukwu .J.
FACULTY: Health Science and Technology
DEPARTMENT: Nursing Sciences
REG.NO: 20122383CA
Economic Analysis involves the formulation of law and its generalization through two major methods, DEDUCTIVE and INDUCTIVE method.
1.DEDUCTIVE METHOD: In this method, hypothesis or theory is built using logical abilities or analytical abilities and when verified we get general economic reasoning or law. In this reasoning, we go
from general to specific. This is also called ‘A Priori Reasoning’
The stages in this method involve;
a) Information/assumption/perception.
b) Observation of a task or issue/Perception
c) Making the hypothesis
d) Testing the hypothesis using more observation
Advantages of Deductive method;
1)The deductive method only requires simple deductive logic, doesn’t involve the use of any complex software analysis and so on. The reasoning starts from assumptions, therefore if the assumptions
are logically flawed/wrong the whole process becomes faulty.
2)This method is also important for economists as it focuses upon economical reading which is of great importance.
2.INDUCTIVE METHOD: In this method, information and facts are collected then move towards providing evidence using economic theory and facts.
The stages in this method involve;
a) Observation
b) Formulation of hypothesis
c) Generalizing principles
d) Verifying against actual facts.
This method formulates principles using; Observation, Experimentation and statistical methods.
Advantages of Inductive Method;
1)This method is more realistic and reliable because it is based on facts.
2)This method is more acceptable universally because it uses statistical methods and experimentations rather than depending on mere reasoning and logic, which makes it more scientific.
3)It is easier to rely on its scientific method because of the dynamic nature of the economical environment.
There are two economic analysis
1.Deductive analysis
2. Inductive analysis
Deductive Method of Economic Analysis
Deductive method is known as the analytical abstract a priori method. Here we start with certain formal data and assumptions. Then by logical reasoning we arrive at certain conclusions. We start with
undisputed fundamental facts and after adding some assumptions we build up a theory. For instance, it is assumed that businessmen aim at maximum profit. It follows from this that businessmen buy the
materials in the cheapest market and sell it in the dearest market.
In Deductive method of Economic Analysis we proceed from the general to the particular. This is also known as an hypothetical method for some of the assumptions may not correspond to actual facts,
but very near actual facts which may be used as premise for starting, reasoning and drawing conclusions. In economics we start with very simple premises and work up gradually or more and more complex
A complete form of deductive method consists of three stages, viz.,
deductive reasoning and
instance and testing by means of further observations.
Deductive reasoning provides us with hypotheses or generalizations. If the hypotheses are tested and verified with relevance to facts, we have valid economic laws.
Advantages of Deductive Method of Economic Analysis
Deductive method has the following ‘merits’
1. Deductive method is exceedingly simple. For example, the law that the utility derived by an individual from a commodity goes on diminishing with every successive addition is a self-evident truth
from which we may draw many logical conclusions, viz., larger the stock of money, the lower shall be the utility of money; rich persons have lesser marginal utility of money than the poor people; so
taxes should not be levied on proportional basis. If taxes are levied proportionately, the sacrifice of the poor will be larger than the rich. This is against the Canon of equity, etc. Thus the
principle of progressive taxation is derived from the law of diminishing utility through deductive reasoning.
2. Deductive method obviates the necessity of experimentation. Economics being a social science, experimentation may not be available as in the case of physics or chemistry. So, the next best
alternative to experiment is deductive reasoning. According to Boulding this method of deductive reasoning is the method of intellectual experiment.
3. The deductive method results in accuracy and exactness in generalization, because of logical reasoning. The method gives a very high standard of precision in abstract economic reasoning.
Disadvantages of Deductive Method of Economic Analysis
Deductive method has its drawbacks also:
1. Deduction is based mainly on assumptions which are perfectly valid. If assumptions are wrong, generalizations made on the basis of wrong assumptions will be imperfect and invalid. All economic
laws are based on too many assumptions where there are more scope for committing errors through wrong hypotheses.
2. In deduction there is too much of abstraction and economists by means of their intellectual exercises produce only “intellectual toys” having little connection with reality.
3. Deductive generalizations started on wrong premises will be dangerous when such generalization claim universal validity. Then such faulty generalizations are made use of in framing government
policies, the results would be nothing but disastrous. For example, J.B.Say, claimed universal validity for his ‘Law of Markets’ in which he maintained that supply creates its own demand and there
will not be over-production in the market. But this celebrated ‘Law of Market’ was torn to pieces when critics proved that Say’s Law was wrong and overproduction would be possible.
Inductive Method of Economic Analysis
In this method, economists proceed from a practical angle to problems of science to reduce the gulf between theory and practice. Induction is done by two forms, viz. experimentation and statistical
form. Facts are collected first, arranged and conclusions are drawn. Then these general conclusions are further verified with reference to actual facts.
The inductive method is generally associated with the statistical form of inductions. The statistical approach has a larger field in economic investigations than the method of experimentation.
Further, the method of statistical induction is indispensable for the formulation of economic policy. Malthus presented his famous theory of population only after studying the facts of population in
various countries; He then used statistics to support his theory. Similarly Engel, the German statistician employed inductive method and used statistics to formulate his law of consumption.
Advantages of Inductive Method of Economic Analysis
Inductive method has the following merits:
1. It is highly practical add realistic as it describes things as they are.
2. It is helpful in verifying the conclusions of the deductive method.
3. Economic laws under this method are not universal but valid only under certain conditions.
Disadvantages of Inductive Method of Economic Analysis
Inductive method has the following limitations:
1. When the investigators lack a balanced judgement there is the risk of drawing hurried conclusions based on inadequate and irrelevant facts and data.
2. Collection of facts in the inductive process is a highly complex and complicated job warranting extraordinary understanding to alienate economic from non-economic factors.
3. Mere induction alone will not deliver goods unless it is supplemented by means of deductive reasoning. Without deduction, the inductive method would result in producing only a mass of unrelated
and unconnected facts.
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Matric number: 20679167HF
Department: Nursing Sciences
Course code: Eco101
Course title: Principles of Economics
Some of the important methods of Economic Analysis include
1) DEDUCTIVE METHOD
This is also called ABSTRACT, ANALYTICAL and PRIORI method and represents an abstract approach to derivation of economic generalizations and theories. Steps in the process of deriving economic
generalizations through deductive logic are
In a scientific enquiry,the theorist or analyst must have a clear idea of the problem to be enquired into. He or she must know the significant variables regarding whose behaviour and
interrelationship he or she wants to derive generalizations. This is by no means an easy task.
This means to define precisely and unambiguously the various technical terms to be used in the analysis as well as to state clearly the assumptions he makes to derive generalizations. Assumptions as
mentioned above, may be behavioral pertaining to the behaviour of the economic variables or they may be technological relating to the state of technology and factor endowments. The crucial
assumptions are made on the basis of observations. Each and every assumption made by a theory may not be realistic. A correct scientific theory or generalization must be expressed in the form of a
hypothesis that is conceivably refutable.
A hypothesis describes relationship between factors affecting a phenomenon; it establishes the cause and effect relationship between the variables having a bearing on the phenomenon. Then through
logical process, hypothesis is deduced from the assumptions made. This logical reasoning may be carried out verbally or it may be conducted in symbolic terms using the language of what is known as
SYMBOLIC LOGIC. The GEOMETRIC or GRAPHIC TECHNIQUE is also usually employed to deduce the hypothesis about the relationship between factors. Besides, the process of logical deduction may be done with
the help of more formal mathematics.
For the verification of hypothesis, economists cannot make controlled experiments, because they have to discover uniformities in behaviour patterns of man. We cannot make experiments with man under
controlled conditions, such as in laboratories as physical scientists make experiments with inanimate objects of mature and biologists make there with animals and plants. So they have to rely on
uncontrolled experience and observations. In the absence of controlled experiments, for the verification of their theories,economists have to rely on the direct observations of events in the real
world. By direct observations, we mean “gathering of information personally or reliance on comparatively unprocessed materials such as files of business firms; to mention but a few.
1) Compared to the inductive method, deductive method is less time consuming and less expensive
2) Useful economic theories can be derived logic without the teinuous and detailed collection and analysis of data which are required under the inductive method
1) The use of deductive method in deriving economic generalizations require the use of high-level competence in logic and theoritical abstractions.
This is also called EMPIRICAL METHOD. It derives economic generalizations on the basis of experience and observations. Detailed data are collected. There are 3 ways which can be used for deriving
economic principles and theories. They are;
A) Experimentations
B) Observations
C) Statistical or economic method
1) Identify the problem
2) Determining technical terms and variables related to the problem
3) Collection of data about the variables related to the problem and during some preliminary thinking about the possible functional relationships between the relevant variables
4) Processing of data collected and finding out what relationship between the variables actually hold goods.
The use of inductive method is not of much value if it is not supported by the economic hypothesis or theory developed by deductivw logic. It can at best be used to empirically test the theory or
hypothesis as to whether it is consistent with or refuted by factor. But there is a general risk of conclusions being drawn from insufficient data.
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1. DEDUCTIVE METHOD:The deductive method is also called abstract analytical and and a prior method and represent an abstract approach. Precisely the technical terms and making of assumptions,
deducing hypothesis and testing the hypothesis, is aslo a process followed in deductive process.Then by logical reason they arrive at a certain conclusions.
2. INDUCTIVE METHOD :It involves observation and measures of deriving economic generalization. In inductive methods facts are collected, arranged and conclusions drawn
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Method of economic analysis.
1. Deductive method: This method of deriving economic analysis and generalization can also be called abstract, analytical and priori method. This method involves the use of reasoning,logic and
hypothesis. Some of its procedures are:
a. Perception of the problem: This means the economist must have an idea on the problem.
b. Defining precisely the technical term.
c. The use of assumption and derivation of hypothesis.
d. Testing of hypothesis.
Advantage of deductive method: It is easy,cheap and simple.
Disadvantage of deductive method: It can be inaccurate because sometimes the assumptions being made can be wrong.
2. Inductive method: This method of deriving economic analysis is also called Empirical method. In this method the economist observes, gathers and uses data inorder to get it’s economic analysis.
Also the use of econometric packages are used for experimentation. Some of the procedures of this method are:
a. Observation and experimentation.
b. Formulation of hypothesis.
c. Generalizing principles.
d. Verifying against actual fact and statistical method.
Advantage of inductive method: It is highly reliable and accurate because data is being gathered and used.
Disadvantage of inductive method: It waste and consumes time. It is also stressful and difficult.
Department: Economics
Reg: 2020/242639
The methods of Economic Analysis
1. Inductive method
This method details the collection of data with regards to a certain economic phenomenon and effort is then made to arrive at certain generalizations which follow the observation collected. It is
neccessary to note that one should not generalize only on a very few observations but large number of observations which can yield a valid generalization.
2. Deductive method
This method consist of deriving conclusion from general truth, takes few general principle and applies them, draw conclusion. For instance, if we accept the general proposition that man is entirely
motivated by self-interest. In applying the deductive method of economic analysis, we proceed from general to particular.
Department: Economics
Reg: 2020/242639
The methods of Economic Analysis
1. Inductive method
This method details the collection of data with regards to a certain economic phenomenon and effort is then made to arrive at certain generalizations which follow the observation collected. It is
neccessary to note that one should not generalize only on a very few observations but large number of observations which can yield a valid generalization.
2. Deductive method
This method consist of deriving conclusion from general truth, takes few general principle and applies them, draw conclusion. For instance, if we accept the general proposition that man is entirely
motivated by self-interest. In applying the deductive method of economic analysis, we proceed from general to particular.
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Basic Methods of Analysis Used by Economists
Economics analysis is defined as the various methodes that Economists use in experiments of models (data)
These are the process and procedures that helps economist during experiment of analysis, observation, construction and investigation of problems to derive an answer.
___ Inductive method
___Deductive method
In Inductive method of analysis, an economist makes use of econometric packages to analyze his data.The econometric packages are
__E – View and
These are the packages used for analysis by using data to test the economy and goes ahead to produce solution (Advice).
In these procedures data are generated through the people’s
An economist takes observation through them to analyze and balance his results which he goes ahead to generate economic advice
In deductive method of analysis, generalization and theory are used in economics based of experiment.
These includes
__perception : this is to perceive the problem and identify the issue to turn generalization to theory.we do this by technical terms of explanation of observation and assumptions of problems for
prove .
__Postulate: this is to assume a result which falls on analysis.
__Hypothesis: this is when an economist goes ahead to compare his analysis with his observation and people’s individual preferences. This actualizes
Alternative hypothesis__this is the end of resul
Null hypothesis __this is the assuming part.
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Department: Combined social sciences (Economics/political science)
Faculty: social sciences
Methods of Economic Analysis:
Some of the most important methods of economic analysis are as follows:
1. Deductive Method
2. Inductive Method.
Economic generalisations describe the laws or statements of tendencies in various branches of economics such as production, consumption, exchange and distribution of in -come. In the view of Robbins,
economic generalisations or laws are statements of uniformities which describe human behaviour in the allocation of scarce resources between alternative ends.
The generalisations of economics like the laws of other sciences, state cause and effect relation ships between variables and describe those economic hypotheses which have been found consistent with
facts or, in other words, have been found to be true by empirical evidence. But a distinction may be drawn between a generalisation (law) and a theory.
A law or generalisation just describes the relationship between variables; it does not provide any explanation of the described relation. On the other hand, a theory provides an explanation of the
stated relation between the variables, that is, it brings out the logical basis of the generalisation. An economic theory or a model derives a generalisation through process of logical reasoning and
explains the conditions under which the stated generalisation will hold true.
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The basic methods of economic analysis are:
a) Inductive method
b) Deductive method
a) Inductive method:It derives economic generalizations on the basis of experience and observations. In this method, detailed data are collected with regard to a certain economic phenomenon and
effort is then made to arrive at certain generalizations which follow from the observations collected. It is also known as Empirical method.
Stages of deriving economic generalizations through inductive method are:
1) Experimentation
2) Observation
3) Statistical or econometric method
Advantages of inductive method
a) Since it is based on facts, it is more realistic and reliable.
b) Using statistical methods and experimentations make the process more scientific, thus more acceptable universally rather than just depending on your own reasoning and logic.
c) Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of inductive method
a) If the data used is insufficient and faulty, it would lead to faulty conclusions making the results less reliable.
b) It is time-consuming and expensive.
c) Collection of all the data is quite stressful and varies from person to person.
d) Deductive method:In this method we go from general reasoning to specific analysis. It is also called abstract, analytical and a priori method and represents an abstract approach to the derivation
of economic generalizations and theories.
Stages of deriving economic generalizations through deductive method
1) Perception of the problem to be inquired about;He must know the significant variable regarding whose behavior and inter-relationship he wants to derive generalizations.
2) Definition of technical terms and making of assumptions;Simplifying assumptions is quite necessary in order to bring out the importance of really significant factors having a bearing on the
problem under investigation. It enables us predict things accurately.
3) Deducing hypotheses through logical deduction;The hypotheses describes the relationship between factors affecting a phenomenon,it establishes the cause and effect relationship between the
variables. Through logical process, hypothesis is deduced from the assumptions made.
4) Testing or verification of hypotheses;Two related distinctions must be borne in mind;first, functional relationship between economic variables and a historically sequence of events must be
distinguished. Second, the actual course of events is governed by several other factors assumed by a generalization which remains constant under the qualification“other things remaining the same”.
Advantages of deductive method
a) It doesn’t involve the use of any complex software analysis, only simple deductive logic is required.
b)It focuses upon economic reasoning which is of paramount importance.
Disadvantage of deductive method
a) Logical fallacy; if the assumptions happen to be logically flawed, the whole process becomes faulty and would give wrong conclusions.
Conclusion:Both methods of economic analysis are complimentary rather than competitive.
Omeje Deborah Mmesoma
Deductive Method derives new conclusion from fundamental assumptions or from truth established by other methods. It involves the process of reasoning from certain laws or principles, which are
assumed to be true, to the analysis of facts. In economics, Deductive method is simple to use because it is analytical, it involves abstraction and simplifies complex problems by deviding it into
different parts. It is also a powerful method for deducing conclusions from facts.
Inductive Method derives economic generalization on the basis of experience and observations. In economics, Inductive method helps in the observation of facts through collection of detailed data and
use of statistical methods to arrive at economic development. Some of the recent researches in the field of macro-economics such as the principle of acceleration describing the factors which
determine investment in the economics have been obtained through the use of Inductive method.
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Economics like every other sciences, employs two essential methods in its investigations and formulation of law and principles. The two methods includes:
1.Deductive method
2. Inductive method
Deductive method is a method of economic analysis that involves the use of logical reasoning to arrive at a conclusion using formal data and assumptions. This method provides us with generalizations
and hypotheses.We have valid economic laws if the hypotheses are tested and verified with relevance to facts.
A complete form of deductive method consist of three stages, viz
1. Observation
2. Deductive reasoning
3. Instance and testing by means of further observation.
The inductive method is sometimes similar to the deductive method. The only thing that differentiates them is that induction uses econometric packages i.e E-views and STATA to run experiment. This
method proceeds from a practical angle to problem of science to reduce the gulf between theory and practice. Induction is done by two form, viz, experimentation and statistical form. Here facts are
first collected, arranged and conclusions are then drawn. Then these general conclusions are further verified with reference to actual facts.
The inductive method is generally associated with the statistical form of induction because statistical approach has a higher field in economic investigations than the method of experiment. The
statistical induction is indispensable for the formulation of economic policy. Malthus and Engel used the statistical induction to present the Theory of Population and Law of Consumption
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Course:Eco 101
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Deductive method: In deductive method of economics analysis we proceed from the general to the particular. This is also known as a hypothetical method for some of the assumption s may not correspond
to actual facts, but very near actual facts which may be used as permise for starting, reasoning and drawing conclusions.
Methods include:
1.Perception of the problem to inquire into.
2. Define precisely the technical terms.
Inductive method: which is also called empirical method was adopted by historical economists. It involves the process of reasoning from particular fact to general principal.
Methods include:
1. Experimentation.
2. Observation.
3. Statistical method.
Name:Anusia goodness tochukwu
Department: Vocational and technical education
Course:Eco 101
Gmail: goodnessanusia@gmail.com
Deductive method: In deductive method of economics analysis we proceed from the general to the particular. This is also known as a hypothetical method for some of the assumption s may not correspond
to actual facts, but very near actual facts which may be used as permise for starting, reasoning and drawing conclusions.
Methods include:
1.Perception of the problem to inquire into.
2. Define precisely the technical terms.
Inductive method: which is also called empirical method was adopted by historical economists. It involves the process of reasoning from particular fact to general principal.
Methods include:
1. Experimentation.
2. Observation.
3. Statistical method.
REG NO_ 2020/242637
_Methods of Economic Analysis_
In economics, broadly we make use of two methods.
(i) Deductive method
(ii) Inductive method
The deductive method is also known as abstract method or analytical method. This method is based on a priori reasoning and conclusions are drawn from certain fundamental assumptions. Deduction method
was very popular among the Greeks. Here is an example :
All men are mortal Socrates is a man Socrates is mortal The deductive method moves from the general assumption to the specific application.
Ricardo, a classical economist, made use of the deductive method.
The inductive method moves from specific observations to generalization. It was Francis Bacon who advocated inductive method in scientific enquiry.
None of the above methods provides satisfactory system for solution of problems. So Darwin, who is famous for this theory of evolution, by introducing the concept of hypothesis, has combined
deductive and inductive methods.
The important elements of Darwin’s deductive-inductive method are:
1 Identification of a problem
2 formulation of hypothesis (a hypothesis is an assumption or an intelligent guess)
3 collection, organization and analysis of data
4 formulation of conclusions
verification, rejection or modification of the hypothesis after testing it.
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Email: emmychi16@gmail.com
There are mainly two basic methods of analysis used by economists :
Deductive method >=> The deductive method is also called abstract, analytical and a priori method and represents an abstract approach to the derivation of economic generalisations and theories. The
principal steps in deriving economic generalizations through deductive logic are: (I) perception of the problem to be enquired into (II) defining the principal terms and making appropriate
assumptions (III) deducing the hypothesis, and then (IV) testing the hypothesis deduced
Inductive method >=> The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are
collected with regard to a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
But, it is worth mentioning that the number of observations has to be large if it can yield a valid economic generalisation. One should not generalise on the basis of a very few observations. There
are three ways which can be used for deriving economic principles and theories. They are:
(a) Experimentation,
(b) observations,
(c) statistical or econometric method.
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Course: eco 101
Faculty: VTE
Dept: Business Education
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1. Deductive (also analytical abstract or prior method): ,it’s consist of deriving conclusions from general truths ,by taking few general truths applying them to draw to conclusion. In deductive
method of Economic Analysis we proceed from the general to the particular. This is also known as an hypothetical method for some of the assumptions may not correspond to actual facts, but very near
actual facts which may be used as premise for starting, reasoning and drawing conclusions. In deductive you take the following steps
I.perception of the problem to be inquired into
ii defining of terms (technical terms used in analysis )
iii deducing hypothesis from assumptions
Iv testing of hypothesis
2 inductive method:it’s starts with the particular and moves to the general . It begins with a particular observation and moves to a general explanation ,it collects observations and develops a
theory to fit the facts . In inductive method the follow steps are maintained
I observation
Ii formation of hypothesis
ii generalization
Iv verification.
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The basic methods of economic analysis are:
*Inductive method
*Deductive method
*Inductive method:It derives economic generalizations on the basis of experience and observations. In this method, detailed data are collected with regard to a certain economic phenomenon and effort
is then made to arrive at certain generalizations which follow from the observations collected. It is also known as Empirical method.
Stages of deriving economic generalizations through inductive method are:
*Statistical or econometric method
Advantages of inductive method
*Since it is based on facts, it is more realistic and reliable.
*Using statistical methods and experimentations make the process more scientific, thus more acceptable universally rather than just depending on your own reasoning and logic.
*Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of inductive method
*If the data used is insufficient and faulty, it would lead to faulty conclusions making the results less reliable.
*It is time-consuming and expensive.
*Collection of all the data is quite stressful and varies from person to person.
*Deductive method:In this method we go from general reasoning to specific analysis. It is also called abstract, analytical and a priori method and represents an abstract approach to the derivation of
economic generalizations and theories.
Stages of deriving economic generalizations through deductive method:
*Perception of the problem to be inquired about;He must know the significant variable regarding whose behavior and inter-relationship he wants to derive generalizations.
*Definition of technical terms and making of assumptions;Simplifying assumptions is quite necessary in order to bring out the importance of really significant factors having a bearing on the problem
under investigation. It enables us predict things accurately.
*Deducing hypotheses through logical deduction;The hypotheses describes the relationship between factors affecting a phenomenon,it establishes the cause and effect relationship between the variables.
Through logical process, hypothesis is deduced from the assumptions made.
*Testing or verification of hypotheses;Two related distinctions must be borne in mind;first, functional relationship between economic variables and a historically sequence of events must be
distinguished. Second, the actual course of events is governed by several other factors assumed by a generalization which remains constant under the qualification“other things remaining the same”.
Advantages of deductive method
*It doesn’t involve the use of any complex software analysis, only simple deductive logic is required.
*It focuses upon economic reasoning which is of paramount importance.
Disadvantage of deductive method
*Logical fallacy; if the assumptions happen to be logically flawed, the whole process becomes faulty and would give wrong conclusions.
Conclusion:Both methods of economic analysis are complimentary rather than competitive.
The two basic methods of analysis used by Economists are Deductive and Inductive method.
1) Deductive Method; This method deals with assumptions/facts and then arrive at certain conclusions using logical analysis or our own analytical abilities. The stages involved in this method are:
I)Observation of the task/issue- there must be a problem to be solved.Here you define the problem precisely.
II)Making hypothesis-Here you make realistic assumptions that are verifiable(postulates).
III) Testing your hypothesis with more observations.
If the hypothesis gets verified, we get economic principles/laws.This method is a simple method that doesn’t involve any complex software analysis and it focuses on economic reasoning which is very
2) Inductive Method:This method formulate principles by using sub-methods (observations, experimentations,statistical methods). The stages involved in this method are;
I) Observation
II) Formulation of hypothesis
III) Generalizing principles
IV) Verifying against actual facts
Since inductive method is based on facts,it is more reliable and realistic. Using statistical methods and experimentations make the process more scientific.
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Level :100level
Reg no: 21276005cf
Course :eco 101
Dep: Business education
1. Deductive (also analytical abstract or prior method): ,it’s consist of deriving conclusions from general truths ,by taking few general truths applying them to draw to conclusion. In deductive
method of Economic Analysis we proceed from the general to the particular. This is also known as an hypothetical method for some of the assumptions may not correspond to actual facts, but very near
actual facts which may be used as premise for starting, reasoning and drawing conclusions. In deductive you take the following steps
I.perception of the problem to be inquired into
ii defining of terms (technical terms used in analysis )
iii deducing hypothesis from assumptions
Iv testing of hypothesis
2 inductive method:it’s starts with the particular and moves to the general . It begins with a particular observation and moves to a general explanation ,it collects observations and develops a
theory to fit the facts . In inductive method the follow steps are maintained
I observation
Ii formation of hypothesis
ii generalization
Iv verification.
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Deductive analysis; this is an approach concerned with developing a hypothesis based on existing theory and then designing a research strategy to test the hypothesis,it means reasoning from the
particular to the general.it begins with an expected pattern that is tested against observation.
Inductive analysis;It refers to the approach that uses detailed reading of raw data to derive concepts and themes.it is used to condense extensive and varied raw data into a brief summary format and
to establish clear links between the research objectives and the summary finding derived from the raw data.
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Nursing sciences
The basic methods of analysis used by economists are: Deductive method and Inductive method
1) Deductive method:
This method represents an approach to the derivation of economic generalisation and theories. In order to derive economic generalisations through deductive logic we begin by identifying the problem,
defining technical terms and relevant variables, making assumptions, processing of logical deduction to derive implication, formulation of hypothesis, making predictions and testing them and finally
making sure the predictions are in agreement with facts.
2) Inductive Method:
The inductive method can also be called Empirical Method. The inductive method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected
with regard to a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
Deductive method: The deductive method is also called abstract, analytical and a priori method and represents an abstract approach to the derivation of economic generalisations and theories.
(a) Perception of the Problem:
In any scientific enquiry, the analyst or theorist must have a clear idea of the problem to be enquired into. He must know the significant variables regarding whose behaviour and interrelationship he
wants to derive generalisations. The perception of the problem is by no means an easy task.
(b) Definition of Technical Terms and Making of Assumptions:
The next step in the process of deriving economic generalisations is to define precisely and unambiguously the various technical terms to be used in the analysis as well as to state clearly the
assumptions he makes to derive generalisations
2. Inductive Method:
The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected with regard to a
certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
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Department: PALG
Deductive method: The deductive method is also called abstract, analytical and a priori method and represents an abstract approach to the derivation of economic generalisations and theories.
(a) Perception of the Problem:
In any scientific enquiry, the analyst or theorist must have a clear idea of the problem to be enquired into. He must know the significant variables regarding whose behaviour and
interrelationship he wants to derive generalisations. The perception of the problem is by no means an easy task.
(b) Definition of Technical Terms and Making of Assumptions:
The next step in the process of deriving economic generalisations is to define precisely and unambiguously the various technical terms to be used in the analysis as well as to state clearly the
assumptions he makes to derive generalisations
2. Inductive Method:
The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected with regard to
a certain economic phenomenon and effort is then made to arrive at certain generalisations
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Department: philosophy
Email: bishopfeargod@gmail.com
The economics methods are:
a. Inductive method and
b. Deductive method
A..Inductive Method:
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates principles
using the sub-methods- Observations, Experimentations, Statistical method.
b. Deductive method of economic analysis involves the process of reasoning analytical and inferring what must necessary follow from a given set of statement that the present will be like the past and
the future will be like the present thought not full assured as change remain constant.
Okeke Juliet Kelechi
Economics dept.
The basic method of economics analysis used by economists are mainly two which are:
(a) Inductive method
(b) Deductive method
(a)Inductive method: it involves the process of reasoning from particular facts to forming a general principle i.e begins with particular observations and moves to general explanations. Inductive
method process can be illustrated as thus :
Observation of the issue——->Formulation of hypothesis——->Generalizing principles——>Verifying principle against actual fact.
(b)Deductive method: It involves the process of reasoning from general principles to a particular fact. It derives new conclusion from existing general theories/principles. Deductive method process
can be illustrated as thus:
Observe an existing theory——-> Formulate hypothesis based on existing theory——-> collect data to verify the hypothesis——-> analyse if the collected data supports the hypothesis.
Name: Caroline Jessica Okeke
Department: Sociology & Anthropology
Matric number: 2020/242834
Email address: carolinejessicaokeke@gmail.com
Every economic analysis necessitate the articulation of laws and conceptions through two methods:
– Deductive reasoning.
-Inductive reasoning.
It begins from undisputed straightforward or introductory facts and then results to resolutions ( construct a hypothesis or theory) using logical analysis or our own analytical abilities. In other
words, it is also called a priori reasoning.
In this form of reasoning, we have 3 stages of deductive reasoning:
– Researching a task.
– Creating hypothesis.
-conducting a test on the hypothesis researched.
This reasoning provides a hypothesis and it is being verified, it results to general economic principle or law.
It is a simple method. It does not involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
This form of reasoning moves from facts to theory. First, Data collection is performed and then providence of evidence using economic theory and facts. This method formulates principles using the
sub-methods- Observations, Experimentations, Statistical methods.
Data collection of a particular economic theory and then conclusions are drawn. The stages in this method are:
-Formulation of a hypothesis.
-Generalizing principles.
-Verifying against actual facts.
Since it is based on facts it is more realistic and reliable.Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just
depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable. It is a time-consuming process and thus expensive as well. The collection of all
the data is not an easy job and varies from person to person. As to how they collect data.
MATRIC. NUMBER: 2018/250299
METHODS OF ECONOMICS ANALYSIS:-In every formulation of generalization, formulations of laws there are steps and methods used to analyze it
1. Deductive Method
2. Inductive Method.
1. Deductive Method: can also be called abstract, analytical and a prior method which represents an abstract approach to derivation of economics generalization through deductive logics.
1. Perception of the problem
2. Precise definition of technical terms and making of assumption(postulates)
3. Deduction of hypotheses
4. Testing of deduced hypotheses.
1. PERCEPTION OF THE PROBLEM: Is any scientific research, the analyst must have a clear idea of the problem to be researched on. There must be significant variables known to him in accordance to the
thing he want to derive generalization on.
2. PRECISE DEFINITION OF TECHNICAL TERMS AND MAKING POSTULATE: This is the next step in deductive economic analysis, It involves explicit definition of various technical terms to be used in the
analysis and clearly stating assumptions. Assumptions may be behaviors pertaining to the behavior of the economic variables or they can be technically related.
3. DEDUCTION OF HYPOTHESES: Hypotheses are deduced from the assumptions or premises taken. Hypothesis explains relationships between factors affecting a phenomenon and establishes cost and effect
relationships between variables.
4 TESTING OF HYPOTHESES: This means verification of the hypotheses and once hypotheses is verified it can be established as generalization or principle of economics.
INDUCTIVE METHOD OF ECONOMICS ANALYSIS: It can also be called empirical method, it derives economic generalization based on experience and observations. It does not accommodate few observations, it
can only be done when very large observations has been made. It uses statistical or Econometric methods.
1.Perception of the problem
2. Precise definition of technical terms and making assumptions
3. Collection of data about the variables
4. Processing of data collected
5. Deduction of hypotheses
6. Testing of hypotheses
1. PERCEPTION OF THE PROBLEM: This is the first step in any scientific research, there must be clear known problem and significant variables known in accordance to the problem.
2. PRECISE DEFINITION OF TECHNICAL TERMS AND MAKING ASSUMPTIONS: it involves simple definition of various technical terms in relation to the course of analysis
And clearly stating the assumptions
3. COLLECTION OF DATA ABOUT THE VARIABLES: Datas should be collected about the variables related to the problem.
4. PROCESSING OF DATA COLLECTED: This helps in finding out the relationships between the variables gathered and doing some preliminary thinking on the possible functional relationships between the
relevant variables.
5. DEDUCTION OF HYPOTHESES: Hypotheses are deduced from the data processed or premises taken. Hypothesis describes relationship between affecting phenomenon. One should endeavor to avoid logical
fallacies in this process.
TESTING OF HYPOTHESES: This means verification of hypotheses, when verified it can be established as generalization.
There are two basic Methods Involved in Economics Analysis Namely:
1. Deductive Method
2. Inductive Method
1. Deductive Method- the method Derives new Conclusion from the fundamental assumption established by other methods.As a Deductive method,it has a prior Reasoning, certain laws and principles which
are assumed to be the analysis of fact .
In Deductive Method,it involves Information, pattern,tenative Hypothesis etc
2. Inductive Method- this method Comes with specific details and ends with an abstract.
The mode of learning becomes more interesting at the outset because of the references students begin with In what they know.
Inductive Method comprises of the theory, hypothesis, observation and confirmation.
Name: umeh success precious
Department: social science education
Reg no:20027052GA
Email: successprecious41@gmail.com
Method of economic analysis is classified into two methods which is 1. Deductive method 2.inductive method
1.deductive method: it starts from unchallenged elementary assumptions and then arrive at conclusions using logical analysis.
It’s stages are:
1.observation of tasks (realistic ones)
2.making the hypothesis
3.testing the hypothesis using more observation.
If this hypothesis gets verified we get general economic principles or laws.
2.inductive method: this type of reasoning flows from facts to theory. First we collect information then move towards providing evidence using economic theories and facts.
Data is collected about a particular economic theory and then conclusion is drawn.
The stages are:
2.fomulating of a hypothesis
3.generalizing principles
4.verifying against actual facts.
The basic methods of analysis used by economists are: Deductive method and Inductive method
1) Deductive method:
This method represents an approach to the derivation of economic generalisation and theories. In order to derive economic generalisations through deductive logic we begin by identifying the problem,
defining technical terms and relevant variables, making assumptions, processing of logical deduction to derive implication, formulation of hypothesis, making predictions and testing them and finally
making sure the predictions are in agreement with facts.
2) Inductive method:
The inductive method can also be called Empirical Method. The inductive method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected
with regard to a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
Name: Caroline Jessica Okeke
Department: Sociology & Anthropology
Matric number: 2020/242834
Email address: Carolinejessicaokeke@gmail.com
Every economic analysis necessitate the articulation of laws and conceptions through two methods:
– Deductive reasoning.
-Inductive reasoning.
It begins from undisputed straightforward or introductory facts and then results to resolutions ( construct a hypothesis or theory) using logical analysis or our own analytical abilities. In other
words, it is also called a priori reasoning.
In this form of reasoning, we have 3 stages of deductive reasoning:
– Researching a task.
– Creating hypothesis.
-conducting a test on the hypothesis researched.
This reasoning provides a hypothesis and it is being verified, it results to general economic principle or law.
It is a simple method. It does not involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
This form of reasoning moves from facts to theory. First, Data collection is performed and then providence of evidence using economic theory and facts. This method formulates principles using the
sub-methods- Observations, Experimentations, Statistical methods.
Data collection of a particular economic theory and then conclusions are drawn. The stages in this method are:
-Formulation of a hypothesis.
-Generalizing principles.
-Verifying against actual facts.
Since it is based on facts it is more realistic and reliable.Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just
depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable. It is a time-consuming process and thus expensive as well. The collection of all
the data is not an easy job and varies from person to person. As to how they collect data.
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Economic analysis involves the formulation of laws and generalization through two methods (a) Deductive (b)inductive.
(1)Deductive method is also called a priori reasoning.it is also called abstract,analytical and represents an abstract approach to the derivation of economic generalisations and theories.it is also
seen as a conclusion after having interpretations from premises.in this kind of reasoning we go from a general to specific.
The stages in deductive includes (i) observation of a task or issue,making the hypothesis.
(ii)Testing the hypothesis using more observations etc.
It is a simple method that doesn’t involve the use of any complex software analysis etc.
(2)Inductive methods which is also called empirical
Method derives economics generalisations on the
Basis of experience and observation.
In this method, detailed data are collected with regardes,a certain economics phenomenon and effort is then made to arrive at certain generalisations which follow from observations collected.but it
is worth mentioning that the number of observations has to be large if it can yield a valid economic generalization.one should not generalize on the basis of a very few observations.
The deductive profiling method relies on the
application of deductive reasoning to the observable evidence.investigators collect general information about something base on the profilers experience, knowledge and critical thinking.
The deductive method involves several distinctive steps
(a)A problem is stated
(b) information is collected
(c)A working hypothesis is formulated
(d) The hypothesis is tested
(e)Result of the test are examined
(f) one or more conclusions are reached
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They are:
1. Deductive Method
2. Inductive Method
1.Deductive Method:
The deductive method is also known as the abstract or analytical method. In this method, conclusions are derived from general truths, i.e. it proceeds from general to particular. The classical and
neo-classical school of economists such as Ricardo, Mill, Malthus, Marshal, Pigou, etc. applied the deductive method in their economic investigations.
In Deductive method of Economic Analysis we proceed from the general to the particular. This is also known as an hypothetical method for some of the assumptions may not correspond to actual facts,
but very near actual facts which may be used as premise for starting, reasoning and drawing conclusions. In economics we start with very simple premises and work up gradually or more and more complex
A complete form of deductive method consists of three stages, viz.,
deductive reasoning and
instance and testing by means of further observations.
1. Deductive method is exceedingly simple. For example, the law that the utility derived by an individual from a commodity goes on diminishing with every successive addition is a self-evident truth
from which we may draw many logical conclusions, viz., larger the stock of money, the lower shall be the utility of money; rich persons have lesser marginal utility of money than the poor people; so
taxes should not be levied on proportional basis. If taxes are levied proportionately, the sacrifice of the poor will be larger than the rich.
2. Deductive method obviates the necessity of experimentation. Economics being a social science, experimentation may not be available as in the case of physics or chemistry. So, the next best
alternative to experiment is deductive reasoning.
3. The deductive method results in accuracy and exactness in generalization, because of logical reasoning. The method gives a very high standard of precision in abstract economic reasoning.
1. Deductive generalizations started on wrong premises will be dangerous when such generalization claim universal validity. Then such faulty generalizations are made use of in framing government
policies, the results would be nothing but disastrous. For example, J.B.Say, claimed universal validity for his ‘Law of Markets’ in which he maintained that supply creates its own demand and there
will not be over-production in the market. But this celebrated ‘Law of Market’ was torn to pieces when critics proved that Say’s Law was wrong and overproduction would be possible.
2. In deduction there is too much of abstraction and economists by means of their intellectual exercises produce only “intellectual toys” having little connection with reality.
3. Deduction is based mainly on assumptions which are perfectly valid. If assumptions are wrong, generalizations made on the basis of wrong assumptions will be imperfect and invalid.
2. INDUCTIVE METHOD
In this method, economists proceed from a practical angle to problems of science to reduce the gulf between theory and practice. Induction is done by two forms, viz. experimentation and statistical
form. Facts are collected first, arranged and conclusions are drawn. Then these general conclusions are further verified with reference to actual facts.
The inductive method is generally associated with the statistical form of inductions. The statistical approach has a larger field in economic investigations than the method of experimentation.
Further, the method of statistical induction is indispensable for the formulation of economic policy. Malthus presented his famous theory of population only after studying the facts of population in
various countries; He then used statistics to support his theory. Similarly Engel, the German statistician employed inductive method and used statistics to formulate his law of consumption.
1. It is highly practical add realistic as it describes things as they are.
2. It is helpful in verifying the conclusions of the deductive method.
3. Economic laws under this method are not universal but valid only under certain conditions.
1. When the investigators lack a balanced judgement there is the risk of drawing hurried conclusions based on inadequate and irrelevant facts and data.
2. Collection of facts in the inductive process is a highly complex and complicated job warranting extraordinary understanding to alienate economic from non-economic factors.
3. Mere induction alone will not deliver goods unless it is supplemented by means of deductive reasoning. Without deduction, the inductive method would result in producing only a mass of unrelated
and unconnected facts.
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1 Inductive method: The inductive method which is also called empirical methods drives economic generally on the basis of experienment and observation. Therefore inductive method or reasoning is a
type of method or reasoning that involves drawing a general conclusion from a set of specific observations. In this method is detailed data are collected with regard to a certain economic phenomenon
and efforts is made to arrive at a certain generalizations which follows from the observations collected.
There are three ways which can be used for driving economic principles and theories
1 Experiementation
2 Observations
3 statistical or econometric methods.
Various steps in inductive method
1 the first step is to identify the problems.
2 The second step is defining technical and variables related to the problem
3 the third step which is very important in the inductive method is the collection of data about the variables related to the problem and doing some preliminary thinking about the possible functional
relationships between the relevant variables.
4 Another important step is the constructions of economic theories: this is processing of data collected and finding out what relations between the variables actually hold good.
2 Deductive method: In deductive method of economic Analysis, we proceed from general to the particular. This is also known as an hypothetical method for some of the assumptioms may not correspond to
actual facts, but very near actual facts which may be used as premise for starting, reasoning and drawing conclusions.
The Deductive method drives new conclusions from fundamental assumptions or from the truth established by other methods. It involves the process of reasoning from certain laws or principles, which
are assumed to be true to the analysis of facts.
They are steps of driving economic generalizations through deductive method:
1 perception of the problem to be enquird into: the analyst must have a clear idea of the problem to be enquird into, in order not to make mistakes.
2 Definition of technical terms and making of assumptions
Deducing hypotheses, that is driving conclusions from the premises through the process of logical reasoning
4 Testing hypothesis deduced.
Deductive reasoning :Deductive method is also known as abstract or analytical method. This method is based on a priori reasoning and conclusions are drawn from certain fundamental assumptions. It
moves from general assumption to the specific application. The reasoning gives hypothesis which when verify gives economic principles or laws.
Inductive reasoning : Inductive method moves from particular facts to generalization.The facts are collected first, arranged and conclusions are drawn. The general conclusions are further verified
with reference to actual facts.
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In economic analysis two methods are being used 1. The deductive method 2.the inductive method.
1.deductive method: it starts from unchallenged elementary assumption and then arrive at conclusions using logical analysis or our analytical abilities. It is also called abstract, analytic method
and a priori reasoning.
The stages are:
-observation of a task (realistic one)
-making the hypothesis
-testing the hypothesis using more observation
Note: if this hypothesis gets verified we get general economic principles or laws.
2.inductive method: this type of reasoning flow from facts to theory. First we collect information and then move towards providing evidence using economic theories and facts.
Data is collected about a particular economic theory then conclusion is drawn.
The stages are:
-formulation of a hypothesis
-generalizing principles
-verifying against actual facts.
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*The two method of economic analysis are*
1. Deductive method
2. Inductive method
(1). Deductive method ::: this is also called a “prior reasoning ” we start by perceiving the problem, give an analysis into the problem, observe the problem, define precisely the technical terms,
“based on the definition ” you make hypotheses (assumption), then the assumption at this stage becomes a postulate, test your hypotheses (this is to know it it will be accepted or rejected), then if
the hypotheses gets verified it becomes a theory.
(2). Inductive method ::: this method also known as empirical method that derives generalization. It is also involves the collection of facts, drawing analytic conclusion with them and testing if
with other facts.
There are basically three ways for deriving economic priciciple and theories they are
1. Experimentation ::: this uses econometri package like e-views, strata.
2. Observation :: you observe your hypotheses
3. Econometri methods ::: makes use of statistical tools and economic theories in combination to estimate the economic variable and to forecast the intended variables.
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There are two basic methods of economic analysis namely
I Deductive method
ii Inductive method
DEDUCTIVE: The deductive method is also called abstract, analytical and a priori method and represents an abstract approach to the derivation of economic generalisations and theories.
The principal steps in the process of deriving economic generalisations through deductive logic are:
(a) Perception of the problem to be enquired into;
(b) Defining precisely the technical terms and making appropriate assumptions, often called postulates or premises;
(c) Deducing hypotheses, that is, deriving conclusions from the premises through the process of logical reasoning; and
(d) Testing of hypothesis deduced.
1 identify the problem
2 Defining technical terms and relevant variables
3 Making Assumption
4 process of logical deduction to derive implications
5 Formulation of hypothesis
6 Making predictions and testing them
7 Predictions are in agreement with facts.
2. Inductive Method:
The inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations. In this method detailed data are collected with regard to a
certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
But, it is worth mentioning that the number of observations has to be large if it can yield a valid economic generalisation. One should not generalise on the basis of a very few observations. There
are three ways which can be used for deriving economic principles and theories.
They are:
(a) Experimentation,
(b) observations,
(c) statistical or econometric method.
Various Steps in Inductive Method:
Various steps are gone through in developing economic theories through inductive method. The first step, as in the deductive approach, is to identify the problem. The second step is defining
technical terms and variables related to the problem.
It is the next step which is peculiar to the inductive method, namely, the collection of data about the variables related to the problem and doing some preliminary thinking about the possible
functional relationships between the relevant variables.
The next important step in the construction of economic theories in this method is the processing of data collected and finding out what relations between the variables actually hold good. From this,
a theory is developed which can be further refined and tested through statistical methods.
Once the theory has been developed one can make predictions on its basis, as is done in the deductive approach. If predictions of theory are in agreement with the facts and actual behaviour of the
economy, then a new reliable theory has been developed. If a new theory explains “how things work” better than the existing ones, it replaces them.
Conclusion: Integration of Two Methods:
Now, the controversy which existed among the earlier economists as to whether deductive or inductive approach is more appropriate in developing economic theories and principles has been resolved. The
modem viewpoint in this regard is that both are needed for the proper development of scientific economic theories. Indeed, the two are complementary rather than competitive.
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The method of economics analysis are
Deductive method
Inductive method
Deductive method is also the analytical abstract or prior method. It derives conclusion from general truths takes few general principles and applies conclusions.
Steps in deductive method
1 perception of the problem to be inquired into
2 Defining of terms
3 Deducing hypothesis from the assumption
3 Testing of hypothesis
Inductive method, it lnvolves the process of reasoning from particular facts to general principle. It derives economic generalization in the basis of experimentations, observation and statistical
Steps in inductive method
Formation of hypothesis
The basic methods of economic analysis used by Economists are:
A. Deductive method
B. Inductive method
A. Deductive method: It is also known as abstract method.
It consists in deriving conclusions from general truths.
It takes a few general principles and applies them,then draws conclusions.
The classical and neo-classical school of Economists like J.S Mill,Malthus,applied this method in their economic investigations.
Steps of Deductive method
1. Perception of the problem to be inquired into: i.e the economist must have a clear and precise idea of the problem to be inquired.
2. Defining of terms: i.e to define clearly the technical terms used in analysis. Further assumptions made by the theory are then made precise.
3. Deducing hypothesis from the assumptions.
4. Testing of hypothesis: i.e verification of hypothesis through direct observation in the real world ,and statistical methods.
Merits of Deductive method
1. It is near to reality,less time consuming,less expensive.
2. Mathematical techniques are used in deducing theories of economics,which brings exactness and clarity in economic analysis.
3. The method is analytical
4. It helps in deriving economic theories using limited scope of experimentation.
Demerits of Deductive method
1. It is simple and precise only if the assumptions are VALID. More often ,the assumptions turn out to be half truths and are misleading,or have no relation to reality.
2. The method is highly abstract,and requires a great deal of care,to avoid bad logic and faulty economic reasoning.
3. Prof Learner described it as “armchair analysis” i.e the premises from which inferences are drawn,may not hold good at all times.
B. Inductive method
It is also called empirical method. It was adopted by the “Historical School of Economists”. It involves the process of reasoning from particular facts to general principles. It derives economic
generalization on basis of:
i. Experimentation
ii. Observation
iii. Statistical methods
In this method,data is collected about a certain economic phenomenon, systematically arranged,and conclusions are drawn.
Steps of Inductive method
1. Observation
2. Formation of hypothesis
3. Generalization
4. Verification
Merits of Inductive method
1. It is based on facts. The method is realistic.
2. The method is more reliable because it makes use of statistical techniques to test economic principles.
3. The method is dynamic.
4. The method helps in future investigations.
Demerits of Inductive method
1. If conclusions are drawn from insufficient data,the generalizations may be faulty.
2. The collection of data is a difficult task and the method employed differs from investigator to investigator. This may lead to different results for same problem.
3. The method is time consuming and expensive.
Both methods have weaknesses. We cannot rely exclusively on any one. Modern Economists are of the view that the methods are complimentary. We can apply any or both,as situation demands.
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Basic methods of analysis used by economist.
1. Deductive method: this is also called abstract method,it represents an abstract approach to the derivation of economic theories. There are certain steps used in deriving these theories and they
a. Perception of the problem to be enquired,
b. Defining the technical terms and making appropriate assumptions,often called postulates,
c. Deducing hypothesis,deriving conclusions through logical reasoning,
d. Testing of hypothesis deduced.
2. Inductive method: also called empirical method. This method derives economic generalizations on the basis of experience and observations. Data are collected with regard to a certain economic
phenomenon and efforts is then made to arrive at certain theories that follows from the observations.
Ways used for deriving economic principles and theories;
a. Experimentations,
b. Observations,
c. Statistical or econometric method.
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Inductive reasoning is a method of reasoning in which premises are viewed as supplying some evidence,but not full assurance,of the truth of conclusion.it is also described as a method where one’s
observation and experience including what is learned from others are synthesized to come up with a general truth.
Deductive reasoning,also known as deductive logic,it is the process of reasoning from one or more statements to reach a logical conclusion as that of contributional, and links premises with
This method as the name implies involves the
reseaoning from the general to the particular. The deductive method provides us with new results from fundamental assumptions or from facts established by other methods. It involves the process of
reasoning from certain laws or principles, which are assumed to be true, to the analysis of facts.
Then inferences are drawn which are verified against observed facts. #BACON himself described deduction method as a “descending process” in which we proceed from a general principle to its
consequences. Mill characterised it as a priori method, while others called it abstract and analytical.
The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis by being very observate.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
#MERITS_OF_DEDUCTION_METHOD .
1. This method only requires simple,deductive and logic work or reasoning.
2. It helps economists as it focus upon economic reasoning which is overriding.
1.This method starts or is headed by an assumption, therefore a faulty conclusion is drawn from any and all assumptions wrongly made.
It can be described as a reasoning which takes place in an ascending order. Here facts are collected, arranged, analysed and then conclusions are drawn from these facts. This method can also be
called the #HISTORICAL_METHOD. This very method requires the economist to draw gereralisations, and verify the conclusions by applying them to subsequent events.
#Stages involved here are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
1. It is based on facts therefore inference drawn from it is more realistic and reliable than that of the #DEDUTION_METHOD
2. Statistical methods and experimentations are employed here, making the process more scientific, thus, more acceptable universally.
1. Once the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
2. It is a time-consuming process and thus expensive as well.
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There two method used in economics analysis.;they are.
No 1.
DEDUCTIVE METHOD: This is also called priori or abstract method. here we start unchallenged elementary or redimentary assumption, then arrive at conclusion.
Stages that it take to reach conclusion are.
a. Observation of task or issue.
b. Making appropriate assumption, often called postulates or premises.
c. Making the hypothesis
C. Testing the hypothesis using more observations.
No 2.
INDUCTIVE METHOD; this type of generalizations flows from facts to theory.it also refers as empirical method.
In inductive method the economist collect information and facts and then move towards providing evidence using economic theory and facts.
This method formulates principles using the sub-methods like. Observation, experimentations, statistical methods.
There are many stages economist can arriveus at his theory are;
b. Formulation of a hypothesis
C. Generalizing the principles
D. Verifying against actual facts.
INDUCTIVE REASONING is a type of reasoning that involves drawing a general conclusion from a set of specific observation.
Advantages of Inductive Reasoning
1. It provides first hand knowledge and information by actual observation.
2, it is future oriented. It gathers specific
information, then draws a general conclusion which predicts what will be found in the future.
3. It increases the creativity of the research.
Disadvantages of Inductive Reasoning
1. It is limited in scope, and inaccurate inference (false conclusions)
Example of inductive Reasoning: ” Pearl leaves for school 7 am, Pearl is always early.”
DEDUCTIVE REASONING is the process of reasoning from one or more statements to reach a logical conclusion. Or a type of logical thinking that starts with general idea and specific conclusion.
Advantages of Deductive Reasoning
1. It is a downward process of thoughts, and leads to useful results.
2. It is straight and to the point.
3. It is less time consuming.
4. It allows more time for practice and application.
Disadvantages of Deductive Reasoning
1. It does not give any new knowledge, because its premises are already tested. It only proves the past or present truths.
2.it is reduced merely to a method for verification.
3. It encourages dependence on other resources.
Example of Deductive conclusion: ” All men are mortal. Raymond is a man”. Therefore, Raymond is mortal.
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Department: Business education.
Any economic analysis involves the formulation of laws and generalizations through two methods: Deductive and Inductive.
Inductive method: is also called empirical method .it involves the process of reasoning from particular facts to general principle. It also makes use of econometric packages.This method derives
economic generalization on the basis of:
*Statistical methods.
Deductive method:In deductive method of economic analysis we proceed from the general to the particular or main.This is also known as hypothetical method for some of the assumptions may not
correspond to actual facts,but very actual facts which may be used as premise for starting, reasoning and drawing conclusions.
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DEPARTMENT: Pure and Industrial Chemistry.
The methods of economic analysis used by economists includes:-
Inductive method and Deductive method.
• INDUCTIVE METHOD:
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates principles
using the sub-methods- Observations, Experimentations, Statistical methods.Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
×Formulation of a hypothesis
×Generalizing principles
×Verifying against actual facts.
This method has it’s advantages and disadvantages,
Its advantages includes:
-Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
-Since it is based on facts it is more realistic and reliable.
-Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Its disadvantages includes:
-It is a time-consuming process and thus expensive as well.
-The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
-If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
• DEDUCTIVE METHOD:
Information~pattern~tentive hypothesis~theory.
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis or
our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
×Observation of a task/ issue
×Making the hypothesis
×Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
This method also has its advantage and disadvantage.
Its advantages includes;
-This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
-It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
Its disadvantage is the fact that in this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong
conclusions. Thus, the logical fallacy is a disadvantage of this method.
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Reg number:20690143BA
Dept: Public Administration and Local Government
An economic theory derives laws or generalization through two methods
(1) Deductive method and
(2) Inductive method.
These two ways of deriving economic generalizations are now explained in brief:
(1) Deductive method of Economics Analysis:
The Deductive method is also named as analytical, abstract,prior method.The deductive method consists in deriving conclusion from general truth , takes few general principles and applies them draw
Inductive method of Economics Analysis:
Inductive method which is called empirical method was adopted by the Historical school of Economist .It involves the process of reasoning from particular facts to general principles.
This method derives economic generalization on the basis of
(1) Experimentations
(2)Observations and
(3)Statistical methods
In this method, data is collected about a certain economic phenomenon .
These are systematically arranged and the general conclusion are drawn from them
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What are the basic methods of analysis used by Economists? Briefly and convincingly discuss each of them.
Any economic analysis involves the formulation of laws and generalizations through two methods- deductive and inductive.
1. Deductive reasoning
2. Inductive reasoning.
* The Deductive reasoning otherwise known as a priori reasoning. We begin with unquestioned basic or rudimentary assumptions/
facts and then use logical analysis or our own analytical ability to get conclusions (create a hypothesis or theory).
We proceed from general to specific in this type of reasoning.The stages in deductive reasoning are:
-Observation of a task/ issue
-Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
*The inductive method involves collection of facts, drawing conclusions from them and testing the conclusions by other facts.
On the basis of experience and observation, the inductive technique, also known as the empirical method, develops economic generalization.
Experimentation, observation, and statistical or econometric methods are the three methods that can be used to derive economic principles and hypotheses.
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1. Deductive Method
This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis or
our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
It is a simple method, doesn’t involve the use of any complex software analysis, etc. only simple deductive logic is required.
This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
2. Inductive Method
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates principles
using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts.
Advantages of Inductive Method
Since it is based on facts it is more realistic and reliable.
Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages of Inductive Method
If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
It is a time-consuming process and thus expensive as well.
The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
Name: Onyeoma Cynthia Amarachi
Reg No: 2019/241511
Department: Pure and industrial chemistry
Email: Amarachi.Onyeoma241511@unn.edu.ng
Topic: what are the basic methods of analysis used by economist
The basic method of analysis used by economist are as follows:
1. Deductive method analysis
2. Inductive method analysis
Deductive method analysis:- it can also be called priority reasoning. In the sense that we go from general to specific, that is we start from unchallenged elementary facts and then arrives at
conclusions using our own analytical ability. The stages in deductive reasoning are listed below.
– Observation of a task or issue which automatically leads to appropriate assumption.
– making the hypothesis which is deriving into conclusion through the process of logical reasoning.
– Testing the hypothesis deducted using more observation
Inductive method analysis:- It can also be called empirical method. In this type of reasoning, collection of information and facts providing evidence using economic theory and facts. Data is
collected about a particular economic theory before conclusion.
The stages in this method are as follows:-
– Observation
– formulation of a hypothesis
– Generalizing principles
– Verifying against actual facts
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Department: pure and industrial chemistry
The two methods used by economists are:
1. Inductive reasoning
2. Deductive reasoning
1. Inductive reasoning: it is a type of logical thinking that involves forming generalizations based on specific incidents you’ve experienced, observations you’ve made, or facts you know to be true
or false.it is an important critical thinking skill that many employers look for in their employees. Bacon described it as “an ascending process”. It expects the economist to be primarily an economic
historian who should first collect material, draw generalizations and verify the conclusions by applying them to subsequent events. Inductive reasoning is dynamic, realistic, future enquiries and
statistical method. It’s demerit is: it is time consuming and expensive.
2. Deductive reasoning: is an inference from the general to the particular or from the universal to the individual. The deductive method derives new conclusions from fundamental assumptions or from
truth established by other methods. It involves the process of reasoning from certain laws or principles, which are assumed to be true, to the analysis of facts, then inferences drawn which are
verified against observed facts. Bacon described deductive reasoning as “a descending process ” in which we proceed from a general principle to it’s consequences. Deductive reasoning is real, simple,
powerful and exact. It’s demerit is: it is based on assumptions and it is abstract
THE BASIC METHOD OF ANALYSIS USED BY ECONOMISTS . . An economy theory derives laws or generalization through two methods.
1.Deductive method. 2.inductive method.
Deductive method of economic analysis- the deductive method is also called analytical, abstract, or prior method .it represent an abstract approach of economic generalization and theories. Deductive
method may involved steps which aids in deriving economic generalization. They are perception of the problem to be inquired into that is the analyst must understand ,interpret and be able to have a
clear idea of the problems he is to handle..
Secondly the next step is to define clearly the technical term used in analysis ,further assumption made for a theory should also be precise. The third step in deriving generalization is making
hypothesis from the assumption taken.
Finally before establishing laws or generalization, hypothesis should be verified through direct observation and through statistical method. Merits of Deductive methods– it is time consuming and
brings exactness and clarity in economic analysis, it also help in deriving economic theories.. Shortcomings or demerits of deductive methods-it is highly demerited because it requires a great deal
of care to avoid bad logic and faulty economic reasoning and other highly unrealistic assumptions which may not have operational significance.
INDUCTIVE METHOD. This is also called the empirical method which derives economic generalization on the basis of experience and observation..the observation has to be large to yield a valid economic
generalization. There are three steps which can be used for deriving economic principle and theories they are 1.experimentation
3.statistical method.
Main step involved in the application of inductive method are observation that is a collection of data then making of hypothesis followed by generalization and lastly verification.
Inductive method is based on facts, that is the method is realistic, further more inductive method is more reliable and is also dynamic and mosty helps in future investigation. These are merits of
inductive method.
It shortcomings or demerit that weakens the method are when conclusion are drawn from insufficient data the generalization obtained may be faulty.
Secondly it is time consuming and also the method or source of collection of data differs from investigators to investigators.
In conclusion deductive and inductive method have both weaknesses and we cannot rely exclusively on any of them but they are highly needed for scientific thought and analysis.
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The basic methods of analysis used by economics are;
1. Deductive method.
2. Inductive method.
The deductive method is also named as analytical, abstract or prior method. The deductive method consists in deriving conclusions from general truths, takes few general principles and applies them,
draw conclusions. For instance if we accept the general proposition that man is entirely motivated by self-interest. In applying the deductive method of economic analysis, we proceed from general to
The main steps involved in deductive logic are under:
i. Perception of the problem to be inquired into: In the process of deriving generalization, the analyst must have a clear and precise idea of the problem to be inquired into.
ii. Defining of terms: The next step in this direction is to define clearly the technical terms used analysis. Further, assumptions made for a theory should be precise.
iii. Deducing hypothesis from the assumptions: The third step is deriving generalizations is deducing hypothesis from the assumptions taken.
iv. Testing of Hypothesis: Before establishing laws or generalizations, hypothesis should be verified through statistical methods. ( Their inverse relationship between price and quantity demanded of
a good is a well established generalizations.
The main merits of deductive method are as under:
i. This method is near to reality. It is less time consuming and less expensive.
ii. The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis.
iii. There being limited scope of experimentation, the methods helps in deriving economic theories.
iv. The method is simple because it is analytical.
i. The deductive method is simple and precise only if the underlying assumptions are valid. More often the assumptions turn out to be based on half truths or have no relation to reality. The
conclusions drawn from such assumptions will, therefore, be misleading.
ii. Professor Learner describes the deductive method as ‘armchair’ analysis. According to him, the premises from which inferences are drawn may not hold good at all times, and places. As such
deductive reasoning is not applicable universally.
iii. The deductive method is highly abstract. It requires; a great deal of care to avoid bad logic or faulty economic reasoning.
As the deductive method employed by the classical and neo-classical economists led to many facile conclusions due to reliance on imperfect and incorrect assumptions, therefore, under the German
Historical school of economists, a sharp reaction began against this method. They advocate a more realistic method for economic analysis known as inductive method.
Inductive method which also called empirical method was adopted by the ” Historical school of Economists”. It involves the process of reasoning with particular facts to general principle.
This method derives economic generalization on the basis of i. Experimentation, ii. Observation and iv. Statistical methods.
For example, we observe 200 persons in the market, we find that nearly 195 persons buy from the cheapest shops, out of the 5 which remains, 4 persons buy local products, while the fifth is a fool.
From this observation, we can easily draw conclusions that people like to buy from a cheaper shop unless they’re guided by patriotism or they are devoid of common Sense.
The main steps involved in inductive method are:
1. Observation
2. Formation of hypothesis
3. Generalization
4. Verification.
1. It is based on facts as such the method is realistic.
2. In order to test the economic principles, methods makes statistical techniques. The inductive method is, therefore, more reliable.
3. Inductive method is more dynamic. The changing economic phenomenon are analyzed and on the basis of collected data, conclusions and solutions are drawn from them.
4. Inductive method also helps in future investigations.
1. If conclusions are drawn from insufficient data, the generalizations obtained may be faulty.
2. The collection of data itself is not an easy task. The sources and methods employed in the collection of data differ from investigator to investigator. The results, therefore, may differ even with
the same problem.
3. The inductive method is time consuming and expensive.
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2. DEDUCTIVE METHOD
INDUCTIVE METHOD: This can also be called emperical method. It derives economic generalizations on the basis of experiment and observation. Detailed data are collected with regard to a certain
economic phenomenon and is made to reach a certain generalization which follow from the observation collected. Experiment, observation and econometric methods can be use to derive economic
DEDUCTIVE METHOD: This can also be called abstract, analytical and prior methods.
The principle steps in the process of economics generalization through deductive methods are:
i Perception of the problem to be inquired
ii Defining precisely the technical terms and making appropriate assumption
iii Deducing hypothesis that is deriving conclusion from the process of logical reasoning
iv Testing of hypothesis deduced
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They are divided into two. They are ;
1. Deductive Method
2. Inductive Method
1. DEDUCTIVE METHOD :
The deductive Method is based on an abstract approach to the derivation of economic generalizations and theories.
The steps involved in deriving these theories and generalizations include:
a) Perception of the problem: This entails conscious understanding of the problem under consideration.
b) Precisely defining the technical terms and making assumptions. These assumptions maybe behavioural (behaviour of economic variables) or technological (relating to the state of technology).
But these assumptions do not apply in some cases.
c) Deduction of hypothesis based on those assumptions made.
Hypothesis can be viewed as an assumption taken to be true for the purpose of further argument or investigation.
d) Testing and verifying these hypothesis:
The deducted hypothesis needs to be verified before they are established as generalizations or Economic principles. Testing of these hypothesis can also be in statistical form.
2. INDUCTIVE METHOD :
The inductive method uses econometric package in experimentations.
It derives Economic generalizations on the basis of experience and observations. It involves data collection with reference to a certain economic phenomenon. These data obtained can help in the
establishment of economic principles and theories.
The three main ways of deriving these economic principles include:
a) Experimentation
b) Observation
c) Econometric / Statistical Method.
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Question : Discussion on the methods of Economic analysis
Economic generalisations describe the laws or statements of tendencies in various branches of economics such as production, consumption, exchange and distribution of income.
The generalisations of economics like the laws of other sciences, state cause and effect relationship between variable and describe these economic hypotheses which have been found consistent with
fact or, in other words, have been found to be true by empirical evidence. But a distinction maybe drawn between a generalisation and a theory.
The methods of economics analysis which have been broadly categorized are;
Deductive method
Inductive method
Deductive method:
The deductive method which is also known as the abstract, analytical or priori method represents an abstract approach to the derivation of economic generalisations and theories.
The principle steps in the process of deriving economic theory through deductive methods are:
A. A clear idea of the problem.
B. Defining precisely the technical terms and making appropriate assumptions often called postulates or premises.
C. Deducing hypotheses, that is deriving conclusions from the premises through the process of logical reasoning.
D. Testing of the hypotheses deduced. This is the final stage in the deductive method.
Inductive method:
This is also called “empirical method”. This method derives economic generalisations on the basis of experience and observations.
There are three ways which can be used for deriving economic principles and theories, which are
– Experimentation
– Observations
– Statistical or econometric method
Some of the recent researches in the field of macroeconomics such as the nature of consumption function describing the relation between income and consumption, the principle of acceleration
describing the factors which determine investment in the economy have been obtained mainly through the use of inductive method. Moreover there is need to emphasize again that the use of induction or
empirical method is not of much value if it is not supported by the economic hypothesis or theory developed by deductive logic. The inductive method can at best be used to empirically test the theory
or hypothesis as to whether it is consistent with or refuted by facts. The inductive method has another limitation in that there is a great risk of conclusions being drawn from insufficient data. To
obtain generalisations through inductive method one should take note that sufficient number of observations or data has been taken into account
Finally, the controversy which existed among the early economists as to whether deductive or inductive approach is more appropriate in developing economic theories and principles has been resolved.
The modern viewpoint in this regard is that both are needed for the proper development of scientific economic theories. Indeed the two are complementary rather than competitive.
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Economists have basic ways through which they analyse Economics, any economic analysis involves the formulation of laws and generalisation through two methods; Deductive and inductive method.
1. Deductive method : this is refered to as the prior reasoning. We start from practical assumptions and arrive at conclusions (hypothesis) using logical analysis or our own analytical abilities.
This method has different stages which are the
* Observation of a task
* Making the hypothesis and;
*Testing the hypothesis using more observations.
When the hypothesis of this stage is verified it becomes an economic principle.
2. Inductive method: this method flows from facts to theory . First, information and facts are collected and then we move towards providing evidence using Economic theory and facts. This method
formulates principles using sub method, observations, experimentation, statistical method.
Data is collected about a particular economic theory and then conclusions are drawn.
The stages are:
* Formulation of hypothesis
* Generalising principles
* Verifying against actual facts.
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Methods of Economic Analysis
Like in any other science, Economics adopts two important methods in it’s investigations and formation of laws and principles. The two methods are:
1. Deductive method
2.inductive methods
1. Deductive method of Economic Analysis
This is alsoMethods of Economics Analysis called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or
theory) using logical analysis or our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation of a task/ issue
Making the hypothesis
Testing the hypothesis using more observations, etc.
2. Inductive method of Economics Analysis
This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws. Inductive Method of Economic Analysis
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates principles
using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
Formulation of a hypothesis
Generalizing principles
Verifying against actual facts
Nnamdi Peace Munachukwumu
Nursing Sciences
2 Methods of Economic Analysis.
1. Deductive Method: This is also called Abstract Analytical and A Prior Method. It’s Derives Economic Generalization on the Basis of an “Abstract Approach”.
Principle Step in the Process of Deriving Economic Generalization through Deductive Logic are:
-Perception of the Problem to be enquired Into.
-Deducing Hypothesis , (Deriving Conclusions through the process of Logical Reasoning).
-Testing of Hypothesis deduced.
2. Inductive Method: This Method is also called “Empirical Method”. It derives Economic Generalization on the Basis of ”Experiment and Observation “.
This Method also involves the Collection of Detailed Data with regards to a certain Economic Phenomenon and Efforts are made to arrive to a Certain Generalization which will be Gotten from the
Observations Collected.
~However, The number of Observation has to be large before it can yield valid Economic Generalization.
Principle steps in the Process if Deriving Economic Generalization through Inductive Logic:
-Statistical Econometric Method.
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Deductive method
Inductive method
This method can also be called a priori reasoning,in this method we starts from the fact then arrive to the conclusion, building a hypothesis or theory using logical or analytical approach or
abilities. This method begins from the general to the specific ,it observes issues or task in this process making of hypothesis then testing the hypothesis using more observations. Stages in this
* Observation of a task/issues
* Making the hypothesis
* Testing the hypothesis
This method deals with data collection about a particular economic theory and then conclusions are drawn .we collect information and facts and then move toward providing evidence using economic
theory and facts, this method formulated principle’s using both experiment and observations. Stages in this method include;
* Observation
* formulation of hypothesis
* Logical reduction
* Test
* Predict agreement
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(1). DEDUCTIVE METHOD.
This is a method of verifying existing knowledge which look deep into complex problem on the basis of generally accepted laws and basic assumption,it is also called abstract method which starts from
a broad sense and narrows down to small point.
(2) INDUCTIVE METHOD
This is based on observation of fact as problem, then establish reasoning and solutions in the method, it is a method of discovering new knowledge, it is also called empirical method.inductive method
uses econometric packages such as e-views ,stats etc in making generalization.
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Method of analysis involves the formulation of laws and generalization through two methods which are Deductive reasoning and Inductive reasoning
1) DEDUCTIVE REASONING : this starts from assumptions and then arrive at conclusions using simple logical analysis. It consist of four steps
a) perception of the problem
b) Definition of technical terms and making of
Assumptions: we define problem and explain
the technical steps then make assumptions
which are also called POSTULATES.
c) Deducing Hypothesis: an hypothesis is formed
based on the observation and assumptions
d) Testing or Verification of hypothesis: more
Observations and experiments are performed
Until the results prove the hypothesis, then it
Is verified and becomes a general economic
Principle or a law.
If the observation at the beginning is wrong or faculty, it would give wrong conclusions.
2) INDUCTIVE REASONING: this starts from the collection of information and facts(data) which has already been established and then move to provide evidence. It uses basic scientific methods,
Statistical methods and Experiments to interpret the data and arrive at better logical conclusions. Based on the conclusions, you can now put ADVICE. It is more reliable because the data is a general
If the data is faulty, or a mistake is made during the experiment, the conclusion would be faulty.
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There are two most important methods of analysis used by economists.They include:
1.Deductive method
2.Inductive method
1.Deductive method:This is also called abstract,analytical priority method and represents an abstract approach to the derivation of economic generalizations and theories.A law of generalizations
describe relationship between variables ,it does not provide any explanation of the described relation.
The principal steps in the process of deriving economic generalizations through deductive logic are:
*Perception of the problem to be enquired
*Defining precisely the technical terms and making assumptions
*Deducing hypothesis
*Testing of hypothesis deduced
Merits of deductive method
*Useful mathematical techniques can be employed to derive laws and theories of economics
*Deductive methods does not require detailed collection of data unlike inductive methods
*It is less time consuming and less expensive
*Shortcomings of deductive analysis may not be overlooked
Demerits of deductive analysis
*It may not have any operational significance based on highly unrealistic assumptions
2.Inductive method:Inductive methods is also called empiral method.In this method detailed data are required and collected with a regard of a certain economic phenomenon which is made to arrive at
certain generalizations which follow from the observation collected
The three ways used are:
*Statistical or econometric method
Merits of inductive analysis
*It is highly practical and realistic
*They are not universal but valid under various efforts
*It’s helpful in varying conclusions
Demerits of inductive analysis
*It is not of much value if it’s not supported by the economic hypothesis or theory developed for deductive logic.
*There is a great risk of conclusion being drawn from insufficient data
*One must make sure they take care of sufficient number of observation or data been taken into account.
*Collection of data is not an easy task
A researcher using inductive method must know how to process and interpret data
*Compared to deductive method ,inductive method is time consuming and expensive.
Conclusions:Distinguishing the two methods if predictions are found to be real with facts ,the theory but if the predictions are found inconsistent with facts ,it is rejected.
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There are two basic methods of analysis
1. Deductive method: This is the first method of economic analysis and it’s method represent an abstract approach to the derivation of economic generalization. There are four steps of deriving this
_Perceiving the problem: The analyst must know the root of the problem to be enquired into.
_Making of assumptions: After perceiving the problem the analyst will go into the next stage by making some observation about the problem which can be behavioural or technological pertaining on the
technological state of the factor.
_Drawimg hypothesis from assumptions taken: This process may be carried out verbally or may be conducted using symbolic logic.
_Testing the hypothesis: For the hypothesis to be verified one will need to back those thesis with proofs.
2. Inductive method: This derives economic generalization on the basis of experience and observation. This method of observation should not be verified on the basis of few but large observations.
Sunday Morewell Chizuru
There are two basic methods of economics analysis
1. DEDUCTIVE METHOD
2. INDUCTIVE METHOD
Deductive method is known as the analytical abstract a priori method. Here we start with certain formal data and assumptions. Then by logical reasoning we arrive at certain conclusions. We start with
undisputed fundamental facts and after adding some assumptions we build up a theory. In Deductive method of Economic Analysis we proceed from the general to the particular. This is also known as an
hypothetical method for some of the assumptions may not correspond to actual facts, but very near actual facts which may be used as premise for starting, reasoning and drawing conclusions. Deductive
reasoning provides us with hypotheses or generalizations. If the hypotheses are tested and verified with relevance to facts, we have valid economic laws.
In this method, economists proceed from a practical angle to problems of science to reduce the gulf between theory and practice. Induction is done by two forms, viz. experimentation and statistical
form. Facts are collected first, arranged and conclusions are drawn. Then these general conclusions are further verified with reference to actual facts.The inductive method is generally associated
with the statistical form of inductions. The statistical approach has a larger field in economic investigations than the method of experimentation. Further, the method of statistical induction is
indispensable for the formulation of economic policy.
Economic analysis in most cases involves the formulation of laws and this can be achieved by these methods – Deductive and Inductive method.
DEDUCTIVE REASONING also known as priori reasoning, involves the observation of issues, making and testing hypothesis using more observation and if generally accepted becomes an Economic law. This
method is simple as only simple deduction is needed and boosts economic reasoning. Sometimes wrong hypothesis made may result to wrong conclusion.
In INDUCTIVE REASONING, facts, information and theories are gathered and tested on through thorough observation and experiment and obtained result may or may not be verified. This method is more
reliable since it is based on facts and statistical methods are used in this approach. It is time consuming and expensive and can be affected by limited data sources.
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There are basically four(4) methods of economic analysis.
This involves the use of particular fact or example to form a general rule and principles. Here, the economist starts with observations and them analysis it data before drawing conclusions from them.
It is the use of knowledge that are generally true in order to understand particular situations or problems. Under this method the economist base their research on an existing theory. Here, the
economist start by setting accepted principles( I.e a theory that is generally know and accepted) and draw interference from them.
An increase in the price of rice can be used to estimate inflation rate.
They are statements about “what is”. In other words, they are factual statements. This tries to point out the good or bad decisions in the society.
Tax increase or increase in school fees will reduce household disposable income.
NORMENTIVE STATEMENTS: They are statements that depends on value judgement (ie issues of personal opinion which may or may not be fact).
Tax reduction will increase household standard of living.
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There are two major methods used by economists in analysing Economic situations, they include:
1. The Deductive Method of Economic Analysis
Deductive method is known as the analytical, abstract or priori method. It starts with certain formal data and assumptions. Then by logical reasoning certain conclusions are made. It is with these
undisputed fundamental facts and after adding some assumptions that theories are arrived at. For instance, it is assumed that businessmen aim at achieving maximum profit. It follows from this that
businessmen buy the materials at the cheapest market and sell it in the most costly market.
In Deductive method of Economic Analysis we proceed from the general to the particular. This is also known as a hypothetical method because some of the assumptions may not correspond with actual
facts, but very near actual facts are to be used as a premise for starting, reasoning and drawing conclusions.
A complete form of deductive method consists of three stages,
i. Observation ot perception of the problem;
ii. Making assumptions from logical reasoning
iii. Formulation of hypothesis, and
iv. Testing the hypothesis
Deductive reasoning provides us with hypotheses or generalizations. If the hypotheses are tested and verified with relevance to facts, they become valid economic laws.
Advantages of Deductive Method of Economic Analysis
1. Deductive method is exceedingly simple.
2. Deductive method obviates the necessity of experimentation. Economics being a social science, experimentation may not be available as in the case of physics or chemistry. So, the next best
alternative to experiment is deductive reasoning.
3. The deductive method results in accuracy and exactness in generalization, because of logical reasoning. This method gives a high standard of precision in abstract economic reasoning.
Disadvantages of Deductive Method of Economic Analysis
Deductive method has its drawbacks also:
1. Deduction is based mainly on assumptions which are perfectly valid but If assumptions are wrong, generalizations made on the basis of wrong assumptions will be imperfect and invalid.
2. In deduction there is too much of abstraction and economists by means of their intellectual exercises produce only “intellectual toys” which have little connection with reality.
3. Deductive generalizations started on wrong premises will be dangerous when such generalization claim universal validity. For instance, if such faulty generalizations are made use of in framing
government policies, the results would be nothing but disastrous.
2. The Inductive Method of Economic Analysis
In this method, economists proceed from a practical angle to problems of science to reduce the gap between theory and practice. Induction is done by two forms, viz. experimentation and statistical
form. Facts are collected first, then arranged and conclusions are drawn. Then these general conclusions are further verified with reference to actual facts.
The inductive method is generally associated with the statistical form of inductions. The statistical approach has a larger field in economic investigations than the method of experimentation.
Further, the method of statistical induction is indispensable for the formulation of economic policy. Practically, Malthus presented his famous theory of population only after studying the facts of
population in various countries; He then used statistics to support his theory. .
Advantages of Inductive Method of Economic Analysis
Inductive method has the following merits:
1. It is highly practical and realistic as it describes things as they are.
2. It is helpful in verifying the conclusions of the deductive method.
Disadvantages of Inductive Method of Economic Analysis
Inductive method has the following limitations:
1. When the investigators lack a balanced judgement there is the risk of drawing hurried conclusions based on inadequate information or data.
2. Collection of data in the inductive process is highly complex and time consuming.
3. Only induction alone will not deliver unless it is complemented by means of deductive reasoning. Without deduction, the inductive method would result in producing only a mass of unrelated and
unconnected facts.
In conclusion, the two methods have to be made use of or combined to achieve the required objective. The two methods, deductive and inductive, are not competitive, but complementary in helping the
investigator arrive at an accurate conclusion.
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1)Deductive Method:This is called prior reasoning , we start from unchallenged elementary or rudimentary assumptions of fact and then arrive at a conclusion ( to build a hypothesis or theories) using
logical analysis or our analytical abilities. In this kind of reasoning will go from general to specific.
The stages in in Deductive Method are
Observation of task or issue
Making the hypothesis
Testing the hypothesis using more observation
this reasoning gives us a hypothesis and if this hypothesis get verified we get general economics principle or law.
2) Inductive Method:this type of reasoning flows from facts to theory
First we collect data and facts and then we move towards providing evidence using economic theories and fact, this method formulate principles using the sub method, observations ,experimentation ,and
statistical method
Data is collected about a particular economic theory then are conclusion drawn.
The stages in this method are
Formulation of hypothesis
Generalizing principles
Verfying against actual facts
Note: inductive is more realistic and reliable
Information Theory
Pattern Hypothesis
Tentative hypothesis Observation
Theory Confirmation
Mbah chidiogo Lilian.
Jamb reg. Number
Department.Nursing science.
Just like every other science Economic adopts it own two important method in investigation and formulation of law and principle.
The two methods are
Deductive method
Inductive method
Deductive method- In this method we start with certain formal data and assumption.Then by logical reasoning we arrive at certain conclusion.it is also known as the ANALYSTICAL ABSTRACT A PRIOY
METHOD.we start with disruptey fundamental facts and after adding some assumpy we build up a theory.In deductive method of economic Analysis we proceed from general to the particular.
This also known as a HYPOTHETICAL METHOD.
In economics we start with a very simple premises and work up gradually or more and more complex hypothesis.
Deductive method consist of three stage.
Deductive reasoning
Instance and testi by means of further observation.
This is another form or method of economic Analysis.
This inductive method is generally associated with the statistical form of induction.
In this method, economic proceed from practical angle to problem of science to reduce the gulf between theory and practice.
The statistical approach has a larger field in economics investigation than the method experiement .
Induction is done by two forms
Experiementation form
Statistical form.
Facto are collected first arranged and conclusion drawn.
Then these general conclusion are further verified with reference to actual facts
Stages of inductive reasoning.
Formulation of hypothesis
Generalization principle
Verifying against actual facts
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What are the basic methods of analysis used by economist? Briefly and convincingly discuss each of them.
The basics methods of analysis used by Economists are:
1) DEDUCTIVE METHOD
2) INDUCTIVE METHOD
The Deductive method is also called “analytical method or prior method”. The Deductive method consists in deriving conclusions from general truths, takes few general principles and applies them to
draw conclusion.
a) PERCEPTION OF THE PROBLEM
The problem which an investigator selects for enquiry must be stated clearly. Maybe very wide like poverty, unemployment, inflation etc or narrow relating to an industry. The narrow the problem the
better it would be to conduct the enquiry.
The next step in deductive is the framing of assumptions which are basis of hypothesis. To be fruitful for enquiry, the assumption must be general. In any economic enquiry, more than one set of
assumptions should be made in terms of which a Hypothesis may be formulated.
The next y is to formulate a hypothesis on the basis of logical reasoning where by conclusions are drawn from propositions.
The final step in the Deductive method is to test and verify the hypothesis. For this purpose, economist now use statistical and econometric methods. A hypothesis is true or not can be verified by
observation and experiment.
1) REAL: This method is near to reality. It is less time consuming and less expensive.
2) EXACT: The use of mathematical techniques in deducing theories of economics brings exactness and clarity in economic analysis.
3) UNIVERSAL: The Deductive method helps in drawing inferences which are universal validity because they are based on general principles such as law of diminishing returns.
i) Deductive method is based mainly on assumptions which are perfectly valid. If assumptions are wrong, generalizations made on the basis of wrong assumptions will be imperfect and invalid.
ii) In deductive there is too much of abstraction and economist by means of their intellectual exercises produce only “intellectual toys” having little connection with reality.
2) INDUCTIVE METHOD
Inductive method which is also called “empirical method” derives economic generalizations on the basis of experience and observation.
a) THE PROBLEM
In order to arrive at a generalisation concerning an Economic phenomenon, the problem should be properly selected and clearly stated.
b) DATA
The second step is the collection, enumeration, classification and analysis of data by using appropriate statistical techniques.
Data are used to make observations about facts concerning the problem.
On the basis of observation, generalisation is logically derived which establishes a general truth from particular facts.
Thus, inductive is the process in which we arrive at a generalisation on the basis of particular observed facts.
i) It is highly practical and realistic as it descry things as they are.
ii) It is helpful in verifying the conclusions of the Deductive method.
iii) Economic laws under this method are not universal but valid only certain conditions.
i) Costly method: The Inductive y is not only time-consuming but also costly. It involves detailed and painstaking process of collection, classification, analyses and interpretation of data.
ii) Difficult to prove Hypothesis: Again, the use of statistics in inductive cannot prove Hypothesis. It can only show that the hypothesis is not inconsistent with the known facts.
The above analysis reveals that independently neither deductive not Inductive method is helpful in scientific enquiry; in reality, both deductive and inductive are related to each other because of
some facts.
Name: Ayogu Timothy peace. Reg no:2020/241317. Department:philosophy. 1, Deductive method is also called a priori reasoning, we begin from unchallenged elementary or rudimentary assumption, facts and
then arrive at conclusion (build a hypothesis or theory) using logical analysis or our own analytical skills *observation of task issue. *Making the hypothesis. *Testing the hypothesis using more
observation etc.. 2, Inductive method flow from fact theory first,we collect facts and informations then move towards providing evidence using economic theory facts. *Observation. *Formulation of
hypothesis. *Generalizing principles. *Verifying against actual facts.
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Assignment on Eco 101
What are the basic methods of analysis used by economists briefly and convincingly discuss each of them.we have two methods of Economic analysis they are no1 deductive method and no2 is inductive
Deductive method: we shall first explain the deductive method of deriving economic generalisations.THe deductive method is also called abstract analytical and a priori method and represents an
abstract approach to the derivation of Economic generalisations and theories.the principal steps in the process of deriving economic generalisations through deductive logic are
(a) perception of the problem to be enquired into
(b). Defining precisely the technical terms and making appropriate assumptions often called postulates or premises
Advertisement:(c) Deducing hypotheses, that is, deriving conclusions from the premises through the process of logical reasoning and (d) testing of hypothesis deduced
(a) perception of the problem:in any scientific enquiry the analyst or theorist must have a clear idea of the problem to be enquired into (b) definition of technical terms and making of
Assumptions:as mentioned above assumptions may be Behavioural pertaining to the behaviour of the economic variable or they may be technological and the factor endowments the crucial assumptions are
made in the basis of observation or introspection.(c) Deducing hypothesis through logical deduction: the next step in deriving generalisations through deductive, logic is Deducing hypotheses from the
assumptions or premises taken
(2) inductive method: the inductive method which is also called empirical method derives economic generalisations on the basis of experience and observations.in this method detailed data are
collected with regards to a certain economic phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.but ,it is worth mentioning that the
number of observations has to be large if it can yield a valid economic generalisation.one should not generalise on the basis of a very few observations, there are three ways which can be used for
deriving economic principles and theories they are
(a) Experimentation
(b) observations.
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They are the Deductive and Inductive methods
DEDUCTIVE METHOD: Is also known as the Analytical, Abstract or Priori method. The method consist in driving conclusions from general truths, takes few general principles and applies conclusions.
For instance if we accepts the general proposition that Manis entirely motivated by self_interest . In applying the deductive method of economic analysis we proceed from general to particular.
In dudective method of economic analysis we proceed from general to the particular. This is also known as Hypothetical method, for some of the assumptions may not correspond to be used as premises to
starting, reasoning and drawing conclusions.
I, Perception of the problem to be inquired into_In the process of driving economic generalizations, the analysis must have a clear and precise idea of the problem to be inquired into.
ii, Deducing hypothesis from the assumptions
III, Definition of terms
2 INDUCTIVE METHOD OF ECONOMIC ANALYSIS : It is also called Empirical method was adopted by the “Historical school of economist; it involves the process of reasoning from particular facts to general
This method derives economic generalizations on the basis of
I, Experimentations
ii, Observations and Statistical methods.
I It based on facts as such the method is realistic
ii, Inorder to test economic principles, method makes statistical techniques, the inductive method is therefore reliable.
III, It is dynamic
iv, Inductive method also helps in future investigation
Deductive method and Inductive methods are both needed for scientific thought, as the right and left foot are both needed for walking.
Economics as a social science has its way of conducting an investigation before the formation of law. They’re the deductive and inductive methods.
1. The deductive method.
The deductive method mostly lies on assumption. It is based on gathered facts and observations from which a conclusion is then derived through logical reasoning. For example, it is noted that prices
would increase when demand is high which means that a sudden large inflow of money will increase the amount of consumers in the market which increases demand thereby causing inflation. That is
observation and deduction. Although not all deductions might be true as they are considered hypothetical until they’re effectively proven. The deductive method of analysis consists of 3 stages.
a) Observation: At this stage, studies are carried out and market trends and changes are being observed in a given period of time. It is from these observations and research that certain deductions
are made.
b) Deductive reasoning: After an observation is made, a deduction is made through logical reasoning.
c) Testing of hypothesis’ model: Not all deductions are true, so they have to be tested both theoretically and practically before they are seen as a fact.
Advantages of deductive reasoning
1. It an easier and a less complicated form of analysis.
2. It is an analysis dispensable of experiments as most of its processes are done intellectually.
3. Due to the use of logic, it gives accurate and reliable results.
Disadvantages of deductive reasoning
1. Deductions made might not be realistic since practical engagements are less.
2. They’re based on assumptions and observations which if wrong, makes the deduction invalid.
3. Deductions might not be generalized since environmental differences might be a barrier for its universal accuracy.
2. Inductive Method
This method involves practical methods of experimentation to approach problems. Facts are gathered through surveys and stats which are then arranged to come up with conclusions that are further
verified. For example, after conducting a research on employees from different locations and discover that 85% spend most of their incomes on shoes, it can be concluded that shoes are the most bought
thing by salary earners. The Inductive method for conclusion is not based on any assumptions but from statiscal evidences which facts are being drawn from to be verified further.
Advantages of the inductive method
1. It lies on established facts, making conclusion’s accuracy not dependable on source.
2. It is future oriented. This means that information gotten can be used for future predictions.
3. It seems to be more realistic when compared to the deductive method.
Disadvantages of the inductive method
1. Due to this method being largely based on statiscal data, informations can be miss-interpreted and mis-used.
2. Approach of experiments might be different with different investigators, resulting to varying results.
3. It involves time and money.
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Economic generalization describe laws that govern the relationship between human behaviour and their location of scarce resources between alternative ends.
Like other science laws, generalization of economic state cause and effect relationship between variables and describe economic hypothesis which have been proven true by a empirical evidence. Before
approving a state a generalization true, steps of processes of logical reasonings and explanations on the stated variables will be carried out. The 2 methods I’ll discuss is :
(a) THE DEDUCTIVE METHOD: This represents an abstract method in approaching generalization theories. the various steps in reaching a conclusion include:
(i) Perception of a problem: The economist must understand the problem he is peering into as well as the variables he will consider and people he will interrogate.
(ii) Defining Technical Terms: The economist must make use of clear terms used in the analysis as well as keeping tabs and records on the assumptions made.
(iii) Deducing Hypothesis: A hypothesis describes relationship between factors affecting a phenomenon; it establishes the cause and effect relationship between the variables having a bearing on the
phenomenon. Through logical process, a hypothesis is drawn from the assumptions made.
(iv) Verification of the hypothesis: Unlike science, economists cannot make controlled experiments and must reply on observations and statistics, so testing and re-testing a given hypothesis must be
carried out before a generalization law is made.
1. Useful mathematical techniques can be employed to derive laws and theories of economics.
2. The use of complex mathematical methods in the deductive approach enables the economists to introduce accuracy in their economic principles and theories.
1. It requires the high level of competence and logic.
2 It depends too much on assumptions.
(b) THE INDUCTIVE METHOD: This is also called the empirical method which is arrived at from observations and experiences. Here, detailed data are collected with regard to a certain economic
phenomenon and effort is then made to arrive at certain generalisations which follow from the observations collected.
the steps in arriving at a generalization from this method is much similar to that of the deductive method but at the third step;
data about variables relating to a problem and doing some preliminary thinking about the possible functional relationships between the relevant variables is done.
The next important step in the construction of economic theories in this method is the processing of data collected and finding out what relations between the variables actually hold good. From this,
a theory is developed which can be further refined and tested through statistical methods.
Once the theory has been developed one can make predictions on its basis, as is done in the deductive approach. If predictions of theory are in agreement with the facts and actual behaviour of the
economy, then a new reliable theory has been developed.
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This is also called a priori reasoning. We start from unchallenged elementary or rudimentary assumptions/ facts and then arrive at conclusions(build a hypothesis or theory) using logical analysis or
our own analytical abilities. In this kind of reasoning, we go from general to specific. The stages in deductive reasoning are:
Observation Of A Task /Issue
1. Making the hypothesis
2. Testing the hypothesis using more observations, etc.
3. This reasoning gives us a hypothesis and if this hypothesis gets verified we get general economic principles or laws.
Advantages of Deductive Method
1. It is a simple method, doesn’t involve the use of any complex software analysis, etc.
2. only simple deductive logic is required.
3. This method is important for economists as it focuses upon economic reasoning which is of paramount importance.
Disadvantages of Deductive Method
In this method of reasoning we start from assumptions, thus, if the assumptions happen to be logically flawed the whole process becomes faulty and would give wrong conclusions. Thus, the logical
fallacy is a disadvantage of this method.
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates principles
using the sub-methods- Observations, Experimentations, Statistical methods.
Data is collected about a particular economic theory and then conclusions are drawn. The stages in this method are:
1. Observation
2. Formulation of a hypothesis
3. Generalizing principles
4. Verifying against actual facts.
Advantages Of Inductive Method
1. Since it is based on facts it is more realistic and reliable.
2. Using statistical methods and experimentations makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
3. Since the economic environment is dynamic and always changing, relying upon a more scientific method always helps reach logical conclusions.
Disadvantages Of Inductive Method
1. If the data used is insufficient and faulty it would lead to faulty conclusions, making the hypothesis less reliable.
2. It is a time-consuming process and thus expensive as well.
3. The collection of all the data is not an easy job and varies from person to person. As to how they collect data.
Name: ONAH JUDITH UGOCHI
Dept: ECONOMICS
matric number: 2020/242646
Level: 100.
The methods used in Economic analysis are;
*) Inductive method and,
*) Deductive method.
INDUCTIVE METHOD: This is also called empirical method. This derives Economic generalizations on the basis of experience and observations. First, we collect information and facts and then move
towards providing evidence using Economic theory and facts.
The stages includes;
a) Observation
b) Formulations of a hypothesis
C) Generalizing principles.
d) verifying against actual facts.
Advantages of inductive methods.
i) It is realistic because it is based in facts and explains them as they actually are.
ii) It helps in future enquiries. For once a generalisation is established, it becomes the starting point of future enquiries.
Disadvantages of inductive methods.
i) Lacks concreteness as sources, definitions, and methods used in statistical analysis differ from investigator to investigator.
ii) The inductive method is not only time consuming but also costly.
2) DEDUCTIVE METHOD: This is also called priori, abstract and analytical reasoning. This method derives Economic generalizations on the basis of assumptions or unchallenged elementary and then arrive
at conclusions using logical analysis or our own abilities.
The stages includes;
a) Observations
b) Making the hypothesis
c) Testing the hypothesis using more observations
Advantages of deductive method.
i) deductive method is indispensable in sciences like Economics where experimentation is not possible.
ii) Deductive method is less time consuming and less expensive when compared to inductive method.
Disadvantages of Deductive method.
i) A good deal of care and objectivity is needed to avoid bad logic or faulty Economic reasoning.
ii) It requires the use of a high level competence in logic and theoretical abstraction.
Basic Methods of Economic Analysis:
We have two methods of Economic Analysis they are:
1) Deductive Method.
2) Inductive Method.
Deductive Method: This method is also called analytical method and it represents an Idealized way to the derivation of Economic generalization and theory.
The four major step involved in the process of Economic Analysis through Deductive Method are:
a) perception or Identification of the product to be enquired about.
b) defining precisely the technical terms and making appropriate assumptions usually called ‘postulate’ or ‘premise’.
c) Deducing hypothesis which means deriving conclusion from postulates through logical reasoning.
d) Testing of the deduced hypothesis.
Merits of Deductive Method
– It is an easy method and doesn’t involve the use of any complex software analysis, only simple Deductive logic is required.
-this method focuses on economic reasoning which is of great importance.
Demerits of Deductive Method.
In this Method of reasoning it begins from assumptions and if the assumption is flawed the whole process becomes faulty and would give a wrong conclusion. Thus, the logical fallacy is a disadvantage
in this method.
2) Inductive Method: This method flows from facts and then move towards providing evidence using economic theory. Through this method, principles are formulated using these stages:
– Observation
– Formulation of a hypothesis
– Generalizing principles
– Verifying against actual facts.
Merits of Inductive Method:
– since it is based on facts it is more realistic and reliable.
– Using statistical method and experiments makes the process more scientific thus more acceptable universally.
Demerits of Inductive Method
– If the data used is faulty, it will then lead to a faulty conclusion, therefore making the hypothesis less reliable.
– It is a time consuming process and also expensive.
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Economic analysis is divided into two, namely:
(1) Inductive reasoning: or inductive logic, is a type of reasoning that involves drawing a general conclusion from a set of specific observations. Inductive reasoning is the opposite of deductive
reasoning. It makes broad generalizations from specific observations. This reasoning is also known as a derivation of generalization based on experience and observations. It is also a practical
approach to the problems of economic science.
(2) Deductive reasoning:is a basic form of valid reasoning. Deductive reasoning, or deduction, starts out with a general statement or hypothesis and examines the possibilities to reach a specific,
logical conclusion.
Deductive research approach explores a known theory or phenomenon and tests if that theory is valid in given circumstances. The deductive approach follows the path of logic most closely. This method
of Economic analysis starts with a theory and leads to a new hypothesis. The hypothesis is then, put to the test by confronting it with observations that either lead to a confirmation or a rejection
of the hypothesis before arriving to a conclusion.
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Some of the most important economic analysis are as follow:
Deductive method
Inductive method
I shall first explain the deductive method of deriving economic generalisation.the deductive method is also called abstract, analytical and priori methods and represent an abstract approach to the
derivation of economic generalisation and theories.
Bachelors are unmarried men,Bill is unmarried therefore Bill is a bachelor.
Indeductive method: which is also called empirical method was adopted by the historical school of economists.its involve in the process of reasoning from particular facts to general principle.this
method derives economics generalisations on basis of
Observation and
Statistical method
In this method,data is collected about a certain economic phenomenon
Steps of indeductive method
Formulation hypothesis
1) DEDUCTIVE METHOD
its a method of economic analysis we proceed from the general to the particular. This is also know as an hypothetical method for some of the assumption may no correspond to actual facts which may be
used as premise for starting reasoning and drawing conclusions. The stages in deductive method are:
1) Observation of tasks/issue
2) Making the hypothesis
3) Testing the hypothesis
1) It focuses upon economic reasoning which is for Paramount importance.
2) It is a simple method, doesn’t involve the use of complex software, etc. Only simple deductive logic is required.
1) It is time-consuming process and this expensive as well
2) The collector of all data is not an easy job and varies from person to person. As to how they collect data.
2) INDUCTIVE METHOD
This type of reasoning flows from facts to theory. First, we collect information and facts and then move towards providing evidence using economic theory and facts. This method formulates principles
using the sub methods observations, experimentation, statistical methods. The stages in the method are; Observation, Formulation of hypothesis, Generalising principles, Verifying against actual
1) It is more realistic and reliable
2) Using statistical method and experimentation makes the process more scientific, thus, more acceptable universally rather than just depending on your own reasoning and logic.
1)It is time consuming process and thus expensive
2)The collection of all data is not an easy job and varies from person to person, As to how they collect data.
Economic analysis involves the formulation of laws and generalizations. Economic generalizations describe the laws or statements of tendencies in various branches of economics such as production,
consumption, exchange and distribution of income.
Economic analysis is done by two major ways; deductive and inductive methods.
1- DEDUCTIVE METHOD: This is also called priori reasoning and in this kind of reasoning, we move from general to specific. It involves three stages;
* Observation of a task or an issue.
* Making hypothesis
* Testing the hypothesis using more observations.
– We start with unchallenged elementary assumptions/facts and then arrive at conclusions ( build a hypothesis) using our own logical analysis or analytical abilities. If the hypothesis is tested and
verified, we get general economic principle or law.
– It is a simple method, does not involve the use of any complex software analysis, only simple deductive loo oguc is required.
– It focuses on economic reasoning which is of paramount importance.
This disadvantage of this method is logical fallacy which may arise, since the assumptions could be logically flawed leading to wrong conclusions.
2- INDUCTIVE METHOD: This type of reasoning flows from facts to theory. It formulates principles using the sub- methods; observation, experimentations, statistical methods. The stages involved here
* Observation
* Formulation of a hypothesis.
* Generalizing principles.
* Verifying against actual facts.
– First, we collect information/ facts and then move towards providing evidence using economic theory/ facts.
– Using statistical methods and experimentations makes the process more scientific and thus, more accepted universally rather than just depending on your own reasoning and logic.
– Due to the dynamic state of the economic environment, relying more on scientific method always help us reach logical conclusions.
– It is time consuming and very expensive.
– The collection of all data is not easy and vaires from person to person.
– If the data used is insufficient or faulty, it makes the conclusions faulty and the hypothesis equally becomes less reliable.
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An economic analysis is a process followed by experts to understand how key economic factors affect the functioning of an organization, industry, region or any other particular population group, with
the purpose of making wiser decisions for the future.
It has two methods, which are:
1.Deductive Method
2.Inductive Method
1.Deductive Method:
According to Aristotle, a deduction is an argument in which, certain things being laid down, something other than these necessarily comes about through them.
The deductive profiling method relies on the application of deductive reasoning to the observable evidence. Investigators collect general information about the crime, and the profiler draws specific
conclusions about the criminal’s characteristics, based on the profiler’s experience, knowledge, and critical thinking. Victimology, the crime scene, forensic evidence, and behavioral analysis are
all components of the deductive process.
In Deductive method of Economic Analysis we proceed from the general to the particular. This is also known as an hypothetical method for some of the assumptions may not correspond to actual facts,
but very near actual facts which may be used as premise for starting, reasoning and drawing conclusions. In economics we start with very simple premises and work up gradually or more and more complex
The deductive method involves several distinct steps:
1. A problem is stated.
2. Information is collected.
3. A working hypothesis is formulated.
4. The hypothesis is tested.
5. Results of the test are examined.
6. One or more conclusions are reached.
Hypotheses can be tested using if/then thinking. We might start with a hypothesis such as “Hackers are mostly harmless.” If our hypothesis is correct, the data should show that the vast majority of
hacking incidents cause no monetary loss or other harm to the companies or individuals whose systems are hacked. Finding one or two incidences of loss or harm would not disprove the hypothesis—but if
we find large numbers of cases that are inconsistent with our hypothesis, we can consider it to be invalid. Our conclusion, then, could be the opposite of the hypothesis we started with: Hackers are
not “mostly harmless.”
Perhaps one of the most famous proponents of deductive reasoning was Sir Arthur Conan Doyle, the Scottish writer and physician who created the Sherlock Holmes character in the 1880s. Doyle summed up
the deductive method rather succinctly: “It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth.”
1. Nearer to reality : Deductive method is nearer to reality. It helps us to make deductions from the complex conditions of the world.
2. Simple : Deductive method is very simple in nature. It avoids the collection of statistical data and information for proving economic laws.
3. Analytical: This method is useful for analyzing complex economic phenomena. It divides a particular economic problem into several components.
4. Universal validity : The inferences adopted and the conclusions made under this method have universal validity. The reason is that the inferences are based on certain general principles.
5. Indispensable : This method is regarded as an indispensable method in Economics. As Gide and Rist pointed out “In a science like Political Economy experiment is practically impossible. Abstraction
and analysis afford the only means of escape from those other influences which complicate the problem so much”.
6. More reliability : In Economics it is difficult to prove certain generalizations through controlled experiments. This is due to the fact that economic phenomena are related to human behavior which
varies continuously.
7.Reveals inconsistencies : This method provides scope for adopting mathematical approach for arriving conclusions. So it reveals the inconsistencies in the economic phenomena.
1. Generalizations – full of faults : The proposers of this wrongly assumed that their abstractions always correspond with the facts. So any research scholar commits the same mistake if he tries to
deduce faulty generalizations.
2. Universal applicability – a myth : The statement that deductive method has universal applicability is not real. Because the causes and conclusions of economic problems differ from country to
country and from time to time. That is why Professor Lerner criticized that this method is simply an ‘arm chair analysis’ which can’t be regarded as universal
3. Based on wrong assumptions : Deductive method is based on certain assumptions. But the assumptions may not be real at all times. So the conclusions based on these assumptions may not be real. For
instance, this method assumes that individuals behave in a rational manner. But no one can definitely say when individuals behave rationally.
4. Makes economics dogmatic : This method makes Economics dogmatic as it refuses to admit that there can be some defects on the assumptions.
5. Difficulty in testing the conclusions : This method make difficult to test the validity of conclusions. The conclusions drawn under this method are neither feasible nor practicable.
6. Inadequate, data : The followers of this method adopted it on the basis of inadequate data. So the conditions arrived from the assumption, were full of inconsistencies.
2. INDUCTIVE METHOD
Inductive method (Inductive Reasoning) is an important method used by the economist for making conclusions on economic phenomena. It involves the process of reasoning from particular facts to the
general principles. When compared to deductive method, inductive method is considered to be the more realistic, concrete and accurate method. It helps in future inquiries and acts as a guide for
future inquiries. It helps in future investigation through discovery and evidence of gener
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Prestige is a mechanic in Incremental Cubes which acts as a "soft reset" function.
Prestiging[ ]
When you Prestige, you lose the following stuff:
• All progress through the Tiers and Phases, resetting you to Tier 1, Phase 2. This means the Cube Level and Cube Size will reset to their base values of 0 and 1 by 1 by 1 respectively.
• All progress on the Power of Cube, including all upgrades, levels and cubes stored.
• All Tick Speed and Cube Multiplier upgrades.
• All Color Meters barring White.
• All Helper Upgrades.
However, the following stuff will remain when you Prestige:
• The Levels of all of your Helpers.
• The Zoom Multiplier and progress towards the next upgrade for it.
• Your Inventory. (but the Item Drop Rate and Rare Item Odds will reset)
• Your Skill Points and Prestige Perks.
• Your Max Damage and Max Cubes Collected.
• Your Rubies.
Also, when you Prestige, you have the chance to spend the Skill Points on Prestige Perks in any and all unlocked Prestige Octahedrons you have access to.
The Prestige Octahedron[ ]
See also: the Prestige Tree
There are seven Prestige Octahedrons which you can work your way through, each of them acting as sort of a Perk Tree. At the start, you can only buy the topmost node of a Prestige Octahedron you have
unlocked, but you are also allowed to buy other nodes connected to the nodes you have brought. You can also sell nodes back to get the Skill Points back, and you can do so even if it would disconnect
a node from having a route of connected nodes to the topmost node. Finally, once all nodes of a single Prestige Octahedron are brought at the same time for the first time, the next Prestige
Octahedron will automatically unlock.
Note that for each node unlocked, you also gain a 10% additive Skill Sphere Multiplier as well.
Tier 1 Octahedron[ ]
The first Prestige Octahedron contains the following Perk Nodes:
Level 1 Node[ ]
• Auto Collect - 1 Skill Point, enables idle Collecting which can be toggled on and off
Level 2 Nodes[ ]
• Auto Attack - 1 Skill Point, enables idle Attacking which can be toggled on and off
• Attack +5% - 2 Skill Points, boosts cube-based Attacks by an mutilative 5%
• Bonus Multiplier +5% x2 - 2 Skill Points each, boosts the value of all cubes by an mutilative 5% each
Level 3 Nodes[ ]
• Bluecube +1% x3 - 6 Skill Points each, adds an additive 1% chance each of the White Meter producing a Blue Cube instead
• Attack +5% - 6 Skill Points, boosts cube-based Attacks by an mutilative 5%
• Skill Point Multiplier +5% x2 - 6 Skill Points each, boosts the Skill Points gained from attacking by an additive 5% each
• Bonus Multiplier Multiplier +5% x2 - 6 Skill Points each, boosts the value of all cubes by an mutilative 5% each with this multiplier stacking on top of the normal Bonus Multiplier
Level 4 Nodes[ ]
• Bluecube +1% x2 - 12 Skill Points each, adds an additive 1% chance each of the White Meter producing a Blue Cube instead
• Color Cube Discount +5% x2 - 12 Skill Points each, adds an additive 5% discount each to the Tick Speed cost
Level 5 Node[ ]
• Power of Cube - 24 Skill Points, unlocks the Power of Cube multipliers
Tier 2 Octahedron[ ]
The second Prestige Octahedron contains the following Perk Nodes:
Level 1 Node[ ]
Level 2 Nodes[ ]
• Attack +7% x2 - 43 Skill Points each, boosts cube-based Attacks by an mutilative 7% each
• Bonus Multiplier +7% - 43 Skill Points, boosts the value of all cubes by an mutilative 7%
• Enemy HP -3% - 43 Skill Points, reduces the starting HP of enemies by an additive 3%
Level 3 Nodes[ ]
• Green Cube +0.5% x2 - 125 Skill Points each, adds an additive 0.5% chance each of the White Meter producing a Green Cube instead
• Skill Point Multiplier +7% x3 - 125 Skill Points each, boosts the Skill Points gained from attacking by an additive 7% each
• Enemy HP -3% x2 - 125 Skill Points each, reduces the starting HP of enemies by an additive 3% each
• Bonus Multiplier +7% - 125 Skill Points, boosts the value of all cubes by an mutilative 7%
Level 4 Nodes[ ]
• Green Cube +0.5% x2 - 250 Skill Points each, adds an additive 0.5% chance each of the White Meter producing a Green Cube instead
• Color Cube Discount +7% x2 - 250 Skill Points each, adds an additive 7% discount each to the Tick Speed cost
Level 5 Node[ ]
• Mini Booster - 380 Skill Points, creates a bar which takes about 10s to charge up before emptying over 5s, boosting the White Tick speed when emptying
Tier 3 Octahedron[ ]
The third Prestige Octahedron contains the following Perk Nodes:
Level 1 Node[ ]
Level 2 Nodes[ ]
• Bonus Multiplier +9% x2 - 650 Skill Points each, boosts the value of all cubes by an mutilative 9% each
• Attack +9% - 650 Skill Points, boosts cube-based Attacks by an mutilative 9%
• Enemy HP -4% - 650 Skill Points, reduces the starting HP of enemies by an additive 4%
Level 3 Nodes[ ]
• Skill Point Multiplier +9% x2 - 1930 Skill Points each, boosts the Skill Points gained from attacking by an additive 9% each
• Orange Cube +0.25% x4 - 1930 Skill Points each, adds an additive 0.25% chance each of the White Meter producing an Orange Cube instead
• Color Cube Discount +9% x2 - 1930 Skill Points each, adds an additive 9% discount each to the Tick Speed cost
Level 4 Nodes[ ]
• Attack +9% - 3860 Skill Points, boosts cube-based Attacks by an mutilative 9%
• Bonus Multiplier +9% - 3860 Skill Points, boosts the value of all cubes by an mutilative 9%
• Orange Cube +0.25% - 3860 Skill Points, adds an additive 0.25% chance of the White Meter producing an Orange Cube instead
• Enemy HP -4% - 3860 Skill Points, reduces the starting HP of enemies by an additive 4%
Level 5 Node[ ]
• Attack Bonus Collect +10% - 5800 Skill Points, when attacking, an additive 10% of the damage dealt will be added to your Cube Balance
Tier 4 Octahedron[ ]
The fourth Prestige Octahedron contains the following Perk Nodes:
Level 1 Node[ ]
Level 2 Nodes[ ]
• Attack +11% - 8.65k Skill Points, boosts cube-based Attacks by an mutilative 11%
• Bonus Multiplier +11% x2 - 8.65k Skill Points each, boosts the value of all cubes by an mutilative 11% each
• Enemy HP -5% - 8.65k Skill Points, reduces the starting HP of enemies by an additive 5%
Level 3 Nodes[ ]
• Attack Bonus Collect +5% x2 - 26k Skill Points each, when attacking, an additive 5% each of the damage dealt will be added to your Cube Balance
• Skill Point Multiplier +11% x2 - 26k Skill Points each, boosts the Skill Points gained from attacking by an additive 11% each
• Color Cube Discount +11% x2 - 26k Skill Points each, adds an additive 11% discount each to the Tick Speed cost
• Red Cube +0.2% - 26k Skill Points, adds an additive 0.2% chance of the White Meter producing a Red Cube instead
• Attack +11% - 26k Skill Points, boosts cube-based Attacks by an mutilative 11%
Level 4 Nodes[ ]
• Bonus Multiplier +11% x2 - 52k Skill Points each, boosts the value of all cubes by an mutilative 11%
• Enemy HP -5% - 52k Skill Points, reduces the starting HP of enemies by an additive 5%
• Red Cube +0.3% - 52k Skill Points, adds an additive 0.3% chance of the White Meter producing a Red Cube instead
Level 5 Node[ ]
• Booster - 78k Skill Points, creates a bar which takes about 10s to charge up before emptying over 5s, boosting the White Tick speed when emptying
Tier 5 Octahedron[ ]
The fifth Prestige Octahedron contains the following Perk Nodes:
Level 1 Node[ ]
Level 2 Nodes[ ]
• Attack +13% x2 - 109k Skill Points each, boosts cube-based Attacks by an mutilative 13% each
• Bonus Multiplier +13% x2 - 109k Skill Points each, boosts the value of all cubes by an mutilative 13% each
Level 3 Nodes[ ]
• Attack +13% x2 - 327k Skill Points, boosts cube-based Attacks by an mutilative 13% each
• Skill Point Multiplier +13% x2 - 327k Skill Points each, boosts the Skill Points gained from attacking by an additive 13% each
• Bonus Multiplier +13% x2 - 327k Skill Points each, boosts the value of all cubes by an mutilative 13% each
• Enemy HP -6% - 327k Skill Points, reduces the starting HP of enemies by an additive 6%
• Color Cube Discount +13% - 327k Skill Points each, adds an additive 13% discount each to the Tick Speed cost
Level 4 Nodes[ ]
• Attack Bonus Collect +7% x2 - 653k Skill Points each, when attacking, an additive 7% each of the damage dealt will be added to your Cube Balance
• Gold Cube +0.125% - 653k Skill Points, adds an additive 0.125% chance of the White Meter producing a Gold Cube instead
Level 5 Node[ ]
• Collect Bonus Attack +10% - 980k Skill Points, when collecting an additive 10% of the cubes collected will be dealt as damage to the enemy
Tier 6 Octahedron[ ]
The sixth Prestige Octahedron contains the following Perk Nodes:
Level 1 Node[ ]
Level 2 Nodes[ ]
• Attack +15% - 1.31M Skill Points, boosts cube-based Attacks by an mutilative 15%
• Bonus Multiplier +15% x2 - 1.31M Skill Points each, boosts the value of all cubes by an mutilative 13% each
• Skill Point Multiplier +15% - 1.31M Skill Points each, boosts the Skill Points gained from attacking by an additive 15%
Level 3 Nodes[ ]
• Enemy HP -7% - 3.93M Skill Points, reduces the starting HP of enemies by an additive 7%
• Bonus Multiplier +15% x2 - 1.31M Skill Points each, boosts the value of all cubes by an mutilative 13% each
• Attack Bonus Collect +9% x3 - 3.93M Skill Points each, when attacking, an additive 9% each of the damage dealt will be added to your Cube Balance
• Skill Point Multiplier +15% x2 - 3.93M Skill Points each, boosts the Skill Points gained from attacking by an additive 15% each
Level 4 Nodes[ ]
• Collect Bonus Attack +5% x2 - 7.87M Skill Points each, when collecting, an additive 5% each of the cubes collected will be dealt as damage to the enemy
• Platinum Cube +0.05% x2 - 7.87M Skill Points each, adds an additive 0.05% chance each of the White Meter producing a Platinum Cube instead
Level 5 Node[ ]
• Delta Booster - 11.8M Skill Points, adds a random multiplier (between 1.00x and 2.00x) to attacks based on the meter
Tier 7 Octahedron[ ]
The seventh (and final as of Version 1.3) Prestige Octahedron contains the following Perk Nodes:
Level 1 Node[ ]
Level 2 Nodes[ ]
• Attack +17% - 15.3M Skill Points each, boosts cube-based Attacks by an mutilative 17%
• Bonus Multiplier +17% x2 - 15.3M Skill Points each, boosts the value of all cubes by an mutilative 17% each
• Skill Point Multiplier +15% - 15.3M Skill Points each, boosts the Skill Points gained from attacking by an additive 15%
Level 3 Nodes[ ]
• Enemy HP -8% - 46M Skill Points, reduces the starting HP of enemies by an additive 8%
• Bonus Multiplier +17% x2 - 46M Skill Points each, boosts the value of all cubes by an mutilative 17% each
• Attack Bonus Collect +11% x2 - 46M Skill Points each, when attacking, an additive 11% each of the damage dealt will be added to your Cube Balance
• Skill Point Multiplier +17% x2 - 46M Skill Points each, boosts the Skill Points gained from attacking by an additive 17% each
• Collect Bonus Attack +7% - 46M Skill Points each, when collecting, an additive 7% of the cubes collected will be dealt as damage to the enemy
Level 4 Nodes[ ]
• Collect Bonus Attack +7% x2 - 92M Skill Points each, when collecting, an additive 5% each of the cubes collected will be dealt as damage to the enemy
• Enemy HP -8% - 92M Skill Points each, reduces the starting HP of enemies by an additive 8% each
Level 5 Node[ ]
• Bonus Collect Bonus Attack +50% - 138M Skill Points, 50% of all cubes collected will be dealt as damage to the enemy, and 50% of all damage dealt when attacking will be added to your Cube Balance
- this bonus stacks additively with both Attack Bonus Collect and Collect Bonus Attack
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Printable Calendars AT A GLANCE
Multiplication Table 1 12 Free Printable
Multiplication Table 1 12 Free Printable - Multiplication tables are essential for students working out math problems. Web this multiplication table 1 to 12 is consist of 12 rows with a respective
operation of multiplication, which is very beneficial to learn the basic multiplication of 1 to 12 table. Printable multiplication flash cards where kids can review facts from 1 to 12. Students can
use this simple multiplication table chart as a reference tool to solve simple equations. It is in standard a4 size so you can easily print it at home. You can use it as a reminder or to learn your
times tables up to 12x12 multiplication. This is a multiplication chart that shows how to multiply different numbers. Users can enter numbers in. Web free printable multiplication charts (times
tables) available in pdf format. Web it is a chart with a grid of numbers from 1 to 12, which can help you learn to multiplication quickly, either using the table or in your head.
Web here are free printable times tables charts from 1 to 12 and many other great resources designed for your students/kids! This multiplication table from 1 to 12 is useful for kids learning how to
multiply. Users can enter numbers in. By clicking on the button above, you can print or download this pdf chart. Web worksheets math drills multiplication facts multiplying by 12 multiplying by 12
multiplication facts with 12's students multiply 12 times numbers between 1 and 12. Web it is a chart with a grid of numbers from 1 to 12, which can help you learn to multiplication quickly, either
using the table or in your head. There are printable tables for individual sets of math facts, as well as complete reference multiplication tables for.
Web here are free printable times tables charts from 1 to 12 and many other great resources designed for your students/kids! This multiplication table from 1 to 12 is useful for kids learning how to
multiply. Print the multiplications facts worksheets This is a multiplication chart that shows how to multiply different numbers. A multiplication table is born with mathematics.
Multiplication Facts 1 12 Printable Times Tables Worksheets
Web these are perfect multiplication worksheets for grade 3 to help kids slowly learn the multiplication tables starting with 1s and inching your way up to 12s. Children will need a thorough
understanding of each to excel in maths lessons throughout their time in education. Use these colorful multiplication tables to help your child build confidence while mastering the multiplication.
Multiplication Table 112 Free Printable Paper
Web looking for a smaller or larger multiplication table? Web here is the printable multiplication chart (pdf) from the 1 time table up to the 12 times table, it's a free resource. Multiplication
tables are essential for students working out math problems. A multiplication table is born with mathematics. Use these colorful multiplication tables to help your child build confidence.
112 Multiplication Chart Free Download
These math multiplication worksheets are free and a great way to get 3rd graders started on the concept of single digit multiplication. Memorizing the times table gives children a foundation on which
they can build their mathematical skills.paper size: A multiplication table is born with mathematics. November 25, 2022 1 comment. Printable multiplication flash cards where kids can review facts.
Free Printable Multiplication Chart 112 Table PDF
Frequently asked questions on tables 1 to 12 Print the multiplications facts worksheets These table charts are suitable for the kids from the 1st standard to the 5th standard. Use these colorful
multiplication tables to help your child build confidence while mastering the multiplication facts. We have multiplication tables of 1 and 12 on our platform.
Math Tables 1 to 12 Printable Multiplication Chart 1 to 12 Maths
This multiplication table from 1 to 12 is useful for kids learning how to multiply. Feel free to color it to memorize more easily. Web this multiplication table 1 to 12 is consist of 12 rows with a
respective operation of multiplication, which is very beneficial to learn the basic multiplication of 1 to 12 table. Hang this pdf multiplication.
Multiplication Chart 1 12 Free Printable
A multiplication table is born with mathematics. Web it is a chart with a grid of numbers from 1 to 12, which can help you learn to multiplication quickly, either using the table or in your head. Web
what is the total amount of money he earned for 8 hours? This multiplication table from 1 to 12 is useful for.
Multiplication Chart 112 Free Printable Paper
Printable multiplication flash cards where kids can review facts from 1 to 12. Multiplication tables are essential for students working out math problems. You can use the blank times table chart to
practice multiplication facts and the prefilled multiplication charts to place on the kids’ room or classroom wall. The total amount of money michael earned for 8 hours is.
Printable 112 Multiplication Chart
Frequently asked questions on tables 1 to 12 This multiplication table from 1 to 12 is useful for kids learning how to multiply. The total amount of money michael earned for 8 hours is 10 x 8 = 80 $.
You can use the blank times table chart to practice multiplication facts and the prefilled multiplication charts to place on.
Free Multiplication Chart Printable Paper Trail Design
Memorizing the times table gives children a foundation on which they can build their mathematical skills.paper size: I have got you covered with free printable pdfs to download and print! There are
printable tables for individual sets of math facts, as well as complete reference multiplication tables for. This is a multiplication chart that shows how to multiply different numbers..
Multiplication Table 1 12 Free Printable - I have got you covered with free printable pdfs to download and print! Print the multiplications facts worksheets There are printable tables for individual
sets of math facts, as well as complete reference multiplication tables for. Web here are free printable times tables charts from 1 to 12 and many other great resources designed for your students/
kids! This is a multiplication chart that shows how to multiply different numbers. We have multiplication tables of 1 and 12 on our platform. You can use it as a reminder or to learn your times
tables up to 12x12 multiplication. November 25, 2022 1 comment. Web here is the printable multiplication chart (pdf) from the 1 time table up to the 12 times table, it's a free resource. If you love
mathematics, then you need to love multiplication tables.
Web this multiplication table 1 to 12 is consist of 12 rows with a respective operation of multiplication, which is very beneficial to learn the basic multiplication of 1 to 12 table. Web here is the
printable multiplication chart (pdf) from the 1 time table up to the 12 times table, it's a free resource. These math multiplication worksheets are free and a great way to get 3rd graders started on
the concept of single digit multiplication. This is a multiplication chart that shows how to multiply different numbers. Worksheet #2 worksheet #3 100 questions:
Our list of tips and games makes multiplication easy and fun. Frequently asked questions on tables 1 to 12 When you are just getting started learning the multiplication tables, these simple printable
pages are great tools! This multiplication table from 1 to 12 is useful for kids learning how to multiply.
Feel Free To Color It To Memorize More Easily.
Printable multiplication flash cards where kids can review facts from 1 to 12. For more ideas see printable paper and math drills and math problems generator. Students can use this simple
multiplication table chart as a reference tool to solve simple equations. This times tables chart is a colorful and engaging resource that you can print and use at home or in the classroom.
A Multiplication Table Is Born With Mathematics.
There are printable tables for individual sets of math facts, as well as complete reference multiplication tables for. These table charts are suitable for the kids from the 1st standard to the 5th
standard. Web it is a chart with a grid of numbers from 1 to 12, which can help you learn to multiplication quickly, either using the table or in your head. Web free printable multiplication charts
(times tables) available in pdf format.
You Can Use The Blank Times Table Chart To Practice Multiplication Facts And The Prefilled Multiplication Charts To Place On The Kids’ Room Or Classroom Wall.
Frequently asked questions on tables 1 to 12 This multiplication table from 1 to 12 is useful for kids learning how to multiply. To get the pdf of 1 to 12 table, click the download option and take a
print of this 1 to 12 multiplication table. Web worksheets math drills multiplication facts multiplying by 12 multiplying by 12 multiplication facts with 12's students multiply 12 times numbers
between 1 and 12.
Worksheet #2 Worksheet #3 100 Questions:
Children will need a thorough understanding of each to excel in maths lessons throughout their time in education. Web what is the total amount of money he earned for 8 hours? Web here are free
printable times tables charts from 1 to 12 and many other great resources designed for your students/kids! The total amount of money michael earned for 8 hours is 10 x 8 = 80 $.
Related Post:
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Measure the length ,breadth and height of different rooms of your house and find volume and surface area of it
1 thought on “Measure the length ,breadth and height of different rooms of your house and find volume and surface area of it<br /><br />”
1. Answer:
Out of the four walls to be painted,
2 wall have the dimensions (8×4) cm
and other 2 walls have the dimensions (6×4) cm
So, total wall area to be painted =2(8×4)+2(6×4)
=112 cm
Rate of cost of painting =0.045 /cm
So, total cost =0.045×112
Step-by-step explanation:
Leave a Comment
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Vectomorph allows the exploration of synthesis using vector oscillators.
This oscillator waveform is made up from 4 lines where each line is described by a level (affecting rate of change) and a point in time for the line to end. The start and end point of each cycle is
zero so this needs 4 levels but only 3 time-points, since the end time of the cycle is the same as the start of the next cycle.
The fiendishly clever Martin Vicanek designed the oscillator which uses parabola oscillators and varies the amplitude and phase of each to produce linear sections. This method allows for further
variations of the curviness of the lines by controlling the relative amplitudes of the parabola waves. The curviness subtly affects the higher harmonic content. The oscillators produce a clean sound
due to employing anti-aliasing techniques.
In addition, a sawtooth wave can be added to increase the amplitude of higher harmonics. A noise source is provided (3 types) and a state variable filter.
The parameters that control the wave shape, noise level and filter settings can be modulated in real-time, and in the Vectomorph this is realised by shifting between 2 sets of controls. The shifting
produces true morphing of the wave shape between the controls’ settings and can be achieved manually, with an LFO, or a multi-stage envelope generator, or any combination of these 3 sources.
There are 2 identical generators provided and each can be tuned individually to further increase the range of possibilities.
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uniform distribution matlab
Open Live Script. This distribution is appropriate for representing round-off errors in values tabulated to a particular number of decimal places. The result p is the probability that a single
observation from a uniform distribution with parameters a and b falls in the interval [a x].. For an example, see Compute Continuous Uniform Distribution cdf.. Descriptive Statistics. Example 3 in
the documentation shows how to apply it to a uniform distribution. As for all discrete distributions, the cdf is a step function. The lowest-level (built-in), fastest functions are: rand for a
continuous uniform distribution on (0,1), randn for a normal (Gaussian) distribution with mean 0 and variance 1, and randi for a uniform discrete distribution. Further to Colin's answer, goodness of
fit for uniform distribution can be calculated using a Pearson's chi-squared test. The result p is the probability that a single observation from a uniform distribution with parameters a and b falls
in the interval [a x].. For an example, see Compute Continuous Uniform Distribution cdf.. Descriptive Statistics. The mean of the uniform distribution is μ = 1 2 (a + b).. The variance of the uniform
distribution is σ 2 = 1 12 (b − a) 2. If you have access to the Matlab stats toolbox you can perform this fairly simply by using the chi2gof function. The discrete uniform distribution is a simple
distribution that puts equal weight on the integers from one to N. Examples Plot a Discrete Uniform Distribution cdf. ... Run the command by entering it in the MATLAB Command Window. The
distribution-specific functions can accept parameters of multiple uniform distributions. This MATLAB function generates random numbers from the discrete uniform distribution specified by its maximum
value n. The discrete uniform distribution is a simple distribution that puts equal weight on the integers from one to N. Examples Plot a Discrete Uniform Distribution cdf The uniform distribution
has a constant probability density function between its two parameters, lower (the minimum) and upper (the maximum). Learn more about distribution, pdf, cdf, uniform, gaussian Statistics and Machine
Learning Toolbox Use generic distribution functions (cdf, icdf, pdf, random) with a specified distribution name ('Uniform… The variance of the uniform distribution is σ 2 = 1 12 (b − a) 2. The mean
of the uniform distribution is μ = 1 2 (a + b).. ... Los navegadores web no admiten comandos de MATLAB. The discrete uniform distribution is a simple distribution that puts equal weight on the
integers from one to N. × MATLAB Command. It is true you can generate just about anything from rand but that it isn't always convenient, especially for some complicated distributions.. MATLAB has
introduced Probability Distribution Objects which make this a lot easier and allow you to seamless access mean, var, truncate, pdf, cdf, icdf (inverse transform), median, and other functions.. You
can fit a distribution to data. Open Live Script. Use the randi function (instead of rand) to generate 5 random integers from the uniform distribution between 10 and 50. r = randi([10 50],1,5) r =
1×5 43 47 15 47 35 Random Complex Numbers. Evaluate and generate random samples from continuous uniform distribution
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Introduction to Review Control
What is/are Review Control?
Review Control
The analysis data is fed to a novel fuzzy preview controller which would anticipate the condition of the finger as ill-conditioned which will settle the final position of the finger. ^[1] This paper
presents a control technique for reverse parking car-like vehicles based on deep reinforcement learning and preview control. ^[2] The Preview Control concept was used. ^[3] Using published data sets,
we review controls on Mg/Ca in laboratory cultures of planktonic foraminifera Globigerinoides ruber (white), Trilobatus sacculifer, Globigerina bulloides, and Orbulina universa. ^[4] To design
distributed optimal preview controllers, restricted system equivalent (r. ^[5] The active suspension is controlled by a linear quadratic regulator (LQR) in combination with road preview control,
while the semi-active suspension is controlled by a clipped-optimal LQR approach. ^[6] This paper presents an active roll preview control with vehicle-to-vehicle (V2V) communication. ^[7] This paper
purposes a new method of designing a preview controller for speed control of the DC motor system based on evolutionary algorithm. ^[8] In this paper, the optimal tracking control problem for
discrete-time with state and input delays is studied based on the preview control method. ^[9] This paper aims to present a Preview Controller by taking State-Dependent Riccati Equation (SDRE)
approach to the standard Preview Control solution based on Linear Quadratic (LQ) framework. ^[10] The proposed methodology of designing this controller is based on the application of theH∞ optimal
control techniques to a discrete-time preview control problem. ^[11] In this paper, the optimal preview tracking control problem for a class of linear discrete-time periodic systems is investigated
and the method to design the optimal preview controller for such systems is given. ^[12] This paper presents a neuro-fuzzy controller based on preview control and deep reinforcement learning for
reverse parking truck-trailer vehicles. ^[13] This paper presents observer-based active roll preview control with V2V communication. ^[14] An active preview control strategy is presented to suppress
the vibration of hydrostatic guideway under dynamic machining force. ^[15] This paper is concerned with the design of the preview controller for a class of fault systems. ^[16] In this paper, a
fault-tolerant preview controller is designed for a class of impulse controllable continuous time descriptor systems with sensor faults. ^[17] Based on this, a preview controller for the original
system is proposed. ^[18] In this paper we propose a novel hybrid walking pattern generator which combines results from the virtual constraints and the preview control theories for bipedal
locomotion. ^[19] This paper reports dynamic wind tunnel test results of gust alleviation using preview control. ^[20] A novel fuzzy preview controller is proposed which uses the concept of fuzzy
logic controllers which will define the controller for the plant. ^[21] An active preview control strategy is presented to suppress the vibration of hydrostatic guideway under dynamic machining
force. ^[22] The CoM trajectory is calculated using preview control based on the dynamics model and current state of the robot. ^[23] Simulation and test bench results all show that the proposed
preview control algorithm has better dynamic response and adaptability under different loads compared to the optimal linear quadratic regulator (LQR) controller and the standard PID controller. ^[24]
We design and implement a closed loop control strategy (preview control), that minimizes the tracking error and rejects disturbances generated by uncertainties and unmodeled dynamics. ^[25] The CoM
trajectory is re-planned in each control cycle with a short cycle preview controller. ^[26] While an LMI synthesis condition for preview control has yielded both feedback gain and preview feedforward
compensation simultaneously in previous research, the proposed approach can derive feedforward compensation when a state/output feedback controller has already been designed in some standard way. ^
[27] This paper deals with a gust alleviation (GA) control system using gain-scheduled (GS) discrete-time preview control. ^[28] This paper considers the preview control problem for switched systems
for tracking a previewable reference input. ^[29] A robust preview control scheme and an autoregressive (AR) model prediction scheme are originally applied to the automatic carrier landing system
(ACLS). ^[30] Based on this improved model, the preview control as control strategy for water pipe temperature was proposed, and its robustness and stability were discussed. ^[31] Based on preview
control theory and the predictor method, a predictor-preview controller was derived to realize delay compensation and interference preview compensation. ^[32] The proposed control method exhibits
smaller lateral errors than either the single-point preview control or the fixed-weight multi-point preview approaches. ^[33] The preview control system is developed based on a reduced-order linear
aeroelastic model and employs a two-loop control scheme. ^[34] Meanwhile, the static output preview control gains are solved explicitly by the proposed conditions. ^[35] An augmented error system is
constructed for the transformed ordinary linear system, the appropriate performance index function is introduced and relevant results of the optimal preview control are applied to design the optimal
preview controller for the augmented error system when the reference signal is previewable. ^[1] In this paper, the problem of preview control for continuous-time singular stochastic systems is
studied by the augmented error system approach. ^[2] ABSTRACT In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied
based on the augmented error system method. ^[3] The proposed methodology of designing this controller is based on the application of theH∞ optimal control techniques to a discrete-time preview
control problem. ^[1] ABSTRACT In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error
system method. ^[2] This paper considers the preview control problem for switched systems for tracking a previewable reference input. ^[3] An active preview control strategy is presented to suppress
the vibration of hydrostatic guideway under dynamic machining force. ^[1] An active preview control strategy is presented to suppress the vibration of hydrostatic guideway under dynamic machining
force. ^[2] In this paper we propose a novel hybrid walking pattern generator which combines results from the virtual constraints and the preview control theories for bipedal locomotion. ^[1] Based
on preview control theory and the predictor method, a predictor-preview controller was derived to realize delay compensation and interference preview compensation. ^[2]
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To convert a fraction to a percentage, we need to multiply the fraction by 100. So, to find the percentage of 15/10, we can multiply it by 100.
Now, we can simplify this fraction by dividing both the numerator and denominator by 10.
To understand this concept better, we can think of a percentage as a way of expressing a fraction out of 100. So, 150% means 150 out of 100, which is the same as 15/10.
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Understanding Mathematical Functions: How Can You Compare Two Function
Mathematical functions are a fundamental concept in the world of mathematics, playing a crucial role in various fields including science, engineering, and economics. Comparing two functions is an
essential aspect of understanding their behavior and relationships. By analyzing and contrasting their properties, we can gain valuable insights into their similarities, differences, and overall
performance. In this blog post, we will delve into the importance of comparing functions and explore different methods to effectively undertake this task.
Key Takeaways
• Mathematical functions are crucial in various fields and comparing them provides valuable insights into their behavior and relationships.
• Understanding the definition, purpose, and examples of common mathematical functions is essential for effective comparison.
• Graphical comparison involves plotting functions on the same graph and observing their intersection points and relative positions.
• Algebraic comparison includes evaluating functions at specific values and comparing their rates of change over a specific interval.
• Considerations such as the domain, range, symmetry, and behavior of functions are important when comparing them.
Understanding Mathematical Functions
In the field of mathematics, functions play a crucial role in representing and modeling various real-world phenomena. They are essential for understanding and analyzing the relationships between
different variables. Here, we will discuss the definition and purpose of mathematical functions, along with examples of common mathematical functions such as linear, quadratic, and exponential.
A. Definition and purpose of mathematical functions
A mathematical function is a rule that assigns each input exactly one output. It provides a way to describe how one quantity depends on another. Functions are used to study the change in one variable
in relation to another, and to make predictions based on these relationships.
1. Definition of a function
• A function is a relation between a set of inputs (the domain) and a set of outputs (the range), where each input is related to exactly one output.
• The input of a function is usually denoted by the variable x, while the output is denoted by the variable f(x) or y.
2. Purpose of functions
• Functions are used to model real-world phenomena, such as population growth, financial trends, and physical processes.
• They allow for the analysis of relationships between variables, enabling predictions and decision-making in various fields such as economics, engineering, and science.
B. Examples of common mathematical functions (linear, quadratic, exponential)
There are various types of mathematical functions, each with its own unique characteristics and applications. Three common examples of mathematical functions are linear, quadratic, and exponential
1. Linear function
• A linear function is a function that can be represented by a straight line on a graph.
• It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.
• Linear functions describe a constant rate of change and are commonly used to represent simple proportional relationships.
2. Quadratic function
• A quadratic function is a function that can be represented by a parabola on a graph.
• It has the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.
• Quadratic functions describe a curved relationship and are often used to model situations involving acceleration, projectile motion, and optimization.
3. Exponential function
• An exponential function is a function that can be represented by a curve that increases or decreases rapidly.
• It has the form f(x) = a^x, where a is a constant and x is the exponent.
• Exponential functions describe exponential growth or decay and are widely used in finance, biology, and physics.
Methods for comparing two functions
When it comes to comparing two mathematical functions, there are several methods you can use to determine how they are similar or different. The two most common methods for comparing functions are
graphical comparison and algebraic comparison.
A. Graphical comparison
Graphical comparison involves plotting the graphs of the two functions on the same set of axes and analyzing their behavior visually.
1. Plotting the graphs
• Start by identifying the domain and range of the functions.
• Plot the points on the graph by substituting different values of x into the functions and calculating the corresponding y-values.
• Connect the points to create the graph of each function.
2. Analyzing the graphs
• Compare the shape and direction of the graphs to see if they are similar or different.
• Look for common points of intersection or points where the graphs diverge.
• Identify any asymptotes, maxima, or minima to determine the behavior of the functions.
B. Algebraic comparison
Algebraic comparison involves analyzing the expressions of the two functions and comparing their properties using mathematical operations.
1. Simplifying the functions
• Use algebraic techniques to simplify the functions by factoring, combining like terms, or performing operations such as addition, subtraction, multiplication, or division.
• Identify any common factors or terms in the functions.
2. Analyzing the properties
• Compare the coefficients of the functions to see if they are proportional or if they have any common patterns.
• Calculate the derivatives of the functions and compare their behavior to determine if they have similar rates of change.
• Identify any common roots or solutions to the functions to see if they intersect at specific points.
Graphical Comparison
When comparing two mathematical functions, one of the most common approaches is to make a graphical comparison. This method involves plotting the functions on the same graph and observing their
intersection points and relative positions. This can provide valuable insights into the similarities and differences between the two functions.
Plotting the functions on the same graph
• Step 1: Start by selecting a suitable graphing method, such as using graphing software or plotting points manually.
• Step 2: Plot the points for each function on the graph, ensuring that the scale and axes are properly labeled for accuracy.
• Step 3: Connect the points for each function to create the actual graphs.
Observing the intersection points and relative positions of the graphs
• Intersection points: Identify the points where the graphs of the two functions intersect. This can provide information about the common solutions or roots of the functions.
• Relative positions: Observe the general shape, slope, and behavior of the graphs in relation to each other. This can reveal how the functions behave in different regions of the graph.
Algebraic comparison
When comparing two mathematical functions, it is important to understand how to analyze and compare them algebraically. This can be done by evaluating the functions at specific values and comparing
the rates of change of the functions over a specific interval.
A. Evaluating the functions at specific values
One way to compare two functions is by evaluating them at specific values. By plugging in the same value for the independent variable in both functions, you can compare their outputs to see which
function yields a greater or smaller result. This can give you an idea of which function is larger or smaller for certain inputs.
B. Comparing the rates of change of the functions over a specific interval
Another method of comparison is to compare the rates of change of the functions over a specific interval. This can be done by finding the derivatives of the functions and analyzing their behavior.
You can compare the slopes of the tangent lines to the functions at different points to determine which function is increasing or decreasing at a faster rate.
Considerations when comparing functions
When comparing mathematical functions, there are several key considerations to take into account in order to understand how they relate to each other. Two important aspects to consider are the domain
and range of the functions, as well as the symmetry and behavior of the functions.
Domain and range of the functions
• Domain: The domain of a function refers to the set of all possible input values for the function. When comparing two functions, it is important to ensure that their domains are compatible,
meaning that they cover the same range of input values. If the domains are different, it may not be valid to directly compare the functions.
• Range: The range of a function refers to the set of all possible output values for the function. When comparing functions, it is important to consider whether their ranges overlap or are
disjoint. This can provide insights into how the functions behave and how they relate to each other.
Symmetry and behavior of the functions
• Symmetry: Some functions exhibit symmetry, meaning that they remain unchanged when certain transformations are applied. When comparing functions, it is important to consider whether they exhibit
any symmetry, as this can indicate similarities or differences between the functions.
• Behavior: The behavior of a function refers to how it changes as its input values vary. When comparing functions, it is important to analyze their behavior over the entire domain, as well as at
specific points of interest. This can provide insights into how the functions compare in terms of their overall characteristics.
Understanding and comparing mathematical functions is crucial in various fields, including engineering, economics, and physics. By being able to compare functions, we can analyze their behavior and
make informed decisions. I encourage you to practice comparing various functions to gain proficiency in the topic. The more you practice, the more confident and skilled you will become in handling
mathematical functions.
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Trig functions - Math Steps, Examples & Questions
Write the answer with the correct units.
A useful analogy to help understand \sin^{-1}(\sin(\theta))=\theta\text{:}
Imagine throwing a ball straight up in the air, and then catching it in exactly the same place the ball started.
Here, the ball is \theta.
Let the function \sin represent throwing the ball (\theta).
Let the function \sin^{-1} represent catching the ball (\theta).
Throwing the ball is an action on the ball. Catching the ball is the opposite action on the ball. If you throw the ball, then catch the ball in exactly the same place, nothing about the ball or its
position have changed as both of the acts on the ball have canceled each other out. In essence, nothing has happened.
So catch(throw(ball)) = ball or \sin^{-1}(\sin(\theta))=\theta
What are the basic trigonometric functions?
The three basic trigonometric functions are sine (\sin), cosine (\cos), and tangent (\tan).
What are the reciprocal trigonometric functions?
The reciprocal functions are cosecant (\csc), secant (\sec), and cotangent (\cot).
What is the unit circle, and how does it relate to trig functions?
The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane.
Trig functions for an angle \theta can be defined using the coordinates of points on the unit circle:
Β° \sin (\theta) is the y -coordinate
Β° \cos (\theta) is the x -coordinate
The unit circle also helps determine values of trig functions for any angle, not just those in a right triangle.
What are periodic functions, and how do they relate to trig functions?
Periodic functions repeat their values at regular intervals, called the period.
Trigonometric functions like sine and cosine are periodic because their values repeat every 360^{\circ}, while tangent repeats every 180^{\circ}.
This periodicity is key to understanding the cyclical nature of trig functions.
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Maths problem solving software
maths problem solving software Related topics: solving polynomials
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Author Message Author Message
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knowing how to start . I’m desperately in need of Even I faced similar difficulties while solving graphing
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showing the steps and how to answer it in a organized Reg.: 22.10.2001 typing in the problem workbookand clicking on Solve
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kfir Posted: Saturday 06th of Jan 07:18 classes - Pre Algebra, Pre Algebra and Algebra 1. I
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The Firebird 5.0 Language Reference | SELECT | ROWS
Retrieves a slice of rows from an ordered set
SELECT <columns> FROM ...
[WHERE ...]
[ORDER BY ...]
ROWS <value-expression> [TO <value-expression>]
Table 1. Arguments for the ROWS Clause
Argument Description
value-expression Any integer expressions
Note ROWS is non-standard syntax
ROWS limits the amount of rows returned by the SELECT statement to a specified number or range.
The ROWS clause also does the same job as the FIRST and SKIP clauses, but neither are SQL-compliant.Unlike FIRST and SKIP, and OFFSET and FETCH, the ROWS and TO clauses accept any type of integer
expression as their arguments, without parentheses.Of course, parentheses may still be needed for nested evaluations inside the expression, and a subquery must always be enclosed in parentheses.
• Numbering of rows in the intermediate set—the overall set cached on disk before the “slice” is extracted—starts at 1.
Important • OFFSET/FETCH, FIRST/SKIP, and ROWS can all be used without the ORDER BY clause, although it rarely makes sense to do so—except perhaps when you want to take a quick look at the table
data and don’t care that rows will be in a non-deterministic order.For this purpose, a query like “SELECT * FROM TABLE1 ROWS 20” would return the first 20 rows instead of a whole table
that might be rather big.
Characteristics of Using ROWS m Without a TO Clause:
Calling ROWS m retrieves the first m records from the set specified.
• If m is greater than the total number of records in the intermediate data set, the entire set is returned
• If m = 0, an empty set is returned
• If m < 0, the SELECT statement call fails with an error
Characteristics of Using ROWS m With a TO Clause:
Calling ROWS m TO n retrieves the rows from the set, starting at row m and ending after row n—the set is inclusive.
• If m is greater than the total number of rows in the intermediate set and n >= m, an empty set is returned
• If m is not greater than n and n is greater than the total number of rows in the intermediate set, the result set will be limited to rows starting from m, up to the end of the set
• If m < 1 and n < 1, the SELECT statement call fails with an error
• If n = m - 1, an empty set is returned
• If n < m - 1, the SELECT statement call fails with an error
Not Possible to Use a TO Clause Without a ROWS Clause:
While ROWS is an alternative to the FIRST and SKIP syntax, there is one situation where the ROWS syntax does not provide the same behaviour: specifying SKIP n on its own returns the entire
intermediate set, without the first n rows.The ROWS … TO syntax needs a little help to achieve this.
With the ROWS syntax, you need a ROWS clause in association with the TO clause and deliberately make the second (n) argument greater than the size of the intermediate data set.This is achieved by
creating an expression for n that uses a subquery to retrieve the count of rows in the intermediate set and adds 1 to it, or use a literal with a sufficiently large value.
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Pythagoras Theorem
Prime purpose of this lecture is to present on Pythagoras Theorem. In mathematics, the Pythagorean theorem, also known as Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among
the three sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This proof was discovered by President J.A. Garfield in
1876. The key is the formula for the area of a trapezoid – half sum of the bases times the altitude – ½ * (a+b) * (a+b).
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Constraint MDD
The constraint mdd, see [CY08], [CY10] and [PR14], ensures that the sequence of values assigned to the variables it involves follows a path going from the root of the described MDD (Multi-valued
Decision Diagram) to the unique terminal node.
mdd($X$,$M$) with $X=\langle x_1,x_2,\ldots,x_r \rangle$ and $M$ a MDD, iff $x_1 x_2 \ldots x_r \in L(M)$ where $L(M)$ denotes the language recognized by the MDD $M$.
Because the graph is directed, acyclic, with only one root node and only one terminal node, we just need to introduce transitions. The syntax for mdd is:
<list> (intVar wspace)+ </list>
<transitions> ("(" state "," intVal "," state ")")+ </transitions>
As an example, the constraint of scope $\langle x_1,x_2,x_3 \rangle$ is defined from the simple MDD depicted below (with root node r and terminal node t) as:
We obtain:
<list> x1 x2 x3 </list>
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Calculate Price With a Simple Markup Calculator Tool
Robin Lamb | Published 13 March 2023 | Updated 14 March 2023
Looking for an easy way to calculate product markups? Look no further than this handy markup calculator tool! Quickly and accurately figure out pricing with its simple yet effective user interface,
perfect for those who need fast results on the go.
Input the cost of the items you are selling.
Get started by inputting the cost of each item you are selling into the calculator. This is important because it allows you to accurately determine how much you should charge for your product. In
addition, it helps you understand what your profit margins will look like and gives you a better sense of how much markup is necessary to cover overhead expenses.
Add your desired markup percentage to the item's cost.
To calculate the total cost of your item, add the desired markup percentage on top of the item's cost. This is done to ensure you profit from each item sale. Therefore, it's essential to remember the
correct markup rate for each item. As a general rule of thumb, consider the industry norm when deciding how much to mark up a product or service. The calculator will then automatically calculate the
total cost of your product so you can set fair prices for your customers.
See an accurate breakdown of your markup, quotient and price with taxes included.
With the markup calculator, you'll get an accurate breakdown of the formula used in calculating the total cost amount. Not only that, but it will also include the final quotient and price with taxes
included (if applicable). This lets you easily set your prices confidently, knowing they consider all relevant factors such as taxes and expenses.
Create a Price Structure.
Setting up a pricing structure is integral to any product or service. Having a good markup calculator allows you to calculate prices accurately and quickly. Using the tool, you can set price tiers
based on units or product size and discounts and fees that apply in certain situations. As a result, you'll have a dependable structure for setting prices without falling victim to guesswork or
inaccurate calculations.
Markup Formula.
The simplest way to calculate a price is to use a markup formula. This formula considers your desired gross margin and any other fees or discounts that must be included. To calculate your price,
simply multiply the base cost of the product/service by 1 plus the desired gross margin percentage, and then add any applicable discounts or fees. For example, if you want a 40% gross margin on a
product with an initial cost of $50, you would calculate the price as follows: ($50 x 1.4) + 0 (if no discount or fee applied).
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A model for Nash-Cournot oligopolistic markets with concave cost functions and a differentiated commodity is analysed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the
minimization of a suitable merit function, a general algorithmic scheme for solving them is provided. Two concrete algorithms are therefore designed that converge under suitable convexity and
monotonicity … Read more
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In Home & Online 2nd Grade Math Tutoring - Club Z! Tutoring
2nd Grade Math Tutoring: In-Home & Online
Adjusting to 2nd grade math can be a tricky transition for many students. From complex math problems, times tables, long division math and dealing with large numbers, there’s a mix of concepts that
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2nd Grade Math Tutoring Subjects
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dBV, dBmV, dBuV, dBnV Converter
This tool converts between any of the following deciBel Volt (dBV) units:
To use the converter,
• In the input area, enter the value and the unit using the drop down menu
• Select the output units
This converter can also be used to convert units of Electromagnetic Field Strength. For example: dBV/m to dBµV/m.
• dBmV = dBV + 60
• dBµV = dBV + 120
• dBnV = dBV + 180
Example Calculations
• 10 dBV = 70 dBmV
• 20 dBV = 200 dBnV
• 50 dBµV/m = -70 dBV/m
dBV stands for “decibels relative to one volt” and is a unit of measurement used to express voltage levels or voltage ratios on a logarithmic scale. dBV quantifies the ratio of a voltage level to one
volt (1 V) as a decibel value.
It is commonly used in electronics, audio engineering, and telecommunications to describe voltage levels and signal amplitudes.
The formula for calculating dBV is as follows:
dBV = 20 * Log[10](V / 1 V)
In this formula:
• dBV represents the voltage level in decibels relative to one volt.
• V is the actual voltage level that you want to express in dBV.
• dBnV = 20 * Log[10](V / 1 nV)
• dBµV = 20 * Log[10](V / 1 µV)
• dBmV = 20 * Log[10](V / 1 mV)
• 1 nV = 10^-9 V
• 1 µV = 10^-6 V
• 1 mV = 10^-3 V
• 0 dBV represents 1 volt (1 V) of voltage.
• 20 dBV represents 10 volts (10 V) of voltage.
• -20 dBV represents 0.1 volts (0.1 V) of voltage.
dBV is a valuable tool for engineers and technicians working with electronic and audio systems because it simplifies the representation and comparison of voltage levels, particularly when dealing
with signals of varying amplitudes and power levels.
dBV/m provides a logarithmic representation of the Electric Field Strength, making it easier to compare and analyze measurements over a wide range of field strengths.
It is commonly used in the field of radio frequency (RF) engineering and EMC testing to assess the levels of electromagnetic interference (EMI) or radiation generated by electronic devices and
equipment. It helps determine whether the emissions from a device comply with established EMC standards and regulations.
The table below shows emission limits in dBuV/m of field strength.
Related Calculators
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Zeller's Birthday
What day of the week were you born on? Do you know? Here's a way to find out.
What day of the week were you born on? Do you know?
Here's a way to find out.
For example, if your date of birth was 6 July 1989 :
$D = 6$ , $M = 7$ , and $Y = 1989$
If $M$ had been a 1 or 2, subtract 1 from $Y$ and add 12 to $M$.
$Y_F$ is made from the first two digits of $Y$ and $Y_L$ is made from the last two digits of $Y$.
To begin, work out the sum of all the integer parts of $2.6M - 5.39$ , of $\frac{Y_F}{4}$ , and of $\frac{Y_L}{4}$
Add $D$ and $Y_L$ into that total, and then subtract 2 lots of $Y_F$
Divide that final answer by 7 and notice the remainder .
A remainder value of 0 means the date was a Sunday, 1 means it was a Monday, 2 for a Tuesday, and so on.
Can you follow the method (what you actually have to do) ?
You could check some dates you happen to know the answer for ?
When you are getting good at using the method start to ask yourself how it works and why does it give the right result?
Why 2.6 and why 5.39?
Getting Started
The calculation must 'count back', or 'count forward', from somewhere in some way.
First in whole weeks, then the bit that is left (the days that don't make a whole week) could indicate the position in the week, ie. 'day'
Student Solutions
Basic Idea
The algorithm essentially counts the number of days that have passed between a fixed date (this will be 1st January 0 AD) and a chosen date (our birthday). By taking this number and finding its
remainder when divided by 7, provided we know what day of the week it was on 1st January 0 AD we will know what day we were born on.
Modular Arithmetic
We do not need to know the exact number of days that have passed since our fixed date and our birthday, just the remainder when this number is divided by 7. To make our algorithm easier to work with,
then, we will be taking certain shortcuts, so that what we calculate is not actually the exact number of days, but a smaller number which has the same remainder when divided by 7 (if this is
confusing, don't worry, it will make sense later).
Consequently, we'll be using the ideas of 'modular arithmetic', or 'clock arithmetic'. If you have not encountered these ideas before, you should read the NRICH article on
modular arithmetic
. We want to know the number days between 1 Jan 0 and our birthday
mod 7
The Algorithm
A date can be divided into the following four bits information: the number of hundreds of years, the number of additional years, the number of months,and number of days that have passed since 1
January 0 AD. Suppose our birthday is 23rd September 1989. To count the days that have passed since 1 Jan 0, we will use four steps: count the days up to 1 Jan 1900, then the days between 1 Jan 1900
and 1 Jan 1989, the days between 1 Jan 1989 and 1 Sep 1989, and finally the days between 1 Sep 1989 and 23 Sep 1989.
The number of days between 1 Sep 1989 and 23 Sep 1989 is obviously 23, or in general our number $D$. Years and months are a bit more difficult.
$$\frac{365}{7}=52\times 7+1$$ so there are exactly 52 weeks and one day in a year. This means that our birthday moves forward by one day each year i.e. 1 year $=$ 365 days $\equiv$ 1 day (mod 7).
So, mod 7, is the number of days between 1 Jan 0 and 1 Jan 1989 is just 1989?
Unfortunately, we have to take leap years into account. There are 366 days in a leap year, and our birthday moves forward 2 days. We need to add an extra 1 for each leap year on top of the total
number of years. How many leap years have passed since 1 Jan 0? You probably know that we get a leap year every four years, in fact precisely on those years which are divisible by 4. However, there
is one more rule you may not know: if a year is divisible by 100 but not divisible by 400 then it is
a leap year. For example, 1900 is divisible by 4, but not 400, so 1900 AD was not a leap year.
The number of leap years between $Y_F$01 and $Y_F$99 is always 24, so if for a moment we ignore leap years on the turn of the century, every 100 years our birthday moves forward 100 + 24 = 124 days =
18$\times$7 - 2 $\equiv$ -2 (mod 7). Now we add 1 for the leap year on 0 AD and an additional 1 every 400 years up to $Y_F$00 (this number is $1+\big[ \frac{Y_F}{4}\big]$, where $[x]$ denotes the
integer part of $x$. In general, then, between 1 Jan 0 and $Y_F$00 there are: $$-2Y_F+ 1 + \Big[ \frac{Y_F}{4} \Big]$$ days mod 7. Up to 1 Jan 1900 this number is $19\times -2 + 1 + \big[ \frac{19}
{4} \big] = -33 \equiv2$.
Thinking a similar way we can show that between 1 Jan $Y_F 00$ and 1 Jan $Y_F Y_L$ there are $$Y_L \Big[ \frac{Y_L}{4} \Big] - 1$$ days mod 7,the -1 coming from the fact that we have taken account of
leap years occuring on centuries in out previous formula. Putting the two parts of the year formula together, up to 1 Jan $Y_F Y_L$ days are given by:$$-2Y_F+ 1 + \Big[ \frac{Y_F}{4} \Big] + Y_L + \
Big[ \frac{Y_L}{4} \Big] - 1= Y_L - 2Y_F+ \Big[ \frac{Y_L}{4} \Big] + \Big[ \frac{Y_F}{4} \Big]$$
The number of days mod 7 up to 1 Jan 1989 is $2 + 89 +\big[ \frac{89}{4}\big] - 1 = 112 = 0$ mod 7.
Months are tricky because they contain different numbers of days. Coming up with a formula for the number of days in the first $M$ months in terms of $M$ is requires some thought. This is by far the
most difficult part of the algorithm to derive. The first columns of the chart below show the months $M$, days mod 7 in that month, and the days mod 7 before the $M$th month.
We want to come up with a formula that will approximate the number of days before $M$ months mod 7, in the hope that we can make it exact by taking its integer part. Our problem month is February,
which at only 28 days long makes it hard to average out the months.The average number of days mod 7 in months
February is around 2.6. So we take as a first approximation $2.6 \times M$.
$M$ $\quad$ Days mod 7 in $M \quad$ days mod 7 before $M \quad$ $2.6M$ mod 7 $\quad$ $2.6M-4$ mod 7 $\quad$ $[2.6M-4]$ mod 7 $\quad$ $2.6M-4.39$ mod 7 $\quad$ $[2.6M-4.39]$ mod 7 $\quad$
1 3 0 2.6 5.6 5 5.21 5
2 0 3 5.2 1.2 1 0.81 0
3 3 3 0.8 3.8 3 3.11 3
4 2 6 3.4 6.4 6 6.01 6
5 3 1 6 2 3 1.61 1
6 2 4 1.6 4.6 4 4.21 4
7 3 6 4.2 0.2 0 6.81 6
8 3 2 6.8 2.8 2 2.41 2
9 2 5 2.4 5.4 5 5.01 5
10 3 0 5 1 1 0.61 0
11 2 3 0.6 3.6 3 3.21 3
12 3 5 3.2 6.2 6 5.81 5
13 3 1 5.8 1.8 1 1.41 1
14 0 4 1.4 4.4 4 4.01 4
If we subtract 4 from our first approximation, then the integer part of this is very close to an exact formula. You will notice if we subtract a further number between 0.2 and 0.4, then the integer
part of our approximation will be correct for all months apart from Jan and Feb - months 1 and 2. However, if we extend our table and replace months 1 and 2 by 13 and 14 then our formula is exact for
all months. Therefore, given that if $M$ is 1 or 2, it is replaced by 13 or 14 and $Y_L$ is decreased by 1, the month part of the algorithm is given by $[2.6M-4.39]$
So the number of days between 1 Jan 1989 and 1 Sep 1989 is $[2.6\times 9 - 4.39] = [19.01] = 19 \equiv5$.
Putting everything together
The final step is to calculate the sum of our individual parts. If we work backwards it turns out that 1 Jan 0 AD was a Monday, so we tweak our formula and subtract 1 from our sum to ensure that 0 is
Sunday instead. Our final formula, then, is $$D + [2.6M-4.38] + \Big( Y_L - 2Y_F+ \Big[ \frac{Y_L}{4} \Big] + \Big[ \frac{Y_F}{4} \Big] \Big) - 1 = D + Y_L -2Y_F + [2.6M-5.39] + \Big[ \frac{Y_L}{4} \
Big] + \Big[ \frac{Y_F}{4} \Big]$$ For 23 Sep 1989 we get 23 + 5 + 0 - 1 = 27 = 6 mod 7. So 23 Sep 1989 was a Saturday.
Teachers' Resources
Why do this problem?
This problem introduces students to the idea of an algorithm. We hope that the context of finding the day of the week for key dates adds a little extra interest. Beneath it all is the important idea
of modulo arithmetic.
Possible approach
Start with some dates for which students feel confident they know the day of the week. It might be a recent date (Christmas last year, or a recent wedding) or something like a major sporting event
which happens on a particular day (often Saturday).
Ask if any student happens to know the day in the week on which they were born. Students might ask their parent or guardian in preparation for this lesson.
Then invite students to try out the algorithm with some birth dates.
Check that the method is understood and practised to the point of familiarity.
That brings the group to the heart of the problem : how does this algorithm do its job ?
One way to explore that question is to think about the procedure we would need to follow if this was a 'one off' problem and for which we had no ready-made algorithm available.
Key questions
• How does this algorithm do its job ?
• How would you find the day of the week on which you were born if there was no ready-made algorithm available ?
Possible extension
Design a spreadsheet that uses the algorithm to report the day of the week for any given birth date.
Possible support
Students could be introduced to the idea of algorithms using a more familiar context, such as the long multiplication algorithms in this problem.
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Private Equity Glossary of Terms & Acronyms | CEPRES
The simple average (arithmetic mean) of the performance measures of all the funds/deals in a selected universe.
Average Best-Performer
The mean of the upper quartile (top 25% best performing) funds/deals in a selected universe (observations that are higher than the upper quartile value). For instance, the TVPI average best-performer
is calculated by dividing the sum of all TVPIs of the upper quartile funds/deals by the number of funds/deals selected.
Average Worst-Performer
The mean of the lower quartile (25% worst performing) funds/deals in a selected universe (observations that are lower than the lower quartile). For example, the TVPI average worst-performer is
calculated by dividing the sum of all TVPIs of the lower quartile (25% worst performing) funds/deals by the number of funds/deals selected.
Adjusted Funds from Operations
Adjusted funds from operations (AFFO) is a real estate investment measure of cash flow generation available for distribution. It is calculated as funds from operations plus rent increase minus
capital expenditure and maintenance.
Adjusted Valuation
The adjusted valuation within CEPRES is calculated by adding all contributions and subtracting all distributions that occurred in the year after the last available valuation.
Board Representation
Board representation identifies whether the GP has any members on the board of the investee company to represent their interests. Observer rights are not considered as board representation.
The time (measured in years) it takes for the sum of distributions to be equal to the sum of contributions.
Brownfield is a type of infrastructure project where the invested infrastructure assets are pre-existing and typically in need of improvement.
Compound annual growth rate (CAGR) represents an annualized measure of the growth rate of a balance from its initial value to its ending value with an annual compound. When the investment period is
less than one year, CAGR is annualized.
Capital expenditure (CAPEX) is the value of purchases of fixed assets such as property, industrial plants and equipment to support a firm’s new projects or expansion.
Capital Gain
The total gains made on investment, including unrealized value.
Carried Interest
Carried interest (or carry) is the performance fee paid to the fund manager (GP) as their share of profits paid out in compensation. Carried interest is typically based on a payout waterfall often
including preferred returns, hurdle rates, claw-back provisions, catch up, etc. Historically the most common absolute value of carry was 20%.
On the fund net level, a contribution is an investment cash flow from the LP investor to the GP investment manager; whereas on the deal level, a contribution is the investment cash flow from the GP
to the invested asset or portfolio company.
Cost of Debt Service
The last twelve months cost of debt service is the cost of meeting the specific interest and principal payments on a debt, along with any administration charges borne by the borrower.
Cumulated Contribution
The cumulative amount of contributions (including the current year).
Cumulated Distribution
The cumulative amount of distributions (including the current year).
Cumulative Net
The cumulative amount of total net cash flows with both contributions and distributions (including the current year).
Current Interest
The simple coupon rate on the nominal value of the debt.
Downside Deviation
Downside deviation is a measure of downside risks. In CEPRES, it represents the standard deviation of the observations that fall below the mean. For example, if the mean is 10%, then the downside
deviation of returns is calculated as the standard deviation of returns that are lower than 10%.
Default Rate
In CEPRES, the default rate is the percentage of deals that are designated as being defaulted investments. Calculated as total numbers of deals have TVPI below 1 divided by total number of deals.
The distribution to paid-In capital (DPI) is the ratio of total distributed capital to total invested (paid-in) capital. This is also referred to as the “realization multiple”. This ratio gives a
clear indication as to how much of an investment’s return was “realized” or paid back to investors or managers.
An investment (fund or direct deal) is considered a default, if the current TVPI<1.
Dry Powder
Dry powder is the amount of undeployed capital that there is a contractual commitment for LP investors to provide to GP fund managers when requested. Thus representing the total available capital
that could still be deployed at any given time.
Debt Service Coverage Ratio (DSCR)
Debt service coverage ratio (DSCR) is typically used in income-generating assets such as real estate and infrastructure. It measures the ratio of cash flow available to pay current debt obligations.
In CEPRES, it is expressed as a ratio of NOI divided by the total cost of debt service. A DSCR above 1 indicates there is sufficient cash flow from income to cover all debt costs and below 1
indicates there is an insufficient amount of income available to cover debts.
Default or Defaulted Investment
On CEPRES, this is a financial default, i.e. a designation that an investment (fund or direct asset) has lost money for the investor, i.e. when the current TVPI is below 1 distribution. On the fund
net level, distribution is an investment cash flow from the GP investment manager back to their LP investors. On the deal level, distribution is the investment cash flow from the invested asset or
portfolio company back to the GP.
Earnings before interest, Taxes, depreciation and amortization (EBITDA) is an important metric to measure a company’s financial performance in terms of its operating income generation. It is
calculated by first finding a company’s operating profit (EBIT) before subsequently removing the expenses garnered from depreciation and amortization.
Enterprise value is the total value of a company, including both equity value and net debt.
Expected Holding Years
The number of years that an investor plans on owning their investment.
First Distribution
The time (measured in years) from the date of an initial investment until the first cash distribution takes place.
Free Cash Flow
Free cash flow (FCF) measures how much cash an asset generates through operations after subtracting the cost of expenditures. This cash can be used for expansion, dividends, reducing debt or other
purposes. It is calculated by funds from operations minus capital expenditure.
Fully Realized
An investment where any remaining value has been distributed and thus has no outstanding value remaining (including warrants, options, and so on) is said to be an investment that has been fully
Funds from Operations (FFO)
Funds from operations (FFO) refers to the cash generated by real estate investment trusts (REITs) to measure operational performance. It is calculated by net income plus depreciation and amortization
then minus capital gains from property sales.
An analysis at the ‘gross’ level is based on cash flows of only underlying deals without accounting for any fund net cash flows such as management fees, fund expenses amongst others.
Gross Asset Value (GAV)
The gross value of real asset investments including both equity and any debt.
Gross Rent Income
Gross rent income is the amount collected in rent and other related funds from rental properties before deducting any expenses such as insurance, maintenance and any other expenses.
Greenfield is a type of infrastructure project where no pre-existing infrastructure assets are present and a full development project is required.
Hurdle Rate
The minimum required rate of return on an investment based on cost of capital, returns for similar investments, risk and others. Typically, this is the rate of return that the general partners must
achieve to investors before they can collect carried interest.
Interquartile range (IQR) is a measure of the difference between the upper (first) quartile and lower (third) quartile. For example, if there are 100 data points in the sample, the IQR of a metric
would be the difference between the value of the 25th data point and the 75th data point.
Internal rate of return (IRR) is a metric commonly used to evaluate the returns on an illiquid investment. It is the discount rate that makes the net present value (NPV) of all cash flows equal to
zero. IRR is a standard performance measure for private equity because it captures both timing (cash flow pace) and returns.
Invested Capital
Invested Capital is the total money “drawn down” by investment managers/investors into a deal/fund. Invested capital only refers to the sum of a fund’s own committed money; in the context of a
leveraged buyout, the external borrowed debt would be considered as part of any invested capital.
Investment Manager Main Office
The investment manager main office refers to the regional headquarter of a firm. For instance, the main office of a global firm, XYZ Capital would be categorized regionally as XYZ Capital (U.S.), XYZ
Capital (Canada), XYZ Capital (Asia), etc. to reflect their specific geographic locations.
Kurtosis measures the relative distribution of outliers of a distribution curve. In CEPRES, kurtosis is expressed in relation to normal distribution which has a Kurtosis of 3. A kurtosis less than 3
indicates a ‘tighter’ distribution with fewer outliers and smaller ‘tails’. A kurtosis greater than 3 indicates a broader distribution with greater outliers and larger ‘tails’.
Loss given default
Loss given default tells how much capital is lost if the investment turns default. It is expressed as actual loss as a percentage of total invested capital.
Loss Rate
Loss rate is calculated as the ratio of loss in investments on defaulted deals (deals with TVPI of less than 1) and total contributions to all deals.
Loan to Value (LTV)
LTV = total debt / gross asset value (GAV). The loan-to-value (LTV) ratio is a financial term used to express the ratio of a loan to the value of an asset financed. It is calculated as total debt
divided by GAV. The lower the LTV, the greater the owner’s equity in the property and less of a chance that the owner will default on the loan. LTV is expressed as a percentage. For example, when
someone takes out a mortgage to purchase a property, the LTV is the ratio between the mortgage amount and the overall value of the property.
Lost Capital
The total value that has been lost on investment or the current loss on investment. Calculated as the sum of distributions and valuation minus contributions.
Lower Quartile
The lower quartile is the relevant value that represents the 25th percentile of a sorted dataset. For example, given 100 investment records, the lower quartile IRR would be the value of IRR for the
25th record with 24 investments having lower IRR values and 75 investments having higher IRR values.
The lowest value of the performance measures of all the funds/deals in a selected universe.
The highest value of the performance measures of all the funds/deals in a selected universe.
Market Value/ Property Size
Market value/ property size measures the gross price per unit of total property size, e.g. price per sqft/sqm/acre/hectare.
Market Value / Building Size
Market value/ building size measures the gross price per unit of building size, e.g. price per sqft/sqm/acre/hectare of a building.
The simple average (arithmetic mean) of the performance measures of all the funds/deals in a selected universe.
The midpoint of all the performance measures of all the funds/deals in a selected universe. Half of the measures have a higher value and half have a lower value.
A net value means that it is being presented after all relevant deductions. Fund level metrics are often presented based on net figures so investors can see their true performance after subtracting
any management fee, expenses, carried interest and all other related fees.
Net Effective Rent Income
Net effective rent income is a measure of the expected income from a tenant. It is the NPV of all rental payments over the lease period, as well as any abatements (tax exemptions or reductions) or
incentives that add or subtract these payments. For example, the landlord offers a month’s free rent for any new lease that is signed for a period of 12 months. In this case, the actual rental period
is 13 months; if the lease rate is $200,000/month, then the total annual rental paid to the owner is $200,000 x 12 = $2,400,000, therefore the net effective rent income per month is $2,400,000/13 =
Net p.a.
Net cash flow (difference between a company’s inflow and outflow) per annum (year).
Net Profit
Net profit is a measure of the profitability of a company or asset after accounting for all costs and taxes. It is calculated as revenue minus cost of goods sold, operating expenses, other expenses,
interest and taxes from revenue.
Net Operating Income
Net operating income is the expected income to be collected from the operations of properties after deducting all operation-related expenses. It expresses the profitability of real estate investments
that generate income. It is calculated as real estate revenue minus operating expenses.
Number of Financing Rounds
The total number of contributions made to a portfolio company or asset over the life of an investment.
Omega is a risk-return performance measure of an investment asset. It measures the probability of gains versus losses for some threshold return target. Calculated as cumulative probability of upside
returns divided by the cumulative probability of downside returns. For example, the target return is 8%. Omega = 0.5 means the cumulative probability of upside returns (>8%) equals half of the
cumulative probability of downside returns (<8%). Omega = 2 means the cumulative probability of upside returns (>8%) is twice the cumulative probability of downside returns (<8%).
Occupancy Rate
The percentage of rented or used space to the total amount of available units. It helps provide an indication of anticipated cash flows. For example, a shopping center that only has a 25% occupancy
rate, means that tenants are leasing just 25% of the available spaces.
Outstanding/Open Commitment (Dry Powder)
IN CEPRES, Outstanding commitment is the portion of committed funds that is yet to be invested. Committed funds can be called upon to make investments and those making the commitments typically
receive a portion of the return said investment brings. It is calculated as committed capital minus net invested capital.
A pooled metric (e.g. IRR or TVPI, etc.) is derived by pooling all investments in a given data set and calculating the metric based on the aggregation of cash flows associated with that set of
investments. Pooled performance measures are generated correspondingly. For example, to obtain the pooled IRR of venture deals in Asian Healthcare, CEPRES combines all cash flows, together with all
valuations of every deal in the selected universe and applies the IRR calculation methodology as if you had invested in all the deals. This provides a unique and highly valuable way to assess and
compare whole market segments in aggregate.
PME-Nasdaq (pooled)
A simulated cashflow for an investment in Nasdaq is generated corresponding to a private equity investment. IRR of this cashflow is then calculated.
PME-MSCI (pooled)
A simulated cashflow for an investment in MSCI is generated corresponding to a private equity investment. IRR of this cashflow is then calculated.
Payment-In-Kind (PIK)
Payment-in-kind refers to a financial instrument that pays interest or dividends to investors with additional debt or equity securities instead of cash. For example, a GP offers a PIK note worth $2M
to a company with 10% interest. Each year, the note incurs 10% compounding interest, but instead of the company being required to pay cash interest, it is rather added to the debt “in-kind”. Thus,
after the first year, the company owes $2.2 million; after the second year $2.42 million, etc. This amount then continues to grow until the loan matures, at which time the total principal and
interest become due. PIK notes typically have higher income rates, so can drive greater returns, but also have an inherently higher risk because if the company defaults, higher losses could occur.
Public Markets Equivalent (PME)
Public markets equivalent (or PME) evaluates the performance of a private equity investment against a public benchmark or index. CEPRES generates certain cash flow patterns for public market
investments that mimic private market investments. By using the cash flow information for each deal/fund, a purchase (sale) of shares in the benchmark is simulated when a negative (positive) cash
flow occurs for the underlying investment.
PME-S&P 500 (pooled)
A simulated cashflow for an investment in S&P 500 is generated corresponding to a private equity investment. IRR of this cashflow is then calculated.
Q1- Upper
This is a 75th percentile of the performance measure and it splits off the highest 25% of data from the lowest 75%.
Q2- Median
This is a 50th percentile of the performance measure and it splits off the data in half.
Q3- Lower
This is a 25th percentile of the performance measure and it splits off the lowest 25% of data from the highest 75%.
Range represents the difference between the largest value and the lowest value of the performance measures of all the funds/deals in a selected universe. It typically shows the breadth of
distribution in the performance measure.
Recovery Rate
Recovery rate is the ratio of the total value over invested capital for defaulted investments (investments for which the TVPI is less than 1). This is a key measure of manager discipline since all
managers are likely to lose money on some deals, but some managers will have tighter covenants or work out teams that are able to recover more value on the investments. Calculated as total
distributions plus valuation for those deals have TVPI below 1 then divided by total contributions for those deals have TVPI below 1.
Risk Free Rate US
The rate of return an investor can achieve on a 3-month U.S. Treasury bill. The investor incurs essentially minimal risk because of the bill’s stability. This allows investors to evaluate the return
of investments given the additional risk.
Risk Free Rate EU
The rate at which the largest banks operating in the European Union lend money to each other — also known as the "Euro Interbank Offered Rate" or "EURIBOR". Similar to the LIBOR or U.S. Treasury
bill, it is an essentially risk-free rate of return that allows investors to evaluate the return of investments given the additional risk.
Risk Free Rate
In theory, the risk-free rate is the minimum return an investor expects for any investment, where the additional risk is not accepted unless the potential rate of return is greater than the risk-free
The residual value to paid-in (RVPI) is the ratio of unrealized valuation to total invested (paid-in) capital. This ratio gives the private equity investor an idea as to how much of the return was
Skewness is the asymmetry in a statistical distribution. This is where the curve appears skewed either to the left or right. Symmetric data has a skewness near zero (close to the normal
distribution). Given a data sample of performance measures (for example IRR) negative skewness indicates that the IRR distribution is skewed to left, where there are more downside returns than
upside. Whilst a positive skewness indicates that the IRR distribution is skewed to right, where there are more upside returns.
Semivariance can be used to estimate the potential downside risk of an investment portfolio. In other words, the dispersion of all observations that fall below the mean or target value. It is
calculated by dividing the sum of the squared differences between the mean (and the data points that are below the mean) by the total number of data points below the mean.
Sharpe Ratio
Sharpe Ratio is calculated by subtracting the risk-free rate from the portfolio's return and dividing the result by the standard deviation of the portfolio’s excess return. The Sharpe Ratio adjusts a
portfolio’s past performance or expected future performance for the excess risk that the investor took. A higher Sharpe Ratio is better when compared to similar portfolios with lower returns as it
shows a higher risk-adjusted return.
Sortino Ratio
Sortino Ratio measures the risk-adjusted return of an investment. It is a modification of the Sharpe Ratio but only those returns falling below the target or required rate of return – the downside
risk. It is calculated by dividing the excess return (Mean of performance measures less risk-free rate) by downside deviation. Because the Sortino ratio focuses only on the negative deviation of a
portfolio’s return from the mean, it is thought to give a better view of a portfolio’s risk-adjusted performance since positive volatility is a benefit.
Standard Deviation
A statistical measure of the dispersion (spread) of a dataset from the mean. It is also known as the historical volatility and is used as a gauge for the expected amount of volatility. Standard
Deviation is calculated as the square root of the Variance.
Syndicated Transaction
A syndicated transaction is one where multiple Investment Managers are invested into the same investment concurrently. Typically, it is a temporary financial alliance formed for the purpose of
handling a large transaction that would be hard or impossible for a single Investment Manager to handle individually.
Total Value to Paid In capital (TVPI) is the ratio of total distributed capital and remaining unrealized value to total invested capital. TVPI is also more commonly known as the performance multiple
and measures the total value created by a fund or deal.
Termination Income
Termination Income is the expected total amount of fines received from tenants when they terminate their rental contract before the end of the contract. The amount of termination income is generally
specified in the rental contract.
Total Interest
Total interest is calculated as the sum of Current Interest and PIK Interest.
Tranches are different securities linked to the financial structure of a company divided by seniority of claim on the financial assets of the company. In CEPRES underlying tranches are aggregated
into categories of Senior (i.e. 1st Lien), Subordinated/Mezzanine (Subordinated instruments often with equity kickers), Unitranche/Mixed (1st and/or 2nd Lien with additional tranches all transacted
concurrently) and Equity (pure Equity, often as a follow on kicker).
Upside Deviation
Upside Deviation is a measure of upside opportunities. It represents the Standard Deviation of the observations that are larger than the selected target. For example, the upside deviation of returns
is calculated as the standard deviation of returns that are smaller than the mean.
Upper Quartile
The upper quartile is the relevant value that represents the 75th percentile of a sorted dataset. For example, giving 100 investment records, the Upper Quartile IRR would be the value of IRR for the
75th record with 74 investments having lower IRR values and 25 investments having higher IRR values.
A statistical measure used for probability distribution. It captures the variability (volatility) of each data points from the mean and is a typical measure of risk. For example, variance for IRRs is
calculated by dividing the sum of squared differences between each IRR and the arithmetic mean by the number of IRRs in the data set.
Valuation/Cost Ratio
Valuation/Cost Ratio is an indicator of potential remaining upside. It is calculated as ratio of valuation to total invested capital.
Value Creation based on EBITDA Development - Enterprise Value at Entry
It is the sum of the Enterprise Value at Entry for all the deals. Value Creation based on EBITDA Development is measured with Enterprise Value at Entry as a base.
Value Creation based on EBITDA Development - Revenue Growth
It captures the value creation based on EBITDA Development that can be attributed to the effect of revenue growth over the lifetime of the deal. A positive number means the company has been able to
expand their revenues. It is calculated by: Revenue Growth = (Revenue at Exit – Revenue at Entry) Entry EBITDA Margin Entry EBITDA Multiple
Value Creation based on EBITDA Development - Margin Expansion
It captures the value creation based on EBITDA Development that can be attributed to changes on the EBITDA margin over the lifetime of the deal. A positive number means the company has been able to
improve its operational efficiency and earn more of its revenue as EBITDA. It is calculated by: Margin Expansion = (EBITDA Margin at Exit – EBITDA Margin at Entry) Exit Revenue Entry EBITDA Multiple
Value Creation based on EBITDA Development - Multiple Expansion on Exit EBITDA
It captures the value creation based on EBITDA Development that is due to the aggregated effects of revenue growth and changes on the EBITDA multiple over the lifetime of the deal. It is calculated
by: Multiple Expansion on Exit EBITDA = (Exit EBITDA Multiple - Entry EBITDA Multiple) * Exit EBITDA
Value Creation based on EBITDA Development - Enterprise Value at Exit
It is the sum of the Enterprise Value at Current / Exit for all the deals.
Value Creation based on Revenue Development - Enterprise Value at Entry
It is the sum of the Enterprise Value at Entry for all the deals. Value Creation based on Revenue Development is measured with Enterprise Value at Entry as a base.
Value Creation based on Revenue Development - Revenue Growth
It captures the value creation based on Revenue Development that can be attributed to the effect of revenue growth over the lifetime of the deal. A positive number means the company has been able to
expand their revenues. It is calculated by: Revenue Growth = (Revenue at Exit – Revenue at Entry) * Entry Revenue Multiple
Value Creation based on Revenue Development - Multiple Expansion on Exit Revenue
It captures the value creation based on Revenue Development that is due to the aggregated effects of revenue growth and changes on the revenue multiple over the lifetime of the deal. It is calculated
by: Multiple Expansion on Exit Revenue = (Exit Revenue Multiple - Entry Multiple) * Exit Revenue
Value Creation based on Revenue Development - Enterprise Value at Exit
It is the sum of the Enterprise Value at Current / Exit for all the deals.
Vintage Year
In CEPRES, vintage year refers to the year in which a fund makes its initial investment.
Weighted Average
The weighted average return is a type of average when each return in selected universe is multiplied by a predetermined weight before calculation. In CEPRES, the weight is determined by each deals
invested capital.
Poor performing investments that are classified by the investment manager as unrecoverable and usually considered as a complete loss.
Weighted Average Unexpired Lease term (WAULT) is a real estate metric that is a measurement of the value of current rent contracts. It is denoted in years and is calculated as the sum of all future
rent income currently under contract divided by the annual rent income of a specified year.
Write-Off Rate
A Write-Off is an investment that has lost all value. Write-Off rate is the ratio of the number of write-offs divided by the total number of investments, thus those defaulting investments where the
Recovery Rate is 0% and the Loss Rate is 100%.
Year Refurbished
The year that a building/property was last renovated or improved.
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Landing Page A/B test on Data36 (A/B Testing Case Study)
Today, I’d like to give you an insight into an A/B test that I recently ran on my own blog, data36.com.
In the last few years, the Data36 blog has grown slowly but steadily. As of the time I’m writing this article (11 November 2019), the monthly traffic is well above 100,000 unique visitors. I feel
honored to have this many people’s attention from all around the globe…
And this also puts me in an advantageous position:
Finally, I can run A/B tests on my blog with a big enough sample size!
In this article, I’d like to share the result of a landing page A/B test that I ran on data36.com not so long ago and that I found very, very interesting. (It showed something different than I
initially expected.)
Let’s take a look at it!
Also, if you haven’t done so yet, I recommend going through these A/B testing articles, too:
Some context
Before I show you the details of the landing page A/B test itself, let me give you a little bit of context.
I have a 6-week online data science course called the Junior Data Scientist’s First Month. I have a few more products on Data36 but this one is my top priority. It’s a longer course (6 weeks long),
it’s very comprehensive and it’s fairly expensive, too ($497). I’ve worked a lot on it and I’ve been continuously optimizing it ever since its first release, November 2017.
It’s a fairly expensive and very comprehensive product.
In early 2019, I took a few weeks to figure out how I could create a better landing page for the course.
I mean, the original version that I had at that time wasn’t bad… but it wasn’t great either. It had at least a few issues. I know that because I had 1-on-1 Skype meetings with almost all of the
students who actually enrolled in it. So I already started this optimization project with a few important insights.
• I knew all the questions that students had but were not answered on my original landing page,
• I knew what confused them about my copy,
• I knew many of the doubts that they had before actually buying the course.
But I wasn’t sure whether I should address these on the landing page at all.
I was hesitating for one single reason. The original version was long already: 1,500 words long. It took ~7-8 minutes to read. (Plus it had a 5-minute long embedded video, too.) In today’s online
world, you wouldn’t expect people to spend more time than that with your product. Or at least, I didn’t expect it.
(Note: If interested, here is this now-retired version. Note that since I don’t use it anymore, I removed the registration buttons.)
The suspicion that led to the landing page A/B test
However – thanks to the 1-on-1 sessions with the students – I had a hunch:
My suspicion was that not too many people would read through the whole landing page… but those people who really want to buy the course, they would. However long it is.
To get more evidence, I looked at my Google Analytics data and it more or less confirmed my theory. E.g. one of my analyses showed that those readers who ended up buying the course had spent ~18
minutes on average on the page before they decided to enroll.
Note: I know I use a stupid naming convention in GA. 😉
Okay. So people read. (More precisely: real potential customers read.) Great! But how much more information do they want?
That’s something I was never gonna figure out by myself.So I had to run a landing page A/B test.
The new version
It was time to create my “version B” and set up a proper experiment.
I wrote the new, extended version of my landing page. It became ~4,000 words long (that’s ~20 minutes to read) and I added 4(!) embedded videos to it (watching all those takes another 12 minutes). In
• I answered all the questions I could get from students,
• I addressed all their doubts,
• I made everything about the course super transparent.
But the new version became extremely long.
The lengths of the old and new versions. Version B takes ~4 times longer to fully go through.
Okay, I had my A and B variations. (Here’s version B, in real life, by the way.)
The very last step was setting up the actual A/B test… And of course, waiting for the results.
The specifics of the experiment
By the way, here are the specifics of the landing page A/B test:
• I had two variations:
□ Version A: the original 1,500 word-long page with 1 embedded video
□ Version B: the new 4,000 word-long page with 4 embedded videos
• I split the visitors evenly between the two variations:
□ 50% for version A
□ 50% for version B
• The test ran for 3 weeks. (I needed 3 weeks to gather enough data for statistical significance. Having 100,000 unique visitors on the blog sounds nice — but the reality is that only a smaller
portion of them visit this specific landing page.)
• Since I launch this course only 3 times a year and the registration period is only five days, I couldn’t use the number of purchases as my primary metric. So I had to look for the second best
metric to evaluate this experiment: it was the number of waitlist subscriptions. (More accurately, it wasn’t the number but the conversion rate – so a percentage value – of waitlist
• I was aiming for 99% statistical significance and for a minimum 50% conversion increase.
The results
After 3 weeks, I got the result.
And it blew my mind.
Variation B – the extremely long landing page – WON!
• +96%(!) increase in the number of waitlist subscriptions. In other words: I doubled my conversion rate!
• And the statistical significance was 99%+.
Note 1: If you are interested in the exact numbers, too, here they are:
>> version A ~3,300 visitors and 45 conversions
>> version B ~3,300 visitors and 88 conversions
It’s a smaller sample size but because of the huge difference in conversion rates it’s still a 99%+ statistical significance level.
Note 2: It’s also important to mention that later on, I followed up on this landing page A/B test and checked my actual primary metric, the number of purchases. When I launched my course, I saw that
number double, too. So that confirmed the test results!
Without any false modesty I can proudly say: this was one of the most successful A/B tests I’ve run in the last few years.
The takeaway for me
I learned a lot from this experiment.
But my most important takeaway was that people do read – even for 30 minutes – before they buy an expensive product.
Remember, this is a 6-week, in-depth data science course that costs $497. This is a big investment for them, so they want to gather as much information as they can. And the best I can do is to make
that available for them. It doesn’t matter if it takes 4,000 words and 4 videos. Making the course and its value super transparent and helping potential customers to make a good decision is much,
much more important than the final length of the landing page!
This was a great finding for me. And I feel that I’ll be able to apply this to my future courses, too.
After all, I teach data science, so I can expect that the best and smartest readers of the blog will spend time analyzing my products and my offers before they decide to enroll.
The takeaways from this A/B testing case study for you
But that was only my takeaway.
Your takeaways from this A/B testing case study are very different.
Let me point it out because it’s important but maybe it’s not very intuitive on the first read.
1. This A/B test case study doesn’t show that longer landing pages perform better than shorter ones. It shows that they perform better for my audience, for this specific product type and for this
specific price category. To figure out what works for you, you have to run your own research, your own analyses and your own A/B tests.
2. Also: Have you noticed how the A/B testing part was only the very last step of the whole process?
Remember, the original idea came because I talked to the students who took the course and I listened to them. And then I also tried to validate that idea with hard data. When I got to the
experiment part and I created variation B, I was already fairly confident that it might perform great. The landing page A/B test was the final proof — but in itself (without the initial research)
it would have been worth nothing.
Okay, that was it for today.
I hope you enjoyed this short A/B testing case study!
Oh, one more thing.
You might have a question. Something like: “wait a minute, isn’t it the great rule of A/B testing that you can only change one thing at a time between two variations? Tomi changed the whole landing
page. And he still got great results? What’s going on here?”
In my next article, I address a few A/B testing myths and misconceptions. So continue there and find the answer for the above question. Here it is: click.
Tomi Mester
Tomi Mester
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Finite Mathematics
Discover the relevance of mathematics in your own life as you master important concepts and skills in Waner/Costenoble’s FINITE MATHEMATICS, 8th Edition. Updated, numerous examples and applications
use real data from well-known businesses, current economic and life events -- from cryptocurrency to COVID -- to demonstrate how the principles you are learning impact you. Readable, streamlined
content clearly presents concepts while numerous learning features and tools help you review and practice. Spreadsheet and TI graphing calculator instructions appear where needed. In addition,
WebAssign online tools and an interactive eTextbook include teaching videos by an award-winning instructor. You can refine your skills in the necessary math prerequisites with additional examples and
powerful adaptive practice sessions. A helpful website from the authors also offers online tutorials and videos on every topic to support your learning, no matter what your learning style.
Purchase Enquiry INSTRUCTOR’S eREVIEW COPY
0. PRECALCULUS REVIEW.
Real Numbers. Exponents and Radicals. Using Exponent Identities. Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations.
The Coordinate Plane. Logarithms.
Functions from the Numerical, Algebraic, and Graphical Viewpoints. Functions and Models. Linear Functions and Models. Linear Regression.
2. THE MATHEMATICS OF FINANCE.
Simple Interest. Compound Interest. Annuities, Loans, and Bonds.
3. SYSTEMS OF LINEAR EQUATIONS AND MATRICES.
Systems of Two Equations in Two Unknowns. Using Matrices to Solve Systems of Equations. Applications of Systems of Linear Equations.
Matrix Addition and Scalar Multiplication. Matrix Multiplication. Matrix Inversion. Game Theory. Input-Output Models.
5. LINEAR PROGRAMMING.
Graphing Linear Inequalities. Solving Linear Programming Problems Graphically. The Simplex Method: Solving Standard Maximization Problems. The Simplex Method: Solving General Linear Programming
Problems. The Simplex Method and Duality.
6. SETS AND COUNTING.
Set Operations. Cardinality. Decision Algorithms: The Addition and Multiplication Principles. Permutations and Combinations.
7. PROBABILITY.
Sample Spaces and Events. Relative Frequency. Probability and Probability Models. Probability and Counting Techniques. Conditional Probability and Independence. Bayes' Theorem and Applications.
Markov Systems.
Random Variables and Distributions. Bernoulli Trials and Binomial Random Variables. Measures of Central Tendency. Measures of Dispersion. Normal Distributions.
• Stefan Waner
Stefan Waner and Steven R. Costenoble both received their Ph.D.s from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when
Dr. Waner joined Dr. Costenoble at Hofstra University in 1987. Since then, they have coauthored 18 research papers as well as a research-level monograph in algebraic topology. By the early 1990s,
they had become dissatisfied with many of the finite mathematics and applied calculus textbooks available. They wanted textbook choices that were more readable and relevant to students' interests
-- texts that contained engaging examples and exercises and texts that reflected the interactive approaches and techniques they found worked well with their own students. It, therefore, seemed
natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day, they continue to work together on textbook projects, research in
algebraic topology and in their teaching.
• Steven Costenoble
Stefan Waner and Steven R. Costenoble both received their Ph.D.s from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when
Dr. Waner joined Dr. Costenoble at Hofstra University in 1987. Since then, they have coauthored 18 research papers as well as a research-level monograph in algebraic topology. By the early 1990s,
they had become dissatisfied with many of the finite mathematics and applied calculus textbooks available. They wanted textbook choices that were more readable and relevant to students' interests
-- texts that contained engaging examples and exercises and texts that reflected the interactive approaches and techniques they found worked well with their own students. It, therefore, seemed
natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day, they continue to work together on textbook projects, research in
algebraic topology and in their teaching.
• UPDATED, UNSURPASSED EXAMPLES AND EXERCISES HIGHLIGHT REAL, RELEVANT DATA. Many exercises at all difficulty levels integrate data on relatable topics. Updated applications discuss the rapid rise
of cryptocurrencies and the unanticipated global COVID pandemic, while others focus on instantly recognizable corporations or network technology students constantly use. Students work with
relevant topics like car financing, credit cards, subprime mortgages, hybrid cars and nutrition. The inside back cover lists more than 50 corporations referenced in the applications.
• NEW INTERACTIVE ONLINE LEARNING RESOURCES IN WEBASSIGN AND THE AUTHOR WEBSITE REINFORCE MASTERY. Randomizable, interactive versions of key examples, interactive graphs and other learning tools
are available in WebAssign and on the authors' AppliedMathSite.net. Interactive elements in nonrandom mode engage students in class participation. For students experiencing difficulties, adaptive
practice sessions within the interactive examples offer help with prerequisites all the way to basic algebra.
• NEW KEY CONCEPTS AND "PRACTICE THIS SKILL" FEATURES GUIDE STUDENT LEARNING. Each section now opens with a brief margin list of topics and skills discussed in that section. Key Concept boxes
throughout each chapter contain Quick Examples that highlight and reinforce key topics and skills. In addition, "Practice This Skill" features in the margins and examples in the text correspond
with specific exercises that are based on those examples as well as online "Your Turn" interactive exercises. Many of these exercises ask students to revisit the specific examples on which they
are based.
• STREAMLINED INTRODUCTORY CHAPTER ON FUNCTIONS AND APPLICATIONS IS NOW MORE FOCUSED. This chapter is more concise and streamlined while discussion of some topics, like carbon dating, now appears
in later chapters, where it's more appropriate. This edition's approach to data sets is less complex and the section on mathematical models is significantly more concise and manageable.
• NEW AND UPDATED CASE STUDIES ADDRESS CURRENT TOPICS THAT ENGAGE READERS. For example, this edition includes a new case study for matrix algebra that shows its application in social network
• UPDATED PRECALCULUS REVIEW OFFERS A REVISED, DEDICATED APPROACH TO ASSIST STUDENTS IN MASTERY. This review now includes more information on exponents and radicals as well as an extended
discussion of logarithms.
• WEBASSIGN ONLINE COURSE SOLUTION PROVIDES SUPPORT FOR YOU AND YOUR STUDENTS. Fully integrated with this printed edition of the text, WebAssign offers both a powerful online homework and a course
management system that engages students in learning math. New end-of-chapter exercises and pre-built assignments, vetted by trusted subject matter experts, work with robust content, questions and
online testing to help you foster a deeper understanding of course concepts. Many of the online tools available in the authors' website are also accessible in WebAssign.
• PROVEN AUTHOR WEBSITE OFFERS POWERFUL INSTRUCTOR RESOURCES. The authors' website, AppliedMathSite.net -- almost three decades strong -- provides powerful online utilities for the classroom. Tools
support everything from graphing and evaluating functions and matrix operations to solving linear programming problems both graphically and with the simplex method. Use interactive and game
tutorials to encourage class participation. Learning and practice modules with built-in, adaptive practice are also available. An online interactive text and exercises explore topics beyond the
printed book.
• INNOVATIVE PEDAGOGY APPEALS TO STUDENTS. Learning features such as Question-and-Answer Dialogues, End-of-Section FAQs and "Before We Go On" engage learners. Informal question-and-answer dialogues
anticipate student questions and guide students through new concepts. "Before We Go On" discussions follow most examples and offer a check on the answer, a discussion of the feasibility and
significance of a solution or an in-depth look at what the solution means. Quick Examples in the Key Concept boxes include quick, straightforward examples to solidify students' understanding of
each new concept.
• MARGIN TECHNOLOGY NOTES AND END-OF-CHAPTER TECHNOLOGY GUIDES PROVIDE LEARNING SUPPORT. Brief marginal technology notes outline the use of graphing calculator, spreadsheet and website technology
in appropriate examples. When necessary, notes refer the reader to more detailed discussion in an end-of-chapter Technology Guide. These optional Guides provide detailed instruction on using
TI-83/84 Plus and spreadsheets. You can use this material or not, as you prefer. Exercise sets throughout this edition clearly indicate when the use of technology is suggested or required.
• COMMUNICATION AND REASONING EXERCISES STRENGTHEN SKILLS IN WRITING AND DISCUSSION. These exercises, which often have no single correct answer, are designed to broaden students’ grasp of the
mathematical concepts and strengthen their modeling skills. Some exercises ask students to provide their own examples to illustrate a point or design an application for a given solution.
Exercises also include "fill-in-the-blank," discussion and debate and practice that requires students to identify common errors.
• .
• .
• .
• .
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Cengage Testing, powered by Cognero® for Waner/Costenoble's Finite Mathematics, 8th
Cengage Testing, powered by Cognero® for Waner/Costenoble's Finite Mathematics, Instant Access, 8th
Complete Solutions Manual on Instructor Companion Website for Waner/Costenoble's Finite Mathematics, 8th
PowerPoint® on Instructor Companion Website for Waner/Costenoble's Finite Mathematics, 8th
Instructor's Companion Website for Waner/Costenoble's Finite Mathematics
Cengage eBook: Finite Mathematics 12 Months
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Explore projects · GitLab
• An Agda development of set theory inside homotopy type theory.
• An Agda development of set theory inside homotopy type theory.
• Englacial Layer Simulation Architecture (ELSA)
• Curated applications for Kubernetes
• Random stuff that I like to save in git
• Univalent mathematics in Agda
• GNU General Public License v2.0 or later
• Homotopy type theory cheatsheets to read the HoTT Book
• GNU General Public License v3.0 or later
Local copy for demonstration of submodules
• GEANT4 code to calculate Mean free Path and average energy loss of photons at a given altitude and a given energy. Can be easily change to other particle types.
• HEDTOOLS: Fortran Modelling Toolbox
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python – Matplotlib Plot Lines with Colors Through Colormap
Sure! I will provide you with 8 examples of plotting lines with different colors through a colormap in Python using Matplotlib. I will explain each step of the code in detail.
Example 1: Basic Line Plot with Colormap
import numpy as np
import matplotlib.pyplot as plt
# Generate random data
x = np.linspace(0, 10, 100)
y = np.sin(x)
# Create colormap
cmap = plt.get_cmap('viridis')
# Plot the line with colormap
plt.plot(x, y, c=cmap(0.5))
# Show the plot
1. We import the necessary libraries numpy and matplotlib.pyplot.
2. Generate some random data using the `linspace()` function. We create an array of 100 equally spaced values between 0 and 10 for the x-axis values, and compute the corresponding y-axis values using
the `sin()` function.
3. Create a colormap using the `get_cmap()` function. `’viridis’` is one of the built-in colormaps provided by Matplotlib.
4. Plot the line using the `plot()` function. We set the color (`c`) parameter to `cmap(0.5)`. Here, `cmap(0.5)` returns the color at the midpoint of the colormap.
5. Finally, we display the plot using the `show()` function.
Example 2: Plotting Multiple Lines with Different Colors
import numpy as np
import matplotlib.pyplot as plt
# Generate random data
x = np.linspace(0, 10, 100)
y1 = np.sin(x)
y2 = np.cos(x)
# Create colormap
cmap = plt.get_cmap('coolwarm')
# Set up the figure and axes
fig, ax = plt.subplots()
# Plot multiple lines with different colors from the colormap
ax.plot(x, y1, c=cmap(0.2))
ax.plot(x, y2, c=cmap(0.8))
# Show the plot
1. We import the necessary libraries numpy and matplotlib.pyplot.
2. Generate random data, similar to example 1, for the x-axis and compute corresponding y-axis values for two lines: `y1` and `y2`.
3. Create a colormap using the `get_cmap()` function, here using the ‘coolwarm’ colormap.
4. Set up the figure and axes using the `subplots()` function.
5. Plot multiple lines using the `plot()` function on the axes `ax`. We set different colors for each line by passing different values (`0.2` and `0.8`) to the colormap (`cmap`).
6. Finally, we display the plot using the `show()` function.
Continue to next message for example 3.
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Finding biconnected componemts and computing tree functions in logarithmic parallel time
In this paper we propose a new algorithm for finding the blocks (biconnected components) of an undirected graph. A serial implementation runs in O(n+m) time and space on a graph of n vertices and m
edges. 4 parallel implementation runs in O(log n) time and O(n+m) space using O(n+m) processors on a concurrent-read, concurrent-write parallel RAM. An alternative implementation runs in O(n2/p2 time
and O(n2) space using any number p < n2 /log2 n of processors, on a concurrent-read, exclusive-write parallel RAM. The latter algorithm has optimal speedup, assuming an adjacency matrix
representation of the input. A general algorithmic technique which simplifies and improves computation of various functions on trees is introduced. This technique typically requires o(log n) time
using O(n) processors and O(n) space on an exclusive-read exclusive-write parallel RAM.
Original language English (US)
Title of host publication 25th Annual Symposium on Foundations of Computer Science, FOCS 1984
Publisher IEEE Computer Society
Pages 12-20
Number of pages 9
ISBN (Electronic) 081860591X
State Published - 1984
Externally published Yes
Event 25th Annual Symposium on Foundations of Computer Science, FOCS 1984 - Singer Island, United States
Duration: Oct 24 1984 → Oct 26 1984
Publication series
Name Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume 1984-October
ISSN (Print) 0272-5428
Conference 25th Annual Symposium on Foundations of Computer Science, FOCS 1984
Country/Territory United States
City Singer Island
Period 10/24/84 → 10/26/84
All Science Journal Classification (ASJC) codes
• Biconnected components
• Blocks
• Parallel graph algorithm
• Spanning tree
Dive into the research topics of 'Finding biconnected componemts and computing tree functions in logarithmic parallel time'. Together they form a unique fingerprint.
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Wiring diagrams · Catlab.jl
Data structure for (directed) wiring diagrams, aka string diagrams.
A (directed) wiring diagram consists of a collection of boxes with input and output ports connected by wires. A box can be atomic (possessing no internal structure) or can itself be a wiring diagram.
Thus, wiring diagrams can be nested recursively. Wiring diagrams are closely related to what the CS literature calls "directed graphs with ports" or more simply "port graphs". The main difference is
that a wiring diagram has an "outer box": a wiring diagram has its own ports that can be connected to the ports of its boxes.
This module provides a generic data structure for wiring diagrams. Arbitrary data can be attached to the boxes, ports, and wires of a wiring diagram. The diagrams are "abstract" in the sense that
they cannot be directly rendered as raster or vector graphics. However, they form a useful intermediate representation that can be serialized to and from GraphML or translated into Graphviz or other
declarative diagram languages.
Base type for any box (node) in a wiring diagram.
This type represents an arbitrary black box with inputs and outputs.
An atomic box in a wiring diagram.
These boxes have no internal structure.
A port on a box to which wires can be connected.
Kind of port: input or output.
A wire connecting one port to another.
Grapn underlying wiring diagram, including parts for noin-internal wires.
The graph has two special vertices representing the input and output boundaries of the outer box.
Encapsulate multiple boxes within a single sub-diagram.
This operation is a (one-sided) inverse to subsitution, see substitute.
Create an encapsulating box for a set of boxes in a wiring diagram.
To a first approximation, the union of input ports of the given boxes will become the inputs ports of the encapsulating box and likewise for the output ports. However, when copies or merges occur, as
in a cartesian or cocartesian category, a simplification procedure may reduce the number of ports on the encapsulating box.
1. Each input port of an encapsulated box will have at most one incoming wire
from the encapsulating outer box, and each output port of an encapsulated box will have at most one outgoing wire to the encapsulating outer box.
1. A set of ports connected to the same outside (non-encapsulated) ports will be
simplified into a single port of the encapsulating box.
See also induced_subdiagram.
Get all wires coming into the box.
Get all wires coming into the port.
The wiring diagram induced by a subset of its boxes.
See also encapsulated_subdiagram.
Graph underlying wiring diagram, with edges for internal wires only.
Operadic composition of wiring diagrams.
This generic function has two different signatures, corresponding to the "full" and "partial" notions of operadic composition (Yau, 2018, Operads of Wiring Diagrams, Definitions 2.3 and 2.10).
This operation is a simple wrapper around substitute.
Get all wires coming out of the box.
Get all wires coming out of the port.
Wiring diagram with a single box connected to the outer ports.
Substitute wiring diagrams for boxes.
Performs one or more substitutions. When performing multiple substitutions, the substitutions are simultaneous.
This operation implements the operadic composition of wiring diagrams, see also ocompose.
Check compatibility of source and target ports.
The default implementation is a no-op.
Get all wires coming into or out of the box.
Data structure for undirected wiring diagrams.
Abstract type for UWDs, typed or untyped, possibly with extra attributes.
Abstract type for C-sets that contain a UWD.
This type includes UWDs, scheduled UWDs, and nested UWDs.
A typed undirected wiring diagram.
A UWD whose ports and junctions must be compatibly typed.
An undirected wiring diagram.
The most basic kind of UWD, without types or other extra attributes.
Wire together two ports in an undirected wiring diagram.
A convenience method that creates and sets junctions as needed. Ports are only allowed to have one junction, so if both ports already have junctions, then the second port is assigned the junction of
the first. The handling of the two arguments is otherwise symmetric.
FIXME: When both ports already have junctions, the two junctions should be merged. To do this, we must implement merge_junctions! and thus also rem_part!.
Undirected wiring diagram defined by a cospan.
The wiring diagram has a single box. The ports of this box, the outer ports, the junctions, and the connections between them are defined by the cospan. Thus, this function generalizes
See also: junction_diagram.
Wiring diagrams as a symmetric monoidal category.
This module provides a high-level categorical interface to wiring diagrams, building on the low-level imperative interface and the operadic interface. It also defines data types and functions to
represent diagonals, codiagonals, duals, caps, cups, daggers, and other gadgets in wiring diagrams.
Box wrapping another box.
Represents unary operations on boxes in wiring diagrams.
Junction node in a wiring diagram.
Junction nodes are used to explicitly represent copies, merges, deletions, creations, caps, and cups.
Port value wrapping another value.
Represents unary operations on ports in wiring diagrams.
A list of ports.
The objects in categories of wiring diagrams.
Add junction nodes to wiring diagram.
Transforms from the implicit to the explicit representation of diagonals and codiagonals. This operation is inverse to rem_junctions.
Implicit copy in wiring diagram.
Copies are represented by multiple outgoing wires from a single port and deletions by no outgoing wires.
Implicit merge in wiring diagram.
Merges are represented by multiple incoming wires into a single port and creations by no incoming wires.
Wiring diagram of nested caps made out of junction nodes.
Wiring diagram of nested cups made out of junction nodes.
Explicit copy in wiring diagram.
Copies and deletions are represented by junctions (boxes of type Junction).
Explicit merge in wiring diagram.
Merges and creations are represented by junctions (boxes of type Junction).
Merge adjacent junction nodes into single junctions.
Remove junction nodes from wiring diagram.
Transforms from the explicit to the implicit representation of diagonals and codiagonals. This operation is inverse to add_junctions.
Wiring diagram with a junction node for each of the given ports.
Apply functor in a category of wiring diagrams.
Defined by compatible mappings of ports and boxes.
Algorithms on wiring diagrams.
Topological sort of boxes in wiring diagram.
Returns a list of box IDs, excluding the outer box's input and output IDs.
Crossing minimization by sorting a univariate statistic.
The boxes in sources and/or targets are fixed and the boxes in vs are permuted. A permutation σ of the latter is returned, such that vs[σ] are the sorted box IDs. Both one-sided and two-sided
crossing minimization are supported, depending on whether just one, or both, of sources and targets are given.
In this simple but popular heuristic algorithm, the boxes are permuted by sorting a univariate statistic of the positions of incoming and/or outgoing wires. Typical choices are:
• mean: the sample mean, yielding the "barycenter method"
• median: the sample median
In both cases, this algorithm has the property that if there is a permutation with no crossings, it will find it.
Put a wiring diagram for a cartesian category into normal form.
This function puts a wiring diagram representing a morphism in a free cartesian category into normal form. Copies and deletions are simplified as much as possible.
Normalize copies in a wiring diagram.
This function maximizes sharing of intermediate computations in a wiring diagram where copies are natural.
This algorithm is basically the same as the congruence closure algorithm on term graphs, in the special case of the empty relation R = ∅ (Baader & Nipkow, 1998, Term Rewriting and All That, Sec.
4.4). The main difference is the possibility of zero or many function outputs.
Normalize deletions in a wiring diagram.
This function removes all unused intermediate computations in a wiring diagram where deletion is natural.
Conventions for serialization of wiring diagrams.
Defines a consistent set of names for boxes, ports, and wires to be used when serializing wiring diagrams, as well as conventions for serializing box, port, and wire attributes.
Serialize abstract wiring diagrams as GraphML.
Serialization of box, port, and wire values can be overloaded by data type (see convert_to_graphml_data and convert_from_graphml_data).
GraphML is the closest thing to a de jure and de facto standard in the space of graph data formats, supported by a variety of graph applications and libraries. We depart mildly from the GraphML spec
by allowing JSON data attributes for GraphML nodes, ports, and edges.
• GraphML Primer: http://graphml.graphdrawing.org/primer/graphml-primer.html
• GraphML DTD: http://graphml.graphdrawing.org/specification/dtd.html
Generate GraphML representing a wiring diagram.
Parse a wiring diagram from a GraphML string or XML document.
Read a wiring diagram from a GraphML file.
Write a wiring diagram to a file as GraphML.
Serialize abstract wiring diagrams as JSON.
JSON data formats are convenient when programming for the web. Unfortunately, no standard for JSON graph formats has gained any kind of widespread adoption. We adopt a format compatible with that
used by the KEILER project and its successor ELK (Eclipse Layout Kernel). This format is roughly feature compatible with GraphML, supporting nested graphs and ports. It also supports layout
information like node position and size.
• KEILER's JSON graph format: https://rtsys.informatik.uni-kiel.de/confluence/display/KIELER/JSON+Graph+Format
• ELK's JSON graph format: https://www.eclipse.org/elk/documentation/tooldevelopers/graphdatastructure/jsonformat.html
Generate a JSON dict representing a wiring diagram.
Parse a wiring diagram from a JSON string or dict.
Read a wiring diagram from a JSON file.
Write a wiring diagram to a file as JSON.
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Move Zeros to the end of the list
This coding exercise is part of "30-day-leetcoding-challenge" campaign.
The challenge is to shift Zeros to the end of the list, while keeping the relative order of the Non-Zero elements, without using no extra memory. For example:
Input: [0,1,0,3,12]
Output: [1,3,12,0,0]
Solution 1: Bubble sort style
Inspired by Bubble sort, we can compare every two neighbours and swap them if first one is Zero. Eventually, at each step zero values shift one step towards the end of the list.
The time complexity is O(N2), but no extra memory is needed.
for i in range(len(nums)):
for j in range(len(nums)-i-1):
if nums[j] == 0:
# swapp zero with the next value
nums[j] , nums[j+1] = nums[j+1] , nums[j]
Solution 2: using two pointers
In this approach, there are two pointers, one pointer holds the location of next Non-zero Element (the slow pointer), and the second pointer searches for Non-zero elements (fast pointer). This
solution is optimum, has time complexity of O(N) and space complexity of O(1), no extra space is needed.
slowP = 0;
for e in nums:
if e != 0 :
nums[slowP] = e
#once all non zero elements are moved to top of the array
# the rest of the array contains Zero(s)
while slowP < len(nums) :
nums[slowP] = 0
Solution 3: using Python list built in Sort funtion
This solution is not optimum but uses the Python list built in Sort function, which has the time complexity of O(N log N). The code is just one line.
In this code we take the advantage of sort function, which accepts customize sorting function key.
In our case if element is zero, our function evaluates it as True (1), otherwise False (0). Then sort the 1 and 0, which will get us the order we want.
nums.sort( key= lambda x: x==0)
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Statistical methods data science
• 5 basic methods of statistical analysis
Machine learning has the upper hand in Marketing
1 — Linear Regression: 2 — Classification: 3 — Resampling Methods: 4 — Subset Selection: 5 — Shrinkage: 6 — Dimension Reduction: 7 — Nonlinear Models: 8 — Tree-Based Methods:.
• 5 basic methods of statistical analysis
Imputation and outlier detection are the two statistical methods we use for data cleaning in a machine learning project.
Not every variable or observation is relevant while modeling.
The process of data selection is where we reduce the data to make it relevant for predictions..
• How do you do data science statistics?
For this purpose, one can use statistical sampling techniques such as Random Sampling, Systematic Sampling, Clustered Sampling, Weighted Sampling, and Stratified Sampling.
1. Mean.The mean, also known as the average, is a central value of a finite set of numbers.
2. Standard Deviation
3. Covariance
4. Correlation
• How statistical tests are used in data science?
Perform a statistical test that suits our data.
Check the resulting p-Value.
If the p-Value is smaller than our significance level, then we reject the null hypothesis in favor of our alternative hypothesis.
If the p-Value is higher than our significance level, then we go with our null hypothesis..
• What are the statistical methods for decision science?
Statistical methods are the foundation for data science, artificial intelligence, and much of the field of computer science.
Topics include probability, random variables, regression, gradient search, Bayesian methods, graphical methods, and exponential random graph models..
• What are the statistical methods for decision science?
What are Statistical Methods for Decision Making used for? Statistical methods involve hypothesis testing, single variable linear regression, and multiple regression methods to infer any
• What are the statistical methods in programming?
The two types of statistics are: Descriptive and inferential..
• What kind of statistics do data scientists use?
According to Elite Data Science, a data science educational platform, data scientists need to understand the fundamental concepts of descriptive statistics and probability theory, open_in_new
which include the key concepts of probability distribution, statistical significance, hypothesis testing and regression..
• What statistical procedure is used by data scientist?
What are Statistical Methods for Decision Making used for? Statistical methods involve hypothesis testing, single variable linear regression, and multiple regression methods to infer any
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Origins of Newton's laws of motion
Fig. 1. Sir Isaac Newton.
Newton's laws of motion are central to our society's ability to design and build things that move, e.g. aircraft, cars, ships, rockets, turbines, hard disk drives, etc., a lot of our modern
technology. Newton's laws have even been applied to the motion of people and ancient dinosaurs. The three laws of motion were published in 1697 over three centuries ago.
How did Newton come up with these famous laws?
Actually Newton did not discover his laws in isolation. Many people were involved with coming up with pieces of the laws which Newton put together and verified. This posting lists the more famous of
these earlier scholars. There are many more not quite so famous. It may be surprising that the quest had mostly to do with our understanding of how the planets in the solar system move ... that
mankind figured out how objects move on Earth by studying how planets move in space. Furthermore, we were able to do this without modern technology.
Fig. 2. Roman copy of an old Greek bust of Aristotle by Lysippos from 330 BC.
Fig. 3. A 16^th century rendition of Ptolemy's model of the universe showing the Earth at the center with all other heavenly bodies orbiting around the Earth.
Historical people in the quest to uncover the laws of motion:
• Aristotle 384-322 BC: We begin with Aristotle 23 hundred years ago. This philosopher of ancient Greece wrote about many things. Concerning motion, he stated that objects in this world tended to
return to their native state which he deemed was at rest. According to Aristotle an object will continue to move only if there is an active force continuing to push it it, otherwise it would
return to its rest state of not moving. Aristotle was a believer in observing the world around him and this was certainly what he observed in the world as a human, that moving objects naturally
come to rest.
While a few other thinkers argued against this, Aristotle's teachings were generally accepted as the truth for the next 15 hundred years.
• Claudius Ptolemy 90-168 AD: A member and astronomer of the Egyptian ruling class. He used old Babylonian astronomical data as well as his own measurements of stars and planets to create
convenient tables which allowed a person to compute past and future positions of the planets. He viewed the universe as a set of nested spheres, each containing a planet, the Sun, the Moon or the
fixed stars. The Earth was at the center of his model and did not move, while the rest of the heavenly bodies rotated around the Earth, all at different speeds and each with its own specific
oddities. Like Aristotle's teachings, Ptolemy's solar system model was accepted as the truth by the western world for many, many centuries.
• Nicolaus Copernicus 1473-1543: - Mathematician and astronomer of Prussia (now Poland) created a model of the universe with the Sun at its center. His famous book was published in 1543 after his
death, De revolutionibus orbium coelestium (On the revolutions of celestial bodies). His model was based largely on Ptolemy's data with Copernicus adding 27 observations of his own. His model
showed everything except the Moon going around the Sun in perfectly circular orbits. While his model made it much easier to understand the complicated motions of the planets, it required the
Earth to be moving, an idea that the common man and the church found hard to accept.
│ │ 1. There is no one center in the Universe. │
│ │ 2. The Earth's center is not the center of the Universe. │
│ │ 3. The center of the universe is near the Sun. │
│ │ 4. The distance from the Earth to the Sun is imperceptible compared with the distance to the stars. │
│ │ 5. The rotation of the Earth accounts for the apparent daily rotation of the stars. │
│ │ 6. The apparent annual cycle of movements of the Sun is caused by the Earth revolving around it. │
│ │ 7. The apparent retrograde motion of the planets is caused by the motion of the Earth from which one │
│ │ observes. │
│ Fig. 4. Copernicus' vision of the universe in De revolutionibus orbium │ Fig. 5. Main tenets of Copernicus' model of the universe. │
│ coelestium. │ │
│ │ │
│ Fig. 6. Geo-heliocentric model of the universe (1573) - final model espoused by │ Fig. 7. Mural quadrant (1598). One of the instruments to measure star and planet positions by Tycho │
│ Brahe. │ Brahe. │
• Tycho Brahe 1546-1601: A nobleman/astronomer in Denmark (currently Sweden) who is famous for his comprehensive and accurate measurements of planet and star positions over a 20 year period. His
very precise and thorough measurements provided the data for later breakthroughs. Even though he never believed Copernicus' heliocentric model, Brahe's final model of the solar system was very
close to that of Copernicus.
• Johannes Kepler 1571-1630: German mathematician, astronomer and astrologer. His life was filled with hardships: deaths of loved ones and a lack of money. At some point he started working for
Brahe and was given complete use of Brahe's data upon Brahe's death. After ten years of working on the data, Kepler published Astronomia nova (a new astronomy) in 1609 in which he formulated
three laws of planetary motion. In doing so he distilled Brahe's voluminous data into a brief but accurate geometric and mathematical description of the orbits of planets around the Sun.
│ 1. The orbit of every planet is an ellipse │ │
│ with the Sun at one of the two foci. │ │
│ 2. A line joining a planet and the Sun │ │
│ sweeps out equal areas during equal │ │
│ intervals of time. │ │
│ 3. The square of the orbital period of a │ │
│ planet is proportional to the cube of the │ │
│ semi-major axis of its orbit. │ │
│ │ Fig. 9. Illustration showing the orbit (gray ellipse) of a planet around the Sun (in yellow) according to Kepler's first and second laws. The │
│ Fig. 8. Kepler's three laws of planetary │ time it takes for the planet to move from point a to point b is equal to the time it takes it to move from point c to point d. The areas (shown │
│ motion. │ in blue) are equal. In order to better show the concept, this illustration has an exaggerated ellipse. Real planetary orbits are closer to │
│ │ circular. │
Fig. 10. Galileo showing his telescope to nobility.
Fig. 12. Christiaan Huygens.
Fig. 13. Reflecting telescope invented and made by Newton.
• Galileo Galilei 1564-1642: Italian physicist, mathematician, astronomer, and philosopher, supporter of Copernicus' and Kepler's work. Developed and tested the idea that an object in motion stays
in motion without outside forces. For this he used balls rolling down inclined planes. Because of the Earth's curved surface he erroneously believed that planetary elliptical tracks were the
natural unforced continuation of their motion not requiring any force. He also used a telescope, which he invented, to observe mountains on the Moon suggesting to him that the Moon was made of
similar stuff as the Earth and would similarly have inertia.
Fig. 11. Statue of Descartes.
• Rene Descartes 1596-1650: French philosopher, mathematician and writer who developed Cartesian coordinates and put together work by others to develop modern algebra.
• Christiaan Huygens 1629-1695: Dutch astronomer, physicist, probabilist and horologist (expert on clocks). While he developed many important ideas of today's physics, with regard to the laws of
motion he derived the formula for centripetal force which arises in circular motion F = mv^2/r . This formula was essential to Newton's developing his laws of motion and gravity.
• Isaac Newton 1643-1727: English physicist and mathematician. Published Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), in 1687 explaining his famous
laws of motion. Newton was first to develop a set of mathematical laws or equations for the motion of all objects from planets down to those in ordinary human life. His laws also included a law
of gravity. He developed calculus which he used to apply his laws of motion and gravity to explain the orbits of planets, their moons, and comets. [Mathematician Gottfried Wilhelm Leibniz also
developed calculus simultaneous to Newton. Leibniz's notations for calculus are still in use today.]
Fig. 14. Diagram of Copernicus' heliocentric solar system. The Sun is shown at the center with the orbits of the known planets. The Earth has the circular orbit of the Moon around it.
Fig. 15. Galileo's inclined plane experiments. He determined that if the friction is reduced sufficiently, a rolling ball will lose very little of its momentum and will coast up a second inclined
plane to the same height as it started with on the first inclined plane.
The major pieces:
The major threads of thinking that went into the laws of motion were:
1. Understanding the orbits of the heavenly bodies in a simple model that is capable of being explained with just a few laws of motion.
With regard to understanding the motions of the heavenly bodies, Ptolemy started the effort. Copernicus' insight was a tremendous leap forward. Using Brahe's data, Kepler confirmed and extended
Copernicus' model.
2. Understanding the natural undisturbed state of a moving object: without outside forces, will a moving object "return" to a motionless state or will it continue to move with its initial velocity?
With regard to understanding the undisturbed state and inertia, Aristotle set the stage. Galileo experimentally showed Aristotle to be in error and showed that without an outside force, moving
objects will stay in motion. Descartes (and others) modified Galileo's insight with the idea that a moving object without any external force will continue to move in a straight line and not a
curve as Galileo assumed. This meant that a force would be required to make a planet orbit around the Sun as derived by Huygens. Using his invention, the telescope, Galileo observed mountains on
the Moon suggesting that the Moon and other heavenly bodies were massive like the Earth and had inertia.
One of the problems facing the early scholars involved the poorly differentiated concepts of weight, mass, inertia and momentum. Even today, the word "inertia" can refer to either the mass of an
object or to its momentum (the mass times the velocity) and is not considered a precise word to use by physicists. Even so, "inertia" (or "impetus", its equivalent at the time) with its built-in
ambiguity seemed to be the word that the old scholars often used in discussions of the motion of objects. Because of the ambiguity, in his Principia Newton carefully coined the word "mass" to
refer to the mass of an object (separate from its weight), and used the term "quantity of motion" to refer to its momentum. The word "momentum" was coined later (perhaps in 1720 by Jennings).
Fig. 16. Descartes put together and used modern algebraic concepts.
3. Developing the mathematical machinery required for the application of the laws of motion to explain planetary motion, as well as the motion of objects in our everyday lives. Many mathematicians
around the globe developed parts of algebra, but perhaps Descates was first to put it all together. Newton invented calculus to allow him to apply his laws of motion to the orbits of the planets.
Newton puts the pieces together in his laws:
Fig. 17. Sir Isaac Newton.
Fig. 18. Cover of Newton's Principia. This book was instantly a hit in Europe.
Fig. 19. Newton's first law of motion says that without external forces, like friction, a moving object will continue moving forever.
Like most great thinkers, Newton assembled his laws from insights of other thinkers, then extended and verified them. Below are his three laws of motion plus his "universal law of gravity". All four
of these were revealed in his Principia. In this book, Newton provides great numbers of geometry proofs of various assertions and validations. He shows that these laws would cause the planetary
orbits as specified by Kepler, as well as other effects that we observe in the world around us.
Law 1: Every object in a state of uniform motion tends to remain in that state of motion in the same direction unless an external force is applied to it.
This is really a restatement of Galileo's law of inertia with the modification that an unforced moving object will continue on a straight line and not on a curved path.
Law 2: The force required to change the momentum of an object (mass times its velocity) is equal to the change in momentum per unit of time. This law is usually remembered as F = ma , i.e. force
equals mass times acceleration.
Fig. 20. Newton's second law states that the force required for an acceleration a is equal to the accelerated object's mass m times the acceleration, i.e. F = ma where the force is in the same
direction as the desired acceleration.
This is a quantitative extension of the concept in Law 1, i.e. Law 1 addresses the no-force case and Law 2 addresses the force case. Certainly all the scholars who would agree with Law 1, such as
Galileo, had in their mind that a force was required to make an object deviate from a constant velocity path. A lot of the problem was that the instrumentation to measure trajectories and forces with
reasonable precision was lacking at Newton's time. However, because of the fascination of scholars over the centuries with the the motion of heavenly bodies, the planetary trajectories were precisely
known and the force required to keep them in these trajectories also was almost figured out.
Building on Huygens centripetal force, a number of scholars had reached the conclusion that the Sun would need to attract a planet with a gravitational force inversely proportional to the planet's
distance to the Sun squared in order to cause the elliptical orbits that Kepler had discovered. It apparently made sense to Newton that such a force would also need to be proportional to the planet's
mass so that very heavy planets would experience greater force and so be pulled into similar elliptical orbits as lighter ones.
Newton painstakingly verified that this gravitational force along with his Law 2 would produce the motion of the planets as specified by Kepler. A modern derivation of Kepler's laws from Newton's
laws is found here.
Fig. 21. Illustration of Newton's third law and his law of universal gravity. Note that the force exerted on mass 1 is the same magnitude as that on mass 2 but opposite in direction.
Law 3: For every action there is an equal and opposite reaction. This means that if one object exerts a force on a second object, the second object will automatically exert an opposite force on the
first object. The "opposite force" will be exactly equal in magnitude to the first force, but exactly opposite in direction. This means that a force should be considered a symmetrical interaction
between two objects rather than one object affecting the other.
At the time of Newton's work John Wallis had already verified that momentum was conserved during a collision. In order for Newton's dynamics to be consistent with momentum conservation, this third
law was required. It also was consistent with and suggested by the symmetrical nature of Newton's gravitational force equation.
Fig. 22. Cavendish's balance. This extremely sensitive instrument was able to accurately measure the very weak gravitational force between two weights brought near each other, the force predicted by
Newton's equation for gravity.
Fig. 23. Newton's drawing of the orbit of Halley's comet showing the orbit and blown out tail of the comet, as well as the Earth's orbit (G-H). The Sun (not shown) is at the point labeled "D".
Law of gravity: (Partially discussed above with respect to Law 2.) All objects exert attractive gravitational force on all other objects. In the case of two objects this force is proportional to the
product of the masses of the two objects and inversely proportional to the distance between their centers squared. The force on each object is directed towards the center of the other mass.
Today this law is written as F = Gm[1]m[2] / r^2 where G is the gravitational constant. G was initially measured by Henry Cavendish in 1796 and currently is accepted as 6.67×10^-11 N·(m/kg)^2.
As mentioned above under Law 2, a number of scholars of and prior to Newton's time had reached the conclusion that the "gravitational" force the Sun exerts on a planet must be inversely proportional
to the planet's distance to the Sun squared. Adding a proportionality to the mass of the planet just made common sense.
Newton's genius shone when he concluded that perhaps this gravitational force existed between all objects not only between the planets and the Sun. Thus it would apply to the force between the Earth
and the Moon, between the Earth and a comet and between the Earth and terrestrial objects. To make the force equation universally applicable, he also (correctly) guessed that the force must be
proportional to the masses of both objects involved. In the case of a planet and the Sun, it would thus be proportional to the masses of both the planet and the Sun. He carefully verified that his
laws explained the observed orbit of Halley's comet.
1. Numerous sites on Wikipedia e.g. under Newton's laws, Isaac Newton, and the various other people mentioned above. Most sites are linked in the text. Many of the above illustrations are courtesy
of Wikimedia.
2. The Scientists, John Gribbin, Random House, NY, 2002.
3. Isaac Newton, James Gleick, Pantheon Books, NY, 2003.
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30 Best Math Tutors online - Wiingy
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Transactions Online
Yutaka HATA, Naotake KAMIURA, Kazuharu YAMATO, "Design of Multiple-Valued Programmable Logic Array with Unary Function Generators" in IEICE TRANSACTIONS on Information, vol. E82-D, no. 9, pp.
1254-1260, September 1999, doi: .
Abstract: This paper describes the benefit of utilizing the unary function generators in a multiple-valued Programmable Logic Array (PLA). We will clarify the most suitable PLA structure in terms of
the array size. The multiple-valued PLA considered here has a structure with two types of function generators (literal and unary function generators), a first-level array and a second-level array. On
investigating the effectiveness to reduce the array size, we can pick up four form PLAs: MAX-of-TPRODUCT form, MIN-of-TSUM form, TSUM-of-TPRODUCT form and TPRODUCT-of-TSUM form PLAs among possible
eight form PLAs constructing from the MAX, MIN, TSUM and TPRODUCT operators. The upper bound of the array sizes with v UGs is derived as (log[2]ppv + p(n-v) + 1) p^n-1 to realize any n-variable
p-valued function. Next, experiments to derive the smallest array sizes are done for 10000 randomly generated functions and 21 arithmetic functions. These results conclude that MAX-of-TPRODUCT form
PLA is the most useful in reducing the array size among the four form PLAs.
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_9_1254/_p
author={Yutaka HATA, Naotake KAMIURA, Kazuharu YAMATO, },
journal={IEICE TRANSACTIONS on Information},
title={Design of Multiple-Valued Programmable Logic Array with Unary Function Generators},
abstract={This paper describes the benefit of utilizing the unary function generators in a multiple-valued Programmable Logic Array (PLA). We will clarify the most suitable PLA structure in terms of
the array size. The multiple-valued PLA considered here has a structure with two types of function generators (literal and unary function generators), a first-level array and a second-level array. On
investigating the effectiveness to reduce the array size, we can pick up four form PLAs: MAX-of-TPRODUCT form, MIN-of-TSUM form, TSUM-of-TPRODUCT form and TPRODUCT-of-TSUM form PLAs among possible
eight form PLAs constructing from the MAX, MIN, TSUM and TPRODUCT operators. The upper bound of the array sizes with v UGs is derived as (log[2]ppv + p(n-v) + 1) p^n-1 to realize any n-variable
p-valued function. Next, experiments to derive the smallest array sizes are done for 10000 randomly generated functions and 21 arithmetic functions. These results conclude that MAX-of-TPRODUCT form
PLA is the most useful in reducing the array size among the four form PLAs.},
TY - JOUR
TI - Design of Multiple-Valued Programmable Logic Array with Unary Function Generators
T2 - IEICE TRANSACTIONS on Information
SP - 1254
EP - 1260
AU - Yutaka HATA
AU - Naotake KAMIURA
AU - Kazuharu YAMATO
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 9
JA - IEICE TRANSACTIONS on Information
Y1 - September 1999
AB - This paper describes the benefit of utilizing the unary function generators in a multiple-valued Programmable Logic Array (PLA). We will clarify the most suitable PLA structure in terms of the
array size. The multiple-valued PLA considered here has a structure with two types of function generators (literal and unary function generators), a first-level array and a second-level array. On
investigating the effectiveness to reduce the array size, we can pick up four form PLAs: MAX-of-TPRODUCT form, MIN-of-TSUM form, TSUM-of-TPRODUCT form and TPRODUCT-of-TSUM form PLAs among possible
eight form PLAs constructing from the MAX, MIN, TSUM and TPRODUCT operators. The upper bound of the array sizes with v UGs is derived as (log[2]ppv + p(n-v) + 1) p^n-1 to realize any n-variable
p-valued function. Next, experiments to derive the smallest array sizes are done for 10000 randomly generated functions and 21 arithmetic functions. These results conclude that MAX-of-TPRODUCT form
PLA is the most useful in reducing the array size among the four form PLAs.
ER -
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Neutrino Oscillations and Beyond Standard Model Physics
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Neutrino Oscillations and
Beyond Standard Model Physics
Klausurtagung GRK and PRISMA
Thomas Schwetz-Mangold
Bad Kreuznach, 15. Sept. 2015
T. Schwetz
The Standard Model of particle physics
T. Schwetz
Neutrinos are special
very light (neutrino mass . 10−6 electron mass)
the only (electrically) neutral fermions
feel only the weak force and gravitation
most abundant fermion in the Universe
336 cosmic neutrinos/cm3 (comparable to 411 CMB photons/cm3 )
every second 1014 neutrinos from the Sun pass through your body
neutrinos play a crucial role for
T. Schwetz
energy production in the Sun
nucleo sysnthesis: BBN, SN
generating the baryon asymmetry of the Universe (maybe)
In the Standard Model neutrinos are massless.
The observation of neutrino oscillations implies that
neutrinos have non-zero mass.
⇒ Neutrino mass implies physics beyond the Standard Model.
T. Schwetz
Neutrino oscillations
Absolute neutrino mass
How to give mass to neutrinos
Final remarks
T. Schwetz
Neutrino oscillations
Neutrino oscillations
Absolute neutrino mass
How to give mass to neutrinos
Final remarks
T. Schwetz
Neutrino oscillations
Flavour neutrinos
neutrinos are “partners” of the charged leptons
(doublet under the SU(2) gauge symmetry)
A neutrino of flavour α is defined by the charged current interaction
with the corresponding charged lepton, ex.:
π + → µ+ νµ
the muon neutrino νµ comes together with the charged muon µ+
T. Schwetz
Neutrino oscillations
Lepton mixing
Flavour neutrinos να are superpositions of massive neutrinos νi :
να =
Uαi νi
(α = e, µ, τ )
Uαi : unitary lepton mixing matrix:
Pontecorvo-Maki-Nakagawa-Sakata (PMNS)
mismatch between mass and interaction basis
in complete analogy to the CKM matrix in the quark sector
T. Schwetz
Neutrino oscillations
Neutrino oscillations
neutrino source
neutrino oscillations
"long" distance
|να i = Uαi
|νi i
e −i(Ei t−pi x )
Aνα →νβ
= hνβ | propagation|να i =
Pνα →νβ
= Aνα →νβ ∗
|νβ i = Uβi
|νi i
∗ −i(Ei t−pi x )
Uβi Uαi
T. Schwetz
Neutrino oscillations
Neutrino oscillations: 2-flavour limit
∆m2 = m22 − m12
cos θ
− sin θ
sin θ
cos θ
P = sin2 2θ sin2
∆m2 L
→ oscillations are sensitive to mass differences
"very long"
4π / ∆m
∆m2 L
∆m2 [eV2 ] L[km]
= 1.27
Eν [GeV]
sin 2θ
L / Eν (arb. units)
T. Schwetz
Neutrino oscillations
Neutrinos oscillate!
atmospheric neutrinos Super-Kamiokande
1998: strong zenith angle dependence
of the observed flux of νµ
consistent with νµ → ντ oscillations
T. Schwetz
Neutrino oscillations
Neutrinos oscillate!
KamLAND reactor neutrino
experiment (ν̄e → ν̄e )
Data - BG - Geo νe
CHOOZ data
Expectation based on osci. parameters
determined by KamLAND
Survival Probability
L0/Eν (km/MeV)
2004: evidence for spectral distortion
T. Schwetz
Neutrino oscillations
Neutrinos oscillate!
KamLAND reactor neutrino
experiment (ν̄e → ν̄e )
Data - BG - Geo νe
CHOOZ data
Expectation based on osci. parameters
determined by KamLAND
Survival Probability
L0/Eν (km/MeV)
2004: evidence for spectral distortion
MINOS; T2K, 2015 νµ → νµ
T. Schwetz
DayaBay, 2013 ν̄e → ν̄e
Neutrino oscillations
Global data on neutrino oscillations
various neutrino sources, vastly different energy and distance scales:
SuperK, SNO, Borexino
KamLAND, D-CHOOZ
DayaBay, RENO
K2K, MINOS, T2K
global data fits nicely with the 3 neutrinos from the SM
2 , ∆m2
3-neutrino osc. params.: θ12 , θ13 , θ23 , δ, ∆m21
a few “anomalies” at 2-3 σ: LSND, MiniBooNE, reactor anomaly,
no LMA MSW up-turn of solar neutrino spectrum
T. Schwetz
Neutrino oscillations
fit to 3-flavour
fit to oscillation
with C. Gonzalez-Garcia, M. Maltoni, 1409.5439
precision @ 3σ: 2
sin2 θ12
θ12 /◦
sin2 θ23
θ23 /◦
sin2 θ13
θ13 /◦
δCP /◦
Normal Ordering (∆χ2 = 0.97)
bfp ±1σ
3σ range
Inverted Ordering (best fit)
bfp ±1σ
3σ range
xup − xlow
xup + xlow
Any Ordering
3σ range
0.270 → 0.344
0.270 → 0.344
0.270 → 0.344
14% (4.6o)
0.382 → 0.643
0.389 → 0.644
0.385 → 0.644
32% (15o)
0.0186 → 0.0250
0.0188 → 0.0251
0.0188 → 0.0251
15% (1.2o)
10−5 eV2
10−3 eV2
31.30 → 35.90
38.2 → 53.3
7.85 → 9.10
0 → 360
31.30 → 35.90
31.30 → 35.90
38.6 → 53.3
38.4 → 53.3
7.87 → 9.11
7.87 → 9.11
0 → 360
7.03 → 8.09
7.03 → 8.09
+2.317 → +2.607
−2.590 → −2.307
0 → 360
7.03 → 8.09
+2.325 → +2.599
−2.590 → −2.307
T. Schwetz
1. Three-flavour oscillation parameters from our fit to global data after the Neutrino 2014
Schwetz The results are presented for the “Free Fluxes + RSBL” in which reactor fluxes have
Neutrino oscillations
Neutrino mass states and mixing
T. Schwetz
Neutrino oscillations
Consistency checks
T. Schwetz
Neutrino oscillations
Consistency checks
similar to solar/reactor (KamLAND) complementarity in 1-2 sector
T. Schwetz
Neutrino oscillations
The SM flavour puzzle
Lepton mixing:
θ12 ≈ 33◦
θ23 ≈ 45◦
θ13 ≈ 9◦
O(1) O(1)
= √ O(1) O(1) O(1)
O(1) O(1) O(1)
Quark mixing:
θ12 ≈ 13◦
θ23 ≈ 2◦
θ13 ≈ 0.2◦
T. Schwetz
= 1
Neutrino oscillations
Neutrino masses
at least two neutrinos are massive
typical mass scales:
2 ∼ 0.0086 eV ,
2 ∼ 0.05 eV
much smaller than other fermion masses (me ≈ 0.5 × 106 eV)
2 possibilities for the ordering of the mass states: normal vs inverted
almost complete degeneracy in present data (∆χ2 ≈ 1) 2nd lecture
T. Schwetz
Neutrino oscillations
CP violation
Leptonic CP violation will manifest itself in a difference of the vacuum
oscillation probabilities for neutrinos and anti-neutrinos
Cabibbo, 1977; Bilenky, Hosek, Petcov, 1980, Barger, Whisnant, Phillips, 1980
provides mechanism to generate baryon asymmetry in the Universe
requires CP violation at high temperatures
(one of the Sacharov conditions)
possible connection to CP violation in neutrino oscillations
WARNING: model dependent!
T. Schwetz
Neutrino oscillations
The size of leptonic CP violation
Pνα →νβ − Pν̄α →ν̄β ∝ J ,
J = |Im(Uα1 Uα2
Uβ2 )|
J: leptonic analogue to Jarlskog-invariant Jarlskog, 1985
using the standard parameterization:
J = s12 c12 s23 c23 s13 c13
sin δ ≡ J max sin δ
present data at 1 (3) σ NuFit 2.0
J max = 0.0329 ± 0.0009 (±0.0027)
compare with Jarlskog invariant in the quark sector:
JCKM = (3.06+0.21
−0.20 ) × 10
CPV for leptons might be a factor 1000 larger than for quarks
OBS: for quarks we know J, for leptons only J max (do not know δ!)
T. Schwetz
Neutrino oscillations
The size of leptonic CP violation
Pνα →νβ − Pν̄α →ν̄β ∝ J ,
J = |Im(Uα1 Uα2
Uβ2 )|
J: leptonic analogue to Jarlskog-invariant Jarlskog, 1985
using the standard parameterization:
J = s12 c12 s23 c23 s13 c13
sin δ ≡ J max sin δ
present data at 1 (3) σ NuFit 2.0
J max = 0.0329 ± 0.0009 (±0.0027)
compare with Jarlskog invariant in the quark sector:
JCKM = (3.06+0.21
−0.20 ) × 10
CPV for leptons might be a factor 1000 larger than for quarks
OBS: for quarks we know J, for leptons only J max (do not know δ!)
T. Schwetz
Neutrino oscillations
Complementarity between beam and reactor experiments
68.27%, 95.45% CL (2 dof)
sin θ13
NuFIT 1.3 (2014)
J. Elevant, TS, 1506.07685
current data: slight preference for π . δ . 2π over 0 . δ . π
(very low significance!)
T. Schwetz
Neutrino oscillations
Leptonic unitarity triangle
Unitarity triangle based on the 1st and 3rd column of UPMNS
unitarity is assumed (no test of unitarity!)
still far from knowledge we have on UT in quark sector
T. Schwetz
Neutrino oscillations
Leptonic unitarity triangle
Unitarity triangle based on the 1st and 3rd column of UPMNS
unitarity is assumed (no test of unitarity!)
still far from knowledge we have on UT in quark sector
T. Schwetz
Neutrino oscillations
Search for CP violation in future experiments
measure difference in oscillations of νµ → νe and ν̄µ → ν̄e is hard
(cross sections, fluxes, matter effects,....)
long-baseline accelerator experiments
T2K: J-PARC → SuperK / HyperK (285 km)
NOvA: Fermilab → Soudan (800 km)
LBNF: Fermilab → Homestake (1300 km)
ESS-SB: Lund → ? (360/450 km)
Neutrino Factory: ?
T. Schwetz
Absolute neutrino mass
Neutrino oscillations
Absolute neutrino mass
How to give mass to neutrinos
Final remarks
T. Schwetz
Absolute neutrino mass
Absolute neutrino mass
Three ways to measure absolute neutrino mass:
Neutrinoless double beta-decay: (A, Z ) → (A, Z + 2) + 2e −
Endpoint of beta spectrum: 3 H →3 He +e − + ν̄e
T. Schwetz
Absolute neutrino mass
Absolute neutrino mass
Three ways to measure absolute neutrino mass:
Neutrinoless double beta-decay: (A, Z ) → (A, Z + 2) + 2e −
(with caveats: lepton number violation)
Endpoint of beta spectrum: 3 H →3 He +e − + ν̄e
(experimentally challenging)
(with caveats: cosmological model)
T. Schwetz
Absolute neutrino mass
Absolute neutrino mass
Three ways to measure absolute neutrino mass:
sensitive to different quantities
Neutrinoless double beta-decay: (A, Z ) → (A, Z + 2) + 2e −
(with caveats: lepton number violation)
mee = | i Uei2 mi |
Endpoint of beta spectrum: 3 H →3 He +e − + ν̄e
(experimentally challenging)
mβ2 = i |Uei2 |mi2
(with caveats: cosmological model)
i mi
T. Schwetz
Absolute neutrino mass
Σ mν [eV]
KATRIN sens
Planck + BAO + ...
mνe [eV]
mee [eV]
0νββ : Ge: GERDA + HDM + IGEX, Xe: KamLAND-Zen + EXO
ranges due to NME compilation from Dev et al., 1305.0056
cosmology: Planck Dec. 2014
T. Schwetz
How to give mass to neutrinos
Neutrino oscillations
Absolute neutrino mass
How to give mass to neutrinos
Final remarks
T. Schwetz
How to give mass to neutrinos
Masses in the Standard Model
The Standard Model has only one dimension full parameter:
the vacuum expectation value of the Higgs:
hHi ≈ 174 GeV
All masses in the Standard Model are set by this single scale:
mi = yi hHi
top quark: yt ≈ 1
electron: ye ≈ 10−6
T. Schwetz
How to give mass to neutrinos
Masses in the Standard Model: Dirac fermions
Dirac: need 4 independent states to describe a massive
fermion (spin-1/2 particle)
T. Schwetz
How to give mass to neutrinos
Masses in the Standard Model: Dirac fermions
Dirac: need 4 independent states to describe a massive
fermion (spin-1/2 particle)
BUT: in the SM there are no “right-handed neutrinos”
T. Schwetz
complete gauge singlets
(no interaction → “sterile neutrinos”)
no Dirac mass for neutrinos
How to give mass to neutrinos
Let’s add right-handed neutrinos to the Standard Model
Can now use the Higgs to give mass to neutrinos in the same way as
for the other fermions:
Dirac mass:
mD = yν hHi
BUT: need tiny coupling constant: yν . 10−11
(top quark: yt ≈ 1, electron: ye ≈ 10−6 )
T. Schwetz
How to give mass to neutrinos
Majorana fermions
can make a massive fermion out of only two states
T. Schwetz
concept of “particle” and “antiparticle”
a Majorana fermion “is its own antiparticle”
cannot asign a conserved quantum number
→ a charged particle cannot be Majorana
How to give mass to neutrinos
The Standard Model + right-handed neutrinos
As soon as I introduce right-handed neutrinos (NR ) I can write down a
Majorana mass term for them
Dirac mass:
Majorana mass:
mD = yν hHi
(explicit mass term for NR )
MR :
new mass scale in the theory
NOT related to the Higgs vacuum expectation value
it is the scale of lepton number violation
allowed by the gauge symmetry of the Standard Model but breaks
lepton number
T. Schwetz
How to give mass to neutrinos
Remark on pure Dirac neutrinos
Dirac neutrinos correspond to the specific choice of MR = 0 for the
Majorana mass
This choice is technically natural (protected by Lepton number)
the symmetry of the Lagrangian is increased by setting MR = 0
MR will remain zero to all loop order (if there is no other source of
lepton number violation)
Also the tiny coupling constants yν ∼ 10−11 are protected and
technically natural (chiral symmetry)
The values MR = 0 and yν ∼ 10−11 are considered
“special” and/or “unaesthetic” by many theorists...
T. Schwetz
How to give mass to neutrinos
Remark on pure Dirac neutrinos
Dirac neutrinos correspond to the specific choice of MR = 0 for the
Majorana mass
This choice is technically natural (protected by Lepton number)
the symmetry of the Lagrangian is increased by setting MR = 0
MR will remain zero to all loop order (if there is no other source of
lepton number violation)
Also the tiny coupling constants yν ∼ 10−11 are protected and
technically natural (chiral symmetry)
The values MR = 0 and yν ∼ 10−11 are considered
“special” and/or “unaesthetic” by many theorists...
T. Schwetz
How to give mass to neutrinos
Testing the Majorana nature
Neutrinoless double-beta decay: (A, Z ) → (A, Z + 2) + 2e −
observation of this process would prove that lepton number is violated
in this case MR = 0 will no longer be “natural”
Schechter, Valle, 1982; Takasugi, 1984
Σ mν [eV]
mνe [eV]
T. Schwetz
KATRIN sens
Planck + BAO + ...
mee [eV]
How to give mass to neutrinos
Let’s allow for lepton number violation
What is the value of MR ?
T. Schwetz
How to give mass to neutrinos
Let’s allow for lepton number violation
What is the value of MR ?
T. Schwetz
How to give mass to neutrinos
The Seesaw mechanism
let’s assume mD MR , then the mass matrix
0 mD
mD MR
can be
approximately block-diagonalized to
mν = −
where mν is the induced Majorana mass for the Standard Model neutrinos.
T. Schwetz
How to give mass to neutrinos
The Seesaw mechanism
let’s assume mD MR , then the mass matrix
0 mD
mD MR
can be
approximately block-diagonalized to
mν = −
where mν is the induced Majorana mass for the Standard Model neutrinos.
the Standard Model neutrinos are
light because NR are heavy
T. Schwetz
How to give mass to neutrinos
What is the Seesaw scale?
mν = −
mD = yν hHi
assume mD ∼ mt (or yν ∼ 1)
neutrino masses of mν . 1 eV then imply MR ∼ 1014 GeV
very high scale - close to scale for grand unification ΛGUT ∼ 1016 GeV
GUT origin of neutrino mass?
Ex.: SO(10) grand unified theory Mohapatra, Senjanovic,...
16-dim representation contains all SM fermions + NR
T. Schwetz
How to give mass to neutrinos
Sterile neutrinos: at the GUT scale?
T. Schwetz
How to give mass to neutrinos
What is the Seesaw scale?
mν = −
mD = yν hHi
assume mD ∼ me (or yν ∼ 10−6 )
neutrino masses of mν . 1 eV then imply MR ∼ 1 TeV
potentially testable at LHC
(however: couplings are too small...)
T. Schwetz
How to give mass to neutrinos
Sterile neutrinos: at the scale TeV?
T. Schwetz
How to give mass to neutrinos
very economic model with minimal amount of “new physics”
T. Schwetz
How to give mass to neutrinos
Sterile neutrinos at the eV scale?
exper. hints, however, inconsistent with each other and with cosmology
see second lecture
T. Schwetz
How to give mass to neutrinos
Neutrino mass DOES NOT imply right-handed neutrinos!
It is easy to arrange for lepton number violation without introducing
right-handed neutrinos
Ex., extending the scalar sector of the Standard Model
SU(2) triplet Higgs (“type-II Seesaw”)
neutrino mass generation via loop diagrams Zee; Zee, Babu;...
T. Schwetz
typical involve new physics at TeV scale
can also be linked to a DM candidate e.g., Ma, 2006;...
How to give mass to neutrinos
The Weinberg operator
Assume there is new physics at a high scale Λ. It will manifest itself by
non-renormalizable operators suppressed by powers of Λ.
Weinberg 1979: there is a unique dim-5 operator consistent with the
gauge symmetry of the SM, and this operator will lead to a Majorana
mass term for neutrinos after EWSB:
LT H̃ ∗ H̃ † L
mν ∼ y 2
Λ : scale of lepton number breaking
generically effects of “Λ” are either suppressed by the high scale or by
tiny couplings y
hope for other “new physics” effects beyond neutrino mass
T. Schwetz
How to give mass to neutrinos
The Weinberg operator
Assume there is new physics at a high scale Λ. It will manifest itself by
non-renormalizable operators suppressed by powers of Λ.
Weinberg 1979: there is a unique dim-5 operator consistent with the
gauge symmetry of the SM, and this operator will lead to a Majorana
mass term for neutrinos after EWSB:
LT H̃ ∗ H̃ † L
mν ∼ y 2
Λ : scale of lepton number breaking
generically effects of “Λ” are either suppressed by the high scale or by
tiny couplings y
hope for other “new physics” effects beyond neutrino mass
T. Schwetz
How to give mass to neutrinos
Lepton flavour violation
Neutrino oscillations imply violation of lepton flavour, e.g.: νµ → νe
Can we see also LFV in charged leptons?
µ± → e ± γ
τ ± → µ± γ
µ+ → e + e + e −
µ− + N → e − + N
T. Schwetz
How to give mass to neutrinos
Can we see also LFV in charged leptons?
Yes, BUT: µ± → e ± γ in the SM + ν mass:
e Standard Model,
nvolving charged
y the tiny neutrino
X2 �2
3α �
Uei 2νi . 10−54
(µ → eγ) = Br(µ �→ eγ)U=
mW µi 32π
2 �
32π �
Mi W
(U = PMNS
lepton mixing
I unobservably
small (present
limits: ∼
10−13 )and
−54 : inaccessible to experiment!
(µ →
eγ) � 10of µ → eγ implies new physics beyond neutrino mass
I observation
probe of new physics: the observation of e.g.
T. Schwetz
How to give mass to neutrinos
µ → eγ and new physics
generically one expects
Br(µ → eγ) ∼ 10
4 θeµ
we are sensitive to new physics in the range 1 to 1000 TeV
TeV scale SUSY
TeV scale neutrino masses (triplet, Zee-Babu,...)
T. Schwetz
How to give mass to neutrinos
Comments on charged LFV
LFV does NOT probe neutrino Majorana mass
(conserves lepton number)
LFV: dim-6 operators, Majorana mass: dim-5 operator
→ need a lepton number violating process to test mass directly
cLFV is sensitive to new physics at the 1–1000 TeV scale, which will
be (indirectly) related to the mechanism for neutrino mass
let’s hope for a signal!
this will provide extremely valuable information on BSM
ratios of various LFV channels can give crucial insight on the model
T. Schwetz
How to give mass to neutrinos
Comments on charged LFV
LFV does NOT probe neutrino Majorana mass
(conserves lepton number)
LFV: dim-6 operators, Majorana mass: dim-5 operator
→ need a lepton number violating process to test mass directly
cLFV is sensitive to new physics at the 1–1000 TeV scale, which will
be (indirectly) related to the mechanism for neutrino mass
let’s hope for a signal!
this will provide extremely valuable information on BSM
ratios of various LFV channels can give crucial insight on the model
T. Schwetz
How to give mass to neutrinos
Comments on charged LFV
LFV does NOT probe neutrino Majorana mass
(conserves lepton number)
LFV: dim-6 operators, Majorana mass: dim-5 operator
→ need a lepton number violating process to test mass directly
cLFV is sensitive to new physics at the 1–1000 TeV scale, which will
be (indirectly) related to the mechanism for neutrino mass
let’s hope for a signal!
this will provide extremely valuable information on BSM
ratios of various LFV channels can give crucial insight on the model
T. Schwetz
Final remarks
Neutrino oscillations
Absolute neutrino mass
How to give mass to neutrinos
Final remarks
T. Schwetz
Final remarks
Final remarks
We had exciting discoveries in the last years in neutrino physics,
implying that the Standard model has to be extended in some way.
identifying the mechanism for neutrino mass is one of the most
important open questions in particle physics ... may be a difficult task
(the answer could be elusive forever)
Let’s hope for new signals:
collider experiments at the TeV scale (LHC)
searches for charged lepton flavour violation
lepton number violation and absolute neutrino mass
astroparticle physics
neutrinos may provide crucial complementary information on physics
beyond the Standard Model and a possible theory of flavour.
T. Schwetz
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Digital Zen Garden
There is a chance that one or more of the assumptions that we are relating on might be false. That puts the entire project at risk. We can 'De-risk' the project from this issue by identifying
critical assumptions that we are making and testing these assumptions. If they prove to be false, change your strategy accordingly.
Tagged With: #permanent-notes #strategy #risk
Published on Jan 24, 2024
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RF Power vs Frequency Calculator
This tool provides the RF power at a specified distance from a source transmitter and frequency of operation.
• Transmit Power P[t] (select the appropriate units of Watt or dBm)
• Frequency of operation f
• Distance d
• Transmit Antenna Gain G[Tx]
• Receive Antenna Gain G[Rx]
Example Calculation
For a frequency of 1000 MHz and source power of +30 dBm, the received signal power at a distance of 10 meters is -22.45 dBm.
The table below shows the RF power as a function of frequency for the same ten meter distance.
Frequency (GHz) RF Power (dBm)
1 -22.5
2 -28.5
3 -32
4 -34.5
5 -36.4
6 -38
7 -39.3
8 -40.5
9 -41.5
10 -42.5
As frequency increases, the wavelength decreases. With this, the effective aperture of an antenna used to transmit or receive a signal also decreases.
A[eff] = λ^2/4π
The path loss equation is derived from the following equation which shows that the received signal strength at a fixed distance d decreases with decreasing wavelength or increasing frequency.
Pr = (Pt*Gt*Gr*λ^2)*(1/(4π*d^2))
• Pr​ is the power received,
• Pt​ is the power transmitted,
• Gt​ is the gain of the transmitting antenna,
• Gr​ is the gain of the receiving antenna,
• λ is the wavelength of the RF signal,
• d is the distance between the antennas.
It’s also well known that higher frequency signals (such as mmWave) tend to experience greater atmospheric attenuation and absorption, resulting in higher losses over distance.
However the path loss equation does not account for these losses. Only those due to antenna gain, wavelength (frequency) and distance.
Related Posts
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Ask A Scientist: What Should Preschool Math Look Like?
This is the first in a two-part series.
The debate over what early math should look like and what should be included in the Common Core State Standards for math is one of the most contentious in education circles. Bethany Rittle-Johnson is
a professor of psychology and human development at Vanderbilt University in Tennessee who studies early math and specifically the importance of teaching young children about patterns. Patterns were
mostly left out of the common core math standards in the early grades (kindergarten and 1st grade) due to a lack of evidence that they helped children understand later math concepts. Rittle-Johnson’s
research on what children take away form learning repeating patterns, however, along with the research of several others that has come out since the standards were written, suggest that patterns
should be added back in.
We spoke with Rittle-Johnson at length about both her work with patterns and the more wide-ranging question of what math should look like for preschool students. Should students use objects, called
manipulatives, to practice addition? At what point should they begin to learn symbols? Is counting important? How do students figure out math rules?
Our conversation was so engaging, that it will be published on Early Years in two parts. The first part, edited for length and clarity below, is on best practices for early math.
Can you give an overview of what you research and explain why it’s interesting to you?
I study how children learn math. I find that mathematics is a great topic to study with children’s learning because it tells us a lot about how kids think and it has implications for how we can help
them learn the important school subjects.
There’s a debate raging right now, a debate that has been raging for many years probably, about whether it’s best to memorize math facts in early childhood or whether it’s best to learn about the
concepts undergirding mathematics. Which camp do you fall into?
Actually, I think it’s a silly argument because the evidence is pretty clear that children really need to do both things. Understanding is super-important, but understanding relies on knowing enough
that you can understand it. If you have to spend all your time figuring out what two plus three is, then you can’t notice relationships between number pairs, [for example].
What we really need to do, and what I’ve done all my career, is think about how we can help kids learn facts and strategies as well as understanding how those two things actually support each other
instead of work against each other.
Can you give me an example of a way that those two things might work together, say, when solving a math problem in 1st grade?
It’s really important that you figure out that you can add [numbers] in either order and it’s going to get you the same answer. When you figure that out, you understand something important about
addition and you have half as many things to remember.
It’s not very effective to just tell kids that, though. They have to have experiences with it. So if kids can start noticing these patterns like, “Oh boy, when I add two plus three, I get five, and
when I add three plus two, I get five.” Those kinds of experiences can help them understand this idea that the order you add in doesn’t make a difference.
But if I’m spending all of my time going 1, 2, 3 . . . 1, 2 . . . 1, 2, 3, 4, 5 to figure out that three plus two is five, then that takes up all my resources, so I don’t have time to sit back and
realize these relationships. And then also recognize that it’s not true for subtraction. Because some kids decide the order doesn’t matter for addition so it must not matter for subtraction and of
course it matters a great deal for subtraction.
We can’t just hope that kids notice these [math rules], so how we structure problems matters. [For example,] you want to put three plus two and two plus three next to each other [on a worksheet]. If
the problems are randomly distributed, that’s not going to help as much as if they’re together.
Very interesting. Can you give me another example?
A colleague of mine, Nicole McNeil, [a psychology professor at the University of Notre Dame], has done really nice work on how the way we have children practice arithmetic facts can help them
understand the equal sign and get some basic knowledge that’s foundational to algebraic thinking.
As the kids are practicing solving these problems they’re learning their arithmetic facts, and they learn them just as well. [But instead of doing all the addition problems for adding two,] they
might work on all the problems that add up to six.
So instead of two plus two is four, two plus three is five, two plus four is six, they’re going to focus on getting six? To get to six, two plus four or three plus three or five plus one?
Perfect. It’s about the results.
And another thing—kids actually make this very smart inference that just happens to not work very well long-term, which is that the equals sign means: “Add up the numbers.”
We’ve read those textbooks, Nicole [McNeil] and I and others, and 97 percent of the problems [students] see have the equal sign at the end when they’re in 1st, 2nd, and 3rd grade. So they think oh,
it just means. “Get the answer.” And we have really clear evidence that that messes them up when they get to algebra, where you need to understand the equal sign means each side is the same as the
other side. And we see a lot of middle school kids who still don’t really understand the equal sign.
There’s some nice evidence by Nicole McNeil and Eric Knuth, [an education professor at the University of Wisconsin, Madison], and others that kids in middle school are still struggling with the equal
sign. They sort of get it, but not really, so they really struggle in [algebraic] equation-solving.
That makes complete sense, but I wouldn’t have thought it through.
The nice thing that Nicole [McNeil] has been showing in her work with 2nd graders is that the kids learn the arithmetic facts just as well [when problems are arranged by sums, not addends] but they
understand the equal sign a lot better. [Note: That is, instead of seeing a series like 1+6, 2+6, 3+6, etc., students would see 1+5, 2+4, 3+3, etc., because in the latter set, each problem adds up to
six.] Practice can support understanding, but we don’t get that for free. If we can set up practice in smart ways, then we can really help kids understand better.
How important do you think it is for kids in preschool through 1st grade to do this kind of practice with physical manipulatives as opposed to practicing with problems written out on paper?
That’s been an interesting debate, too. I don’t think I’m 100 percent sure of the answer on this, and it’s actually not work I do myself. But Nicole McNeil and some others do work on this. My sense
is that there are advantages to [working with] concrete manipulatives, but there are a lot of advantages to not [working with] them, too. There’s this idea called “concreteness fading,” which is that
you start with [hands-on manipulatives] but then you fade them away until you switch to just the symbols.
I did this work with patterns with these cute plastic bugs, and sometimes the kids just wanted to play with the bugs. Manipulatives can distract kids or they can get them to pay attention to things
like color when it’s irrelevant. So we do need to help bridge kids to abstract symbols. Kids actually can learn a decent amount from abstract symbols.
I think there are some parents out there who would hear about this and say, “Oh, it’s more advanced at an earlier age. We’ve got a ton of 5-year-olds doing pencil-on-paper math computation, and
that’s terrible.” What do you think about that?
I mean I’ve got to tell you, I’m hearing about kids doing worksheets as 3- and 4-year-olds. And I have not done research on this, but it strikes me as a terrible idea. I think this concern, which is
very legitimate, that if kids are just dealing with abstract symbols and they’re just a bunch of gobbledygook to them or just a bunch of memorized things—that’s going to cause some pretty big
problems and also maybe make them start to hate math at a younger age. Little kids don’t hate math.
That’s why this concreteness fading is a nice way to think about how we’re going to be having these concrete, physical things to ground it and give it meaning. But we’re going to push away from that.
I’m trying to think if that research of pushing away to abstract has been done before kids are 5. And I actually don’t know if it has been.
So what should math look like for a preschooler?
The idea that there’s real mathematics in the world that 3- and 4-year-olds can be thinking about is an important message. And there are some nice curriculums out there for preschool math, and you
might hear the word curriculum and think, “Oh my God.” But, you know, they’re preschool curriculums. They’re not 2nd grade curriculums that were just dumbed down or something. So they involve a lot
of activities and sense-making. Some of them have nice computer software where kids are engaging with virtual things. So they’re getting kids to be thinking about and making sense of what they’re
So number and numeracy is super-important, and that’s what’s getting a lot of attention.
Numeracy means knowing that if there’s two dolls on the ground, that’s two dolls and not three dolls? Is that what you mean by numeracy?
Yeah, I do. I think that a lot of people would find it surprising that when children count objects, they don’t know that that last number that they say indicates how many there are. I mean, children
do memorize [numbers]. We really support kids memorizing the count sequence and counting, pointing to objects and counting them. And if they count and I say, “Okay, how many are there?” They just
count over and over again. They don’t actually know: “Because I just counted to four, there are four objects.” If you say, “Can you give me four?” they give you a random handful. Then when you say,
“Oh, that’s not quite four,” they just randomly give you more.
So you really need to understand what four is. You need to understand four objects, the verbal number named four, then eventually the written symbol four. And that’s important, and it doesn’t come
for free. Just because your child can count objects and recite the count word sequence, as we call it, that actually doesn’t mean those words have any meaning to them. And so that’s really important.
That’s the big push.
Middle-class children get a fair amount of support for that knowledge, and that’s certainly something that we see that children from less-advantaged backgrounds can need extra support because they’re
not counting 50 times a week and kind of figuring it out. Numbers and the names and the symbols and the quantities that go together, oftentimes we call that numeracy. Then eventually learning that
six is more than four, so the relative size of numbers is a really important idea that kids really need to get. And I think it gets a lot of attention these days, and I think it deserves a lot of
attention. But I have to say that math is more than numbers.
Which brings us into your research on patterns, right?
Yes, that’s why I’ve been looking at this research on kids thinking about repeating patterns.
Part two of the series continues here.
Photo: Bethany Rittle-Johnson, courtesy Vanderbilt University
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Group theory is the study of groups, sets paired with an binary operation that satisfy the four group axioms.
Basic Group Definition
Groups are algebraic structures consisting of a set, along with a binary operation (known as the group law of the set) that satisfy closure, associativity, identity, and invertibility (four group
axioms). The group can be expressed as $(S, \cdot)$, where $S$ is the set and $\cdot$ is the operation. A basic example is the set of integers along with the addition operation:
1. Closure: ensures the binary operation, when applied to any two elements from the set, produces a third element that is also part of the set. In the example, adding two integers always yields an
2. Associativity: $(a+b)+c = a+(b+c)$ for integers $a$, $b$, and $c$
3. Identity: for any integer $a$, $a+0=a$. $0$ is the identity element of addition.
4. Invertibility: for any integer $a$, there exists an integer $b$ such that $a+b=0$. $b$ is the inverse element of $a$, i.e. $b = -a$.
Rings, fields, and vector spaces can be classified as groups with additional operations and axioms.
Permutation Groups
For a given set $M$, the group $(G,\circ)$ is a permutation group acting on $M$. Here $G$ is a set of bijections from $M$ to itself (i.e. permutations), and the group operation is the composition of
“permutation functions” in $G$. Additionally, if $G$ contains all possible permutations, then $(G,\circ)$ is a symmetric group (commonly written $\text{Sym}(M)$). All permutation groups on $M$ are
subgroups of the symmetric group $\text{Sym}(M)$.
So permutation groups are a useful way to think about and represent transformations (say, to vertices of a polygon). For example (using an example from the Wikipedia article on permutation groups),
let the vertices of a square be labeled 1,2,3,4 in counterclockwise fashion beginning at the top left vertex. Then the permutation (using cyclic notation) (1234) represents a 90 degree CCW rotation
of the square (i.e. each vertex is mapped to the nearest CCW vertex, 1 -> 2, 2 -> 3, etc). The reflection of the square about the vertical center line is (14)(23).
Finite Simple Groups
Groups can, in a sense, be broken down, or “factorized” (like integers can be broken down into prime factors). Simple groups are the basic building blocks of symmetric groups not unlike the way prime
numbers are building blocks of any integer. Simple groups have normal subgroups including only the trivial group and itself. The classification of finite simple groups was a massive mathematical
achievement uncovering a total of 18 families to which finite simple groups belong. There are also 26 exceptions, called the sporadic groups, defining finite simple groups that do not belong to any
of 18 families mentioned above.
Abelian Groups
Abelian groups, or commutative groups, are groups where the order of two group elements does not matter when applying the group operation (i.e. is commutative).
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The Significance of Sports Betting Odds
Comprehending betting odds is essential for becoming a profitable sports bettor.
Read More: sports odds
Although some people think this is a challenging task, reading odds can be mastered with some time and practice.
Knowing odds is useful for a variety of things, including figuring out payouts, bet sizes, and finding (and taking advantage of) value in a betting line.
New bettors can learn how to interpret betting odds and possibly make money by reading the following breakdown.
How Payouts Correspond with Odds
Understanding what betting odds represent is the first thing to know about them.
A tool used to express an oddsmaker’s position on a specific game, event, or proposition is the betting odds. They also show the amount of money bettors have to risk in order to win a particular sum.
Define the Vigorish.
The amount the sportsbook charges you for placing your bet is called vigorish, sometimes referred to as “vig” or “juice.” Consider it to be the casino’s tip for the services rendered.
The amount of vig varies from sport to sport and wager to wager, and figuring out the vig from the odds isn’t always simple.
A coin toss with an equal chance of landing heads or tails would make a good example. For a coin-toss wager, you would anticipate receiving even money due to the hypothetical 50/50 result.
Put differently, if you wager $10 on heads and the coin falls on heads, you should anticipate receiving $20 in total ($10 from your initial wager plus $10 from the profit).
But that’s not how sportsbooks work. Rather, they typically provide -110 odds on both sides of a point-spread bet (we’ll discuss moneyline odds in a later section). Generally, you have to wager $11
for every $10 you hope to win on a spread bet.
In American sports betting, a $11 wager would pay out $11 if the odds were even (+100), for a total return of $22. However, a $11 wager pays out $10 at -110 odds, for a $21 total return.
Assume you wager $100 at odds of -110. In this case, your possible winnings are $90.91. This is the calculation:
The fractional representation of -110 odds is 10/11.
After rounding, 10 divided by 11 equals 0.91.
$90.91 is the result of multiplying 0.91 by $100, the wager amount.
So what accounts for the $9.09 that is missing? It’s the vib.
Traditional Probability
The implied probability, represented by odds, is the expected chance of an outcome as calculated by bookmakers.
Converting odds into implied probabilities is essential for serious bettors who wish to evaluate a bet’s possible value. In theory, you have an advantage over the sportsbook if you give a team a 60%
chance of winning but the team’s implied probability of winning is 40%.
It’s worth your time to learn the somewhat complex math equation required to convert odds to implied probability, especially if you intend to be a serious sports bettor.
What Does a Negative Odds Signify?
A negative (-) symbol on the odds indicates the betting favorite. The amount to bet for each $100 you hope to win is shown by the number that comes after the negative symbol, or the odds.
For instance, you must stake $110 in order to win $100 if the team you are betting on has -110 odds. You have to stake $150 to win $100 if your team’s odds are -150.
How much money must you bet on a favorite with -150 odds in order to win $300? Multiplying $150 by 3 yields $450.
What Does Sports Betting Chalk Mean?
In sports betting, a team that is favored on the oddsboard is referred to as “chalk.” The New England Patriots are a strong favorite when someone says, “The New England Patriots are a big chalk this
week.” On the other hand, a little chalk is a marginal favorite.
There’s no magic number that tells you if a chalk is “big chalk” or “small chalk.” You’ll start to define “big chalk” and “small chalk” according to your own standards the more sports betting you
engage in.
What Does a Positive Odds Signify?
The underdog is indicated by a plus (+) sign in front of the odds. Positive (+) odds indicate how much you will win for every $100 you bet on the underdog, whereas negative (-) odds indicate how much
you must bet on the favorite to win $100.
Therefore, on a $100 wager, a team with odds of +120 would pay out $120 in profits. For a $100 wager, a team with +250 odds would pay out $250 in profits; for a $200 wager, $500; and so on.
What’s the Meaning of a Pick’em?
In sports betting, a game or match without a favorite or underdog is referred to as a pick’em. In this instance, there is no point spread specified and both sides are regarded as equal. There are two
ways to identify pick’em games on the oddsboard.
First, both teams’ moneyline odds (typically -110 to account for the vig) will be the same. The second is that rather than showing a point total for each team, the spread will state “PK” or “Even”
for both.
Frequently Seen Odds for Sports Betting
After you wager on sports long enough, you will run into some standard moneylines, odds, and point spreads. Here are a few illustrations of what to expect (along with an explanation of each):
A team that is +7 is a 7-point underdog. This is what a +7 spread indicates. A team must either defeat its opponent by 6 points or fewer in order to be a 7-point underdog. The game is deemed a push
(tie) if the team loses by exactly seven points, in which case your money is returned.
A team that is +4.5 is a 4.5-point underdog. This is what a +4.5 spread indicates. That half-point, what about it? It guarantees there won’t be any pushing. A 4.5-point underdog “covers the spread”
if it wins or loses by four points or less. The same underdog does not cover the spread if it loses by five points or more. A winner is assured when a half-point is added to a point spread. A tie is
not possible.
What +350 odds signify: A wager with these odds has a 22% implied probability of winning, making it a significant long shot. However, you would receive $350 in profit (plus your initial $100 bet) if
the underdog pulled off an upset and you had wagered $100 on them.
What +125 indicates: A team at +125 is considered a minor (or brief) underdog. At these odds, a $100 wager would profit $125.
What 20-to-1 odds signify: 20-to-1 odds indicate a long shot with little chance of success. When a team is 20 to 1, the implied win probability is 4.76%. If it wins, though, it will pay out $20 in
profits for every $1 wagered. It is rare, but a $100 wager on a 20-to-1 underdog would yield a tidy profit of $2,000.
Related Stories
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Matrix factorisation
Here we derive updates rules for the approximation of a row stochastic matrix by the product of two lower-rank row stochastic matrices using gradient descent. Such a factorisation corresponds to a
$$ p(n|m) = \sum_k p(n|k) \cdot p(k|m) $$
Both the sum of squares and row-wise cross-entropy functions are considered.
Feature scaling and non-negative matrix factorisation
Non-negative matrix factorisation (NMF) is a dimension reduction technique that is commonly applied in a number of different fields, for example:
• in topic modelling, applied to the document x word matrix;
• in speech processing, applied to the matrix of magnitude spectrograms of framed audio;
• in recommendation systems, applied to the user x item interaction matrix.
Due to its non-negativity constraint, it has the wonderful property of decomposing a objects as an additive combination of (often very meaningful) parts. However, as with all unsupervised learning
tasks, it is sensitive to the relative scale of different features.
The fundamental problem is that the informativeness of a feature need not be related to its scale. For example, when processing speech, the highest-energy components of a magnitude spectrogram are
those of the least perceptual importance! So when NMF decides which information to discard into order to achieve a low-rank factorisation that minimises the error function, it can be the signal, not
the noise, that is sacrificed. This problem is not unique to NMF, of course: PCA retains those dimensions of the sample cloud that have the greatest variance.
It is in general better to learn a feature representation jointly with the downstream task, so that the model learns to scale features according to their informativeness for the task. If NMF is for
some reason still desirable, however, it is possible to better control the information loss by choosing an appropriate measure of the matrix factorisation error.
There are three common error functions used in NMF (all of which Bregman divergences): squared Euclidean, Kullback-Leibler (KL) and Itakura-Saito (IS). These are respectively quadratic, linear and
invariant with respect to the feature scale. Thus, for example, NMF with the Euclidean error function gives strong preference to high-energy features, while NMF with the IS error function is agnostic
to feature scale.
Skipgram isn't Matrix Factorisation
The paper Neural Word Embeddings as Implicit Matrix Factorization of Levy and Goldberg was published in the proceedings of NIPS 2014 (pdf). It claims to demonstrate that Mikolov’s Skipgram model with
negative sampling is implicitly factorising the matrix of pointwise mutual information (PMI) of the word/context pairs, shifted by a global constant. Although the paper is interesting and worth
reading, it greatly overstates what is actually established, which can be summarised as follows:
Suppose that the dimension of the Skipgram word embedding is at least as large as the vocabulary. Then if the matrices of parameters $(W, C)$ minimise the Skipgram objective, and the rows of $W$ or
the columns of $C$ are linearly independent, then the matrix product $WC$ is the PMI matrix shifted by a global constant.
This is a really nice result, but it certainly doesn’t show that Skipgram is performing (even implicitly) matrix factorisation. Rather it shows that the two learning tasks have the same global
optimum – and even this is only shown when the dimension is larger than the vocabulary, which is precisely the case where Skipgram is uninteresting.
The linear independence assumption
The authors (perhaps unknowingly) implicitly assume that the word vectors on one of the two layers of the Skipgram model are linearly independent. This is a stronger assumption than what the authors
explicitly assume, which is that the dimension of the hidden layer is at least as large as the vocabulary. It is also not a very natural assumption, since Skipgram is interesting to us precisely
because it captures word analogies in word vector arithmetic, which are linear dependencies between the word vectors! This is not a deal breaker, however, since these linear dependencies are only
ever approximate.
In order to see where the assumption arises, first recall some notation of the paper:
The authors consider the case where the negative samples for Skipgram are drawn from the uniform distribution $P_D$ over the contexts $V_C$, and write
for the log likelihood. The log likelihood is then rewritten as another double summation, in which each summand (as a function of the model parameters) depends only upon the dot product of one word
vector with one context vector:
The authors then suppose that the values of the parameters $W, C$ are such that Skipgram is at equilibrium, i.e. that the partial derivatives of $l$ with respect to each word- and content-vector
component vanish. They then assume that this implies that the partial derivatives of $l$ with respect to the dot products vanish also. To see that this doesn’t necessarily follow, apply the chain
rule to the partial derivatives:
This yields systems of linear equations relating the partial derivatives with respect to the word- and content- vector components (which are zero by supposition) to the partial derivatives with
respect to the dot products, which we want to show are zero. But this only follows if one of the two systems of linear equations has a unique solution, which is precisely when its matrix of
coefficients (which are just word- or context- vector components) has linearly independent rows or columns. So either the family of word vectors or the family of context vectors must be linearly
independent in order for the authors to proceed to their conclusion.
Word vectors that are of dimension the size of the vocabulary and linearly independent sound to me more akin to a one-hot or bag of words representations than to Skipgram word vectors.
Skipgram isn’t Matrix Factorisation (yet)
If Skipgram is matrix factorisation, then it isn’t shown in this paper. What has been shown is that the optima of the two methods coincide when the dimension is larger that the size of the
vocabulary. Unfortunately, this tells us nothing about the lower dimensional case where Skipgram is actually interesting. In the lower dimensional case, the argument of the authors can’t be applied,
since it is then impossible for the word- or context- vectors to be linearly independent. It is only in the lower dimensional case that the Skipgram and Matrix Factorisation are forced to compress
the word co-occurrence information and thereby learn anything at all. This compression is necessarily lossy (since there are insufficient parameters) and there is nothing in the paper to suggest that
the two methods will retain the same information (which is what it means to say that the two methods are the same).
Appendix: Comparing the objectives
To compare Skipgram with negative sampling to MF, we might compare the two objective functions. Skipgram maximises the log likelihood $l$ (above). MF, on the other hand, typically minimises the
squared error between the matrix and its reconstruction:
The partial derivatives of $E$, needed for a gradient update, are easy to compute:
Compare these with the partial derivatives of the Skipgram log-likehood $l$, which can be computed as follows:
Matrix Factorisation and the Eigendecomposition of the Gram Matrix
Here we consider the problem of approximately factorising a matrix $X$ without constraints and show that solutions can be generated from the orthonormal eigenvectors of the Gram matrix $X^T X$ (i.e.
of the sample covariance matrix).
For this we need the eigendecomposition of real symmetric matrices.
Questions, all related to one another:
• What other solutions are there?
• (Speculative) can we characterise the solutions as orbits of the orthogonal group on the solutions above, and on those solutions obtained from the above by adding rows of zeros to $B$?
• Under what constraints, if any, are the optimal solutions to matrix factorisation matrices with orthonormal rows/columns? To what extent does orthogonality come for free?
Eigendecomposition of real, symmetric matrices
We show that a real, symmetric matrix has basis of real-valued orthonormal eigenvectors and that the corresponding eigenvalues are real. We show moreover that these eigenvalues are all non-negative
if and only if the matrix is positive semi-definite.
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Summary of Graph Embedding
What is Graph Embedding?
Graph embedding is a technique that produces the latent vector representations for graphs. Graph embedding can be performed in different levels of the graph, the two predominant levels are:
1. Node Embeddings - Map each node in a graph to a vector.
2. Graph Embeddings - Map the whole graph to a vector.
Each vector yielded from this process is also referred to as an embedding or representation.
The term "latent" suggests that these vectors are inferred or learned from the data. They are created in a way that preserves the structure (how nodes are connected) and/or attributes (node and edge
properties) within the graph, which might not be immediately apparent.
Taking node embeddings as example, nodes that are more similar in the graph will have vectors that are closer to each other in the vector space.
To provide an illustration, below shows the results (on the right) of running node embedding algorithm DeepWalk to the Zachary's karate club graph (on the left). In the graph, the colors of the nodes
indicate modularity-based clustering. Once all the nodes have been transformed into two-dimensional vectors, it becomes evident that nodes within the same community are positioned relatively closer
to each other.
B. Perozzi, et al., DeepWalk: Online Learning of Social Representations (2014)
Closeness of the Embeddings
The notion of closeness among the embeddings generally refers to how near the vectors representing nodes or other graph elements are in the embedding space. In essence, embeddings that exhibit
spatial proximity in the vector space are indicative of a degree of similarity within the original graph.
In practice, gauging the closeness of embeddings involves employing diverse distance or similarity metrics, such as Euclidean Distance and Cosine Similarity.
Embedding Dimension
The choice of the embedding dimension, also known as the embedding size or vector size, depends on factors such as data complexity, specific tasks, and computational resources. While there is no
one-size-fits-all answer, a typical range of embedding dimensions in practice falls between 50 and 300.
Smaller embeddings facilitate faster computations and comparisons. A recommended approach is to begin with a smaller dimension and progressively expand it as needed, relying on experimentation and
validation against performance metrics pertinent to your application.
Why Graph Embedding?
Dimensionality Reduction
Graphs are often deemed high-dimensional due to the complex relationships they encapsulate, rather than the physical dimensions they occupy.
Graph embedding functions as a dimensionality reduction method that strives to capture the most important information from graph data while substantially reducing the complexity and computational
challenges associated with high dimensions. Within the realm of dimensionality reduction and embedding, even a few hundred dimensions are still labeled as low-dimensional relative to the original
high-dimensional data.
Enhanced Compatibility in Data Science
Vector spaces offer dozens of advantages over graphs in terms of seamless integration with mathematical and statistical approaches within the field of data science. Conversely, graphs, constituted by
nodes and edges, are confined to employing only specific subsets of these methodologies.
The inherent advantage of vectors lies in their innate suitability for mathematical operations and statistical techniques, as each vector embodies a composite of numerical features. Basic operations
like addition and dot products manifest with simplicity and computational efficiency in vector spaces. This efficiency frequently translates into swifter computations when contrasted with analogous
operations performed on graphs.
How Graph Embedding is Used?
Graph embedding serves as a bridge, acting as a preprocessing step for graphs. Once we generate embeddings for nodes, edges, or graphs, we can leverage these embeddings for various downstream tasks.
These tasks include node classification, graph classification, link prediction, clustering and community detection, visualization, and more.
Graph Analytics
We have a bunch of graph algorithms cater to diverse graph analysis purposes. While they offer valuable insights, they do have limitations. Often reliant on handcrafted features extracted from
adjacency matrices, these algorithms might not entirely capture intricate data nuances. Furthermore, efficiently executing these algorithms on large-scale graphs demands significant computational
This is where graph embedding comes to play. By creating low-dimensional representations, embeddings provide richer and more adaptable inputs for a wide spectrum of analyses and tasks. These learned
vectors bolster the efficiency and accuracy of graph analytics, outperforming direct execution within the high-dimensional graph domain.
Consider the case of node similarity analysis. Conventional similarity algorithms generally fall into two categories: neighborhood-based similarity and property-based similarity. The former,
exemplified by Jaccard Similarity and Overlap Similarity, relies on the 1-hop neighborhood of nodes and compute similarity scores. The latter, represented by Euclidean Distance and Cosine Similarity,
uses multiple numeric node properties to calculate the similarity scores based on property values.
While these methods have their merits, they often capture only surface-level node features, thus limiting their applicability. In contrast, embedding nodes with latent and advanced information from
the graph enriches the input data for these similarity algorithms. This fusion empowers the algorithms to consider more sophisticated relationships, leading to more meaningful analyses.
Machine Learning & Deep Learning
Contemporary machine learning (ML) and deep learning (DL) techniques have revolutionized various domains. Yet, applying them directly to graphs presents unique challenges. Graphs possess
characteristics distinct from traditional structured data (e.g., tabular data), making them less amenable to standard ML/DL methods.
Although there are ways to apply ML/DL to graphs, graph embedding proves a simple and effective method. By converting graphs or graph elements into continuous vectors, embeddings not only abstract
the complexities of arbitrary graph sizes and dynamic topologies, but also harmonize well with modern ML/DL toolsets and libraries.
However, turning data into a digestible format for ML/DL is not enough. Feature learning is also a significant challenge before inputting data into ML/DL models. Traditional feature engineering is
both time-consuming and less accurate. Embeddings, serving as learned features encapsulating both structural and attribute information, amplify the model's comprehension of the data.
Imagine a social network where nodes represent individuals and edges depict social connections. The task is to predict individuals' political affiliation. A traditional approach might involve
extracting handcrafted features such as the number of friends, average age of friends, and education level of neighbors for each individual. These features would be then fed into a ML model like a
decision tree or random forest. However, this approach fails to capture all the data's nuances, treating each individual's social connections as separate features and disregarding the intricate
relationships within the graph.
In contrast, utilizing graph embeddings enables the creation of more sophisticated integrations for each individual, yielding accurate and context-aware predictions.
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The S&R index level is 900 at t=0. The dividend yield is 3%
p.a. continuously compounded...
The S&R index level is 900 at t=0. The dividend yield is 3% p.a. continuously compounded...
The S&R index level is 900 at t=0. The dividend yield is 3% p.a. continuously compounded and the risk-free rate is 5% continuously compounded.
(a) What is the theoretical forward price with a maturity of 1 year?
(b) Suppose you observe a forward price with a maturity of 1 year equal to 950. What position do you take in order to earn arbitrage profit?
A. Long stock and short forward
B. Long stock and long forward
C. Short stock and long forward
D. Short stock and short forward
(c) Suppose you observe a forward price with a maturity of 1 year equal to 950. What is your arbitrage profit at t=1?
a). Forward price F[0] = S[0]e^(r-d)T
where S[0] = current price = 900
r = risk-free rate = 5%
d = dividend yield = 3%
T = duration = 1 year
F[0] = 900*(e^(5%-3%)*1)
= $918.18
b). If the observed forward price is $950 then long stock and short forward (option A)
c). Borrow $900 at 5% for one year. Amount payable after one year will be 900e^(5%*1) = $946.14
Short a forward contract to sell the stock after one year at $950.
After one year, net profit is 950 - 946.14 = $3.86
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seminars - Tannakian reconstruction of representable presheaves of groups on the category of cocommutative differential graded coalgebras
The reconstruction part of the Tannaka-Krein duality states that a compact group X can be recovered from the category of its finite dimensional unitary representations. Grothendieck suggested and
Saavedra showed in his thesis that an analogous reconstruction holds true for affine group schemes. This result lead to the notion of Tannakian categories, which was further studied by Deligne.
In this talk, we study representable presheaves of groups on the category of cocommutative differential graded coalgebras, motivated by rational homotopy theory. Such presheaves can be considered as
a dual notion to differential graded affine group schemes. We introduce an analogous reconstruction result for these presheaves. More precisely, we reconstruct such presheaf from the category of its
(not necessarily finite dimensional) representations. As a consequence, we give an alternative reconstruction for (differential graded) affine group schemes.
This is a joint work with Jae-Suk Park.
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Title : Trapped modes in thin and infinite ladder like domains. Part1: Existence results
Year : 2017
Type : paper in peer-reviewed journal
Authors : B. Delourme, S. Fliss, P. Joly, E. Vasilevskaya
The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is
a ladder like domain, namely a thin periodic structure (the thickness being characterized by a small parameter ε>0) whose limit (as ε tends to 0) is a periodic graph. The localized
perturbation consists in changing the geometry of the reference medium by modifying the thickness of one rung of the ladder. Considering the scalar Helmholtz equation with Neumann boundary
Abstract conditions in this domain, we wonder whether such a geometrical perturbation is able to produce localized eigenmodes. To address this question, we use a standard approach of asymptotic
: analysis that consists of three main steps. We first find the formal limit of the eigenvalue problem as the ε tends to 0. In the present case, it corresponds to an eigenvalue problem for a
second order differential operator defined along the periodic graph. Then, we proceed to an explicit calculation of the spectrum of the limit operator. Finally, we prove that the spectrum
of the initial operator is close to the spectrum of the limit operator. In particular, we prove the existence of localized modes provided that the geometrical perturbation consists in
diminishing the width of one rung of the periodic thin structure. Moreover, in that case, it is possible to create as many eigenvalues as one wants, provided that ε is small enough.
Numerical experiments illustrate the theoretical results.
Themes :
Reference Asymptotic Analysis - vol. 103(3) (pp 103-134 )
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Simplified Fraction | Lexique de mathématique
Simplified Fraction
Fraction in which the numerator and the denominator do not have a whole common divisor that is different from 1.
in which the numerator and the denominator are
relatively prime
, which means that they do not have a whole common divisor that is greater than 1.
• Fractions like \(\frac{2}{3}\), \(\frac{3}{4}\), \(\frac{5}{13}\) and \(\frac{8}{19}\) are simplified fractions.
• The fraction \(\frac{8}{18}\) is not a simplified fraction because the number 2 is a whole common divisor for 8 and 18. Therefore, the equivalent simplified fraction to \(\frac{8}{18}\) is the
fraction \(\frac{4}{9}\) which is simplified.
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Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
We study the vacuum structure and don spectrum of N=2 supersymmetric gauge theory in four dimensions, with gauge group SU(2). The theory turns out to have remarkably rich and physical properties
which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and dyon masses and the metric on the moduli space of vacua. The description involves a
version of Olive-Montonen electric-magnetic duality. The "strongly coupled" vacuum turns out to be a weakly coupled theory of monopoles, and with a suitable perturbation confinement is described by
monopole condensation.
All Science Journal Classification (ASJC) codes
• Nuclear and High Energy Physics
Dive into the research topics of 'Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory'. Together they form a unique fingerprint.
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Derivation of Multiplier
Another way to derive multiplier is based on the functional relation between consumption and income.
We start with the basis equilibrium condition, i.e.,
Y = C + I (1)
We known that consumption (C) is the function of income (Y). This functional relationship can be expresses as
C = a + bY (2)
Substituting equation (2) in equation (1), we get
Y = a + bY + I
or, Y - bY = a + I
or, (1 - b) Y = a + I
If we denote change in investment by ∆I and change in income by ∆Y, the equilibrium condition becomes
Dropping brackets, the first and last terms cancel out,
For a given change in investment, the change in income is equal to 1/(1 - b) times the change in investment. Thus 1/(1 - b) is the value of multiplier. If we divide both sides of the Equation (3) by
∆I, we get
The ratio ∆Y/∆I is the ratio of change in income to the change in investment which is the definition of the multiplier.
In equation (4), b =MPC
We know MPC+MPS = 1
K = 1 - MPC = 1 - b
Multiplier = K = 1/MPS
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Derivation of Multiplier
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"I thought she would get there first, but I did” primary school lower attainers’ contributions to mixed attainment mathematics
Mixed attainment pairs in primary mathematics are sometimes seen as a way to enable lower attaining pupils to be supported by higher attaining peers and to be exposed to higher levels of mathematical
thinking. Whilst the intent underpinning mixed pairings based on this rationale is not disputed, the research presented in this session began from the premise that this is only part of the picture,
that it omits what the lower attainer may bring to the partnership and contribute during the activity.
Employing a pedagogical focus on mathematical noticing, and based in three primary school classrooms, close video observation of mixed attainment pairs revealed frequent and important mathematical
contributions from lower attaining pupils, together with evident satisfaction from lower attainers in their achievements. This session explores the study and its outcomes, its use of the construct of
mathematical noticing and its conclusion that mixed attainment pairings can produce bi-directional benefits.
Conference Association of Mathematics Education Tutors/National Association of Mathematics Advisors March 2022
Abbreviated title AMET/NAMA March 22
Period 25/03/22 → 26/03/22
Dive into the research topics of '"I thought she would get there first, but I did” primary school lower attainers’ contributions to mixed attainment mathematics'. Together they form a unique
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Looking for SAS regression experts for model comparison? | Hire Someone To Take My SAS Assignment
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tool has previously been available in SAS’s “Early Review Tools” series. The Systemic Inter
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Games and Personal Software
Bruce Incognito 21 July 2013 00:17:49
The "eight queens" problem was first proposed by the German chess player Max Bezzel in 1848. Many mathematicians dabbled with the problem including, most notably, Carl Friedrich Gauss. The first
solution to the problem was given in 1850 by Franz Nauck, who then followed this with a solution to the generalised n-Queens problem (on an n x n chessboard) in 1874. Many mathematicians and computer
scientists have since studied the problem or used it to illustrate theorem proving or problem solving techniques. Perhaps most famously the late, great Edsger Dijkstra used the problem in 1972 to
illustrate the power of "Structured Programming". Most recently the problem is used in the teaching of aspects of logic programming languages such as Prolog, in this scenario the problem is often
posed as "find the number of solutions to the eight queens (or the more generalised n-Queens) problem".
How Many Solutions Are There to the Eight Queens Problem?
In the style of Douglas Adams I could just leave you with the ultimate answer - 92.
However I suspect that as you have read this far you probably expect a little more explanation and information.
In the discussion below queens are described by their position on the chessboard expressed as a Row co-ordinate (1 - 8) and a Column co-ordinate (1 - 8), all aspects of the discussion also pertain to
the more generalised n-Queens problem.
We will start by looking at a program to answer the question about how many solutions there are.
Stating the Problem
Find all possible arrangements of 8 queens placed on an 8 x 8 chessboard such that the arrangement satisfies the three following constraints.
1. No two queens reside on the same row of the board.
2. No two queens reside on the same column of the board.
3. No two queens reside on the same diagonal of the board
We now need to decide how we will represent the problem programmatically so that we can answer the question, we have to create an abstraction of the real-world problem in such a way that we can
derive the answer through computation. This part of the process is often skipped over and neglected in many Computer Science courses and should not be, as this is the most creative and critical step.
A sage word of advice here is to never neglect the obvious, just because some aspect is obvious does not mean that it is either trivial or irrelevant.
It is obvious (but important) from the first constraint that there must be exactly one queen on each row of the board and it is equally obvious (but equally important) that there must be exactly one
queen on each column of the board.
It is a very small conceptual step to see from these obvious observations that we can encode the state of the board containing the 8 queens as a simple one-dimensional array with 8 cells each
representing the different rows on the board and each cell containing a unique integer from 1 to 8 representing the column containing the queen on the row given by the index in the array.
This seems to be a nice compact method of encoding an arrangement of the board but further we observe that the encoding that we have selected actually removes constraints 1 and 2 from any further
consideration as they are always satisfied by any arrangement encoded in this manner, cute eh! This compact form for encoding the problem was first proposed by Gauss in correspondence with his friend
the astronomer H.C. Schumacher in 1850.
Further we observe that if we populate an initial arrangement of the array as representing the queens on a single diagonal from top left to bottom right i.e. Array = [1,2,3,4,5,6,7,8], we can now see
that the abstract problem can be stated as:
Find every permutation of the array [1,2,3,4,5,6,7,8] that satisfies constraint 3.
So how do we test an arrangement to make sure that it satisfies constraint 3? Any two queens can be tested to ensure that they are not on the same diagonal by testing that the absolute (ignore the
sign) of the difference of their respective rows is not equal to the absolute difference of their columns. We can therefore ensure that a complete arrangement satisfies constraint 3 by testing each
queen against each of the other queens to ensure that they all satisfy the inequality.
A Bit More Formally
Find every permutation of the array [1,2,3,4,5,6,7,8] where no pairs of elements (e1, e2) of the array satisfy the condition abs(R(e1) - R(e2)) == abs(e1 - e2). Where R(e1) is the 1 based index of
the element e1 in the array.
Solving the Problem in 'C'
Let us start off by solving the problem in a functional language (let's pick 'C' as an example. The code presented is meant to be illustrative and clear, not stylish!
We will present this "bottom up" starting with a function for testing that an arrangement satisfies constraint 3.
// Test arrangement
int testArrangement(int FArray[])
int iIndex,jIndex; // Generic inexes
for (iIndex = 0; iIndex 7; iIndex++)
for (jIndex = iIndex + 1; jIndex 8; jIndex++)
// Test for a collision on a diagonal
if ((jIndex - iIndex) =abs(FArray[jIndex] - FArray[iIndex])) return 0;
printf("INFO: Solution found: [%i,%i,%i,%i,%i,%i,%i,%i].\r\n",
return 1; // Show that another solution was found
There is nothing too startling about the code, as the inequality is commutative we are able to optimise the two loops a bit by not performing any tests that we have already done the other way round
i.e we don't test row 5 against row 1 because we have already tested row 1 against row 5 and so on.
All that we have to do now is to generate every permutation of the array and pass them in turn to the function to test each arrangement and count up the number of arrangements that satisfy constraint
3. We will use a standard divide and conquer recursive generator to produce the permutations of the array that contains the arrangement.
It should be noted that it is perfectly possible to traverse the complete solution graph recursively, however, in this implementation we sequentially process the breadth of the graph at each level.
// Permute Array
int permuteArray(int FArray[], int FAC, int VArray[], int VAC)
int SolutionsFound = 0; // Count of solutions found
int NewFArray[8] = {0,0,0,0,0,0,0,0}; // New fixed array
int NewVArray[8] = {0,0,0,0,0,0,0,0}; // New variable array
int iIndex,jIndex,kIndex; // Generic indexes
// Copy the fixed and variable arrays
for (iIndex = 0; iIndex 8; iIndex++)
NewFArray[iIndex] = FArray[iIndex];
// Test for the boundary condition - There is only a single element in the variable array
if (VAC == 1)
// Complete the permutation
NewFArray[7] = VArray[0];
SolutionsFound = SolutionsFound + testArrangement(NewFArray);
return SolutionsFound;
// Move one element from the variable array to the fixed array and recursively
// invoke the permuter
for (iIndex = VAC - 1; iIndex >= 0; iIndex--)
NewFArray[FAC] = VArray[iIndex];
kIndex = 0;
for (jIndex = 0; jIndex VAC; jIndex++)
if (VArray[jIndex] != NewFArray[FAC])
NewVArray[kIndex] = VArray[jIndex];
SolutionsFound SolutionsFound + permuteArray(NewFArray, FAC + 1, NewVArray, VAC - 1);
return SolutionsFound;
The function takes each element in the variable array (VArray) and moves it to the next available position in the fixed array (FArray) and then recursively calls the permutation function to do the
same again until there is only one element remaining in the variable array. At that point it adds the last element to the fixed array and then tests that arrangement for for compliance with
constraint 3 by calling the testArrangement() function. The function returns the number of satisfying arrangements found in the branch of the permutation tree that it was called with.
All that remains now is to call the permutation generator with the initial states of the arrays i.e. the fixed array empty and the variable array containing all elements and then report on the number
of satisfying solutions found.
// Main Entry Point
int main(int argc, char *argv[])
int EArray[8] = {0,0,0,0,0,0,0,0}; // Empty array
int IArray[8] = {1,2,3,4,5,6,7,8}; // Initial array
int Solutions; // Count of solutions
// Invoke the permuter to generate the permutations
Solutions = permuteArray(EArray, 0, IArray, 8);
// Show how many solutions were found
printf("INFO: Run completed %i solutions discovered.\r\n", Solutions);
return 0;
All that remains is to add a little preamble and the complete application can be compiled, linked and run.
// Language Includes
// Function prototypes/Forward declarations
int permuteArray(int FArray[], int FAC, int VArray[], int VAC);
int testArrangement(int FArray[]);
Running the program yields a list of each satisfying arrangement found along with the total count.
INFO: Solution found: [2,5,7,1,3,8,6,4].
INFO: Solution found: [2,4,6,8,3,1,7,5].
INFO: Solution found: [1,7,5,8,2,4,6,3].
INFO: Solution found: [1,7,4,6,8,2,5,3].
INFO: Solution found: [1,6,8,3,7,4,2,5].
INFO: Solution found: [1,5,8,6,3,7,2,4].
INFO: Run completed 92 solutions discovered.
The simplicity and elegance of the program to list and count the satisfying arrangements is all down to that important first step of problem abstraction, the importance of which cannot be
overemphasised. As an interesting comparison we will solve the same problem in a declarative language such as Prolog.
Solving the Problem in Prolog
We will use exactly the same problem abstraction to solve the problem in Prolog that we used for the 'C' program. Again we will work bottom up starting with the predicates that are used to test that
an arrangement satisfies the constraints.
% The following predicates test that the current board arrangement satisfies the constraints
testArrangement([_]) :- !.
testArrangement([TheQueen | OtherQueens]) :- !, notake(TheQueen, 1, OtherQueens), testArrangement(OtherQueens).
notake(_, _, []) :- !.
notake(TheQueen, DeltaRow, [NextQueen|OtherQueens]) :- !,
Hit1 is TheQueen + DeltaRow,
NextQueen =\= Hit1,
Hit2 is TheQueen - DeltaRow,
NextQueen =\= Hit2,
NewDeltaRow is DeltaRow + 1,
notake(TheQueen, NewDeltaRow, OtherQueens).
Because we will be using backtracking to find all of the possible solutions we will need a couple of additional predicates to enable us to keep track of the count of solutions found.
% The following predicates count the solutions
initialiseCounter(I) :- retractall(counter(_)), assert(counter(I)).
incrementCounter(I) :- retract(counter(C)), N is C + I, assert(counter(N)), !.
We now add predicates to generate each of the possible arrangements and test each to see if they satisfy the constraints.
% The following predicates generates a permutation of the arrangement
listInsert(A, B, [A | B]).
listInsert(A, [B1 | B2], [B1 | C]) :- listInsert(A, B2, C).
permuteArray([A], [A]).
permuteArray([A | B], C) :- permuteArray(B, C1), listInsert(A, C1, C).
% The following predicates find all of the solutions
findSolution(A, B) :- permuteArray(A, B), testArrangement(B).
findAllSolutions(A) :- initialiseCounter(0), findSolution(A, B), incrementCounter(1), counter(X), print(X), print('. '), print(B), nl, fail.
findAllSolutions(_) :- nl,print('INFO: Run completed '), counter(X), print(X), print(' solutions found.'),nl.
All we need to do now is to trigger the search for all of the solutions by querying the prolog database with the initial arrangement.
?- findAllSolutions([1,2,3,4,5,6,7,8]).
87. [4,8,5,3,1,7,2,6]
88. [4,2,8,5,7,1,3,6]
89. [4,8,1,5,7,2,6,3]
90. [8,2,5,3,1,7,4,6]
91. [8,2,4,1,7,5,3,6]
92. [3,8,4,7,1,6,2,5]
INFO: Run completed 92 solutions found.
All well and good, we have convinced ourselves that there are 92 solutions to the eight queens problem but we know nothing more than that. We have no clues as to why there should be 92 solutions or
how these solutions are formed.
Some Geometry of the Eight Queens Problem
We start off by taking a board arrangement that we discovered in the brute force searches, the compact encoding for this arrangement is [3,8,4,7,1,6,2,5] which was solution 92 from the prolog run to
find all solutions.
We observe that we can rotate the board through 90 degrees clockwise and we have generated another valid arrangement with the compact encoding [4,2,8,6,1,3,5,7]. This makes sense as we would expect
all three constraints for a valid arrangement to hold true under rotation. A quick look at the transformation function for a 90 degree clockwise rotation (R, C) -> (C, 9 - R)
and the inequalities in our constraints will show that the 90 degree clockwise rotation will always result in another satisfying arrangement.
As a single clockwise rotation by 90 degrees yields another unique satisfying arrangement then it should be clear that we can rotate the new arrangement by 90 degrees clockwise again to give yet
another satisfying arrangement and the same yet again. These additional rotations give us [4,7,3,8,2,5,1,6] and [2,4,6,8,3,1,7,5].
We further observe that if we reflect a satisfying arrangement about the bottom edge of the board we derive yet another satisfying arrangement [5,2,6,1,7,4,8,3]. Again a quick look at the
transformation function for the reflection (R, C) -> (9 - R, C) and the inequalities in the constraints shows that again this transform will also yield a satisfying arrangement.
Of course we can then apply the 90 degree clockwise rotation transform to the result of the reflection to give us another three satisfying arrangements [5,7,1,3,8,6,4,2], [6,1,5,2,8,3,7,4] and
So we have made some significant progress in finding some underlying structure to the set of satisfying arrangements for the eight queens problem. We would expect the full set of solution to come in
sets of 8 arrangements that represent the untransformed arrangement plus the seven possible transforms identified above. But hold on a moment our brute force search identified a total of 92
satisfying arrangements and that is not a multiple of 8!
Some analysis of the results from the brute force search reveals that there are in fact 12 unique groups of satisfying arrangements, 11 of which have 8 distinct arrangements in the set and the one
remaining sent only yields 4 distinct satisfying arrangements.
Untransformed [3,5,2,8,1,7,4,6] Rotate 90 [4,6,8,2,7,1,3,5]
Rotate 180 [3,5,2,8,1,7,4,6] Rotate 270 [4,6,8,2,7,1,3,5]
Reflect [6,4,7,1,8,2,5,3] Reflect + Rotate 90 [5,3,1,7,2,8,6,4]
Reflect + Rotate 180 [6,4,7,1,8,2,5,3] Reflect + Rotate 270 [5,3,1,7,2,8,6,4]
The reason that this particular set of arrangements produces isomorphic forms should be readily apparent. The arrangement has two axes of internal rotational symmetry. Split any one of the
arrangements in the set in half about the horizontal or the vertical axis and then rotate one of the halves by 180 degrees and the symmetry is readily apparent.
Left Hand Side of [3,5,2,8,1,7,4,6] Right Hand Side of [3,5,2,8,1,7,4,6] Right Hand Side Rotated 180 degrees
Top Half of [3,5,2,8,1,7,4,6] Bottom Half of [3,5,2,8,1,7,4,6] Bottom Half Rotated 180 degrees
Enough of the structure of the solutions to the "eight queens" problem, click on the following link to find out more about how we use Computer Science in the Q8 Game.
1Abel Laffingboy 29 June 2017 13:41:21 Hilariously Funny! You really made my day by publishing this I am still rolling about the floor with my sides in pain.
2 29 June 2017 13:47:08 A Subject 4U Well I do declare!
3 Benjamin Bollocks 29/07/2017 09:57 The Curious Case of the Disappearing Response You may completely ignore the comment as it is merely a tracking test for: Home Site with an embedded link.
4 Hands Wannapuke 31/07/2017 12:31 Wombat Alert Just thought that I would let you know that we have detected a number of highly mobile Wombat devices in use in the locality.
5 Karl De Kopt 31/07/2017 13:00 Koptic Krunchiness File permissions are a topic that is easily overlooked by the myopic idiot who was setting up the infrastructure to support the comment processing.
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R&D Investment timing, default and capital structure
This paper investigates the interaction between R&D investment timing, probability of default, and capital structure. In particular we are interested in studying the investment behaviour of three
different types of firms according to their capital structure: firms that only use internal funds as a source of funding (unlevered), firms that use debt and that are able to attract unlimited amount
of funds (levered unconstrained) and finally firms that use debt, but are not able to attract all the amount needed (levered constrained). We consider irreversible investments in R&D with uncertain
returns, financed through debt. We show that debt financing (with or without constraints) significantly alters the standard results in the real option literature. First, we show that leverage
distorts the investment threshold and shareholders of a levered firm tend to accelerate investment with respect to an all equity financed firm. This finding is explained by the fact that the increase
in the probability of default, which is positively correlated with leverage, might induce a potential loss of the investment option and thus reduce the value of the option to wait providing equity
holders with an incentive to speed up the investment. Second, if we introduce the financial constraint, the investment threshold is characterized by a U-shaped relation. The latter implies that the
investment threshold diminishes as the financial constraint becomes less stringent, but up to a certain minimum value. After a certain amount of leverage the firm attitude towards R&D investment
changes. The firm becomes more risk adverse, given the much higher probability of default (linked to a much higher leverage in its balance sheet).
• capital budgeting
• debt financing constraint
• real options
Entra nei temi di ricerca di 'R&D Investment timing, default and capital structure'. Insieme formano una fingerprint unica.
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Moscow International School of Physics
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How many ounces in a pint? | HireQuotient
How many ounces in a pint?
Published on July 3rd, 2024
When it comes to understanding measurements in the kitchen or in various industries, knowing how many ounces are in a pint is essential. This knowledge helps in cooking, baking, and even brewing
beer. Let's dive into the specifics of this conversion.
Understanding the Basics
1 Pint = 16 Ounces
In the United States, a pint is equal to 16 fluid ounces. This measurement is used for both liquid and dry ingredients, although there are distinctions to be aware of. Here's a breakdown:
• US Liquid Pint: One US liquid pint equals 16 fluid ounces. This is the standard measurement used for most liquid ingredients.
• US Dry Pint: A US dry pint is slightly different, measuring approximately 18.6 dry ounces. This measurement is often used for dry ingredients like blueberries or flour.
• UK Pint: In the United Kingdom, a pint is equal to 20 fluid ounces. This difference arises from the use of the imperial system.
Knowing these differences is crucial for accurate measurement, especially when following recipes from different countries.
Why the Difference in Measurements?
The variation in pint measurements between the US and the UK stems from historical differences in the systems of measurement. The US uses the customary system, while the UK follows the imperial
system. This leads to variations not only in pints but in other measurements as well. For example, a gallon in the UK is larger than a gallon in the US.
Practical Applications
Understanding how many ounces are in a pint has practical applications in everyday life:
• Cooking and Baking: Recipes often require precise measurements. Knowing that a US pint equals 16 ounces helps ensure accuracy, whether you're measuring milk, cream, or water.
• Brewing: Beer enthusiasts need to understand pint measurements, especially if they're working with recipes or instructions from different countries. In the US, a pint of beer is 16 ounces, while
in the UK, it's 20 ounces.
• Grocery Shopping: When buying items like ice cream or yogurt, it's helpful to know that a pint container holds 16 ounces.
Quick Conversion Formula
For those who need a quick reference, here’s a simple formula to convert pints to ounces:
Ounces = Pints×16
This formula applies to US liquid pints. For dry pints or UK pints, adjustments need to be made.
Conversion Chart
To make it even easier, here’s a handy conversion chart:
Pints (US) Fluid Ounces (US)
1 pint 16 ounces
2 pints 32 ounces
3 pints 48 ounces
4 pints 64 ounces
For dry ingredients:
Pints (US) Dry Ounces (US)
1 pint 18.6 ounces
2 pints 37.2 ounces
3 pints 55.8 ounces
4 pints 74.4 ounces
By understanding these basics and utilizing our conversion chart, you can confidently measure both liquid and dry ingredients accurately, ensuring your recipes turn out perfectly every time.
What is a Pint
Understanding the concept of a pint is essential for anyone working with measurements, whether in cooking, baking, or any other practical application. A pint is a unit of volume commonly used in the
United States and the United Kingdom, but it can vary depending on the system of measurement being used. Let's delve into the details of what defines a pint and how it differs across various
The Basics of a Pint
A pint is a unit of volume or capacity in both the imperial and United States customary measurement systems. The symbol for pint is "pt." One of the most common uses of the pint measurement is in the
food and beverage industry, where it is used to measure liquids and dry goods.
Types of Pints
US Liquid Pint:
• In the United States, a liquid pint equals 16 fluid ounces. This is the standard measure for liquid ingredients like milk, water, and beverages.
• Example: A pint of beer in the US is 16 ounces.
US Dry Pint:
• The US also uses a dry pint, which is a measure for dry ingredients. A dry pint is approximately 18.6 ounces. This measurement is less common but is still used for items like berries or flour.
• Example: A pint of blueberries weighs about 18.6 ounces.
UK Pint:
• In the United Kingdom, a pint is part of the imperial system and is larger than the US pint, equaling 20 fluid ounces. This difference is important to note when using UK-based recipes or buying
beverages in the UK.
• Example: A pint of beer in the UK is 20 ounces.
Historical Context
The term "pint" originates from the Old French word "pinte" and the Latin "pincta," which referred to a painted mark on a container to show its capacity. The pint has been used for centuries, and its
exact volume has varied historically by country and context.
Practical Applications of a Pint
Cooking and Baking:
• When following a recipe, it’s crucial to use the correct pint measurement to ensure accuracy. Using a UK pint instead of a US pint can lead to a difference in the final product due to the
additional 4 ounces in the UK pint.
Brewing and Beverages:
• Pints are commonly used to measure beverages, particularly beer. In the US, a standard pint glass holds 16 ounces, whereas in the UK, a pint glass holds 20 ounces. This distinction is important
for bartenders and beer enthusiasts who need to serve and consume the correct amount.
Grocery Shopping:
• Products like ice cream, yogurt, and even certain fruits are often sold in pint-sized containers. Knowing the difference between a liquid and dry pint can help consumers make better purchasing
Conversion and Measurement
To accurately convert pints to ounces, remember the following:
• US Liquid Pint: Multiply the number of pints by 16 to get the equivalent ounces.
• US Dry Pint: Multiply the number of pints by 18.6 to get the equivalent ounces.
• UK Pint: Multiply the number of pints by 20 to get the equivalent ounces.
Quick Conversion Example:
• If you have 2 US liquid pints, you have 2×16=322 \times 16 = 322×16=32 fluid ounces.
• If you have 2 UK pints, you have 2×20=402 \times 20 = 402×20=40 fluid ounces.
Understanding what a pint is and its different types is fundamental for precise measurements in various contexts. Whether you're following a recipe, serving drinks, or buying groceries, knowing the
difference between US and UK pints, as well as liquid and dry pints, ensures you achieve the desired results every time.
What is an Ounce
Understanding the measurement units used in cooking, baking, and other practical applications is essential for accuracy and success. One such unit is the ounce. Knowing what an ounce is and how it is
used in different contexts will help you make precise measurements, ensuring your recipes turn out perfectly every time. Let's explore the details of what an ounce is and its various uses.
Definition of an Ounce
An ounce is a unit of weight or volume used in both the imperial and United States customary measurement systems. The symbol for ounce is "oz." There are two main types of ounces: fluid ounces and
dry ounces, each serving different purposes.
Types of Ounces
Fluid Ounces:
• Definition: A fluid ounce is a unit of volume commonly used to measure liquids.
• Conversion: In the US, 1 fluid ounce equals approximately 29.57 milliliters.
• Usage: Fluid ounces are used to measure beverages, cooking liquids, and other fluid substances. For example, a standard cup of coffee contains about 8 fluid ounces.
Dry Ounces:
• Definition: A dry ounce is a unit of weight used to measure dry ingredients.
• Conversion: In the US, 1 dry ounce equals approximately 28.35 grams.
• Usage: Dry ounces are used to measure ingredients like flour, sugar, and spices. For instance, a slice of bread typically weighs around 1 ounce.
Historical Context
The term "ounce" originates from the Latin word "uncia," which means a twelfth part. Historically, an ounce was a unit of weight used in various systems, including Roman and medieval English. Over
time, the ounce became standardized in both the imperial and US customary systems, with slight variations in measurement.
Practical Applications of Ounces
Cooking and Baking:
• Precision in Recipes: Knowing how many ounces are in a pint or other measurements is crucial for following recipes accurately. This ensures consistency and success in cooking and baking.
• Common Conversions: For example, 1 cup of flour is approximately 4.5 ounces, and 1 cup of sugar is around 7 ounces. These conversions help in measuring ingredients correctly.
Nutrition and Health:
• Serving Sizes: Nutritional information often uses ounces to describe serving sizes. For example, a serving of meat or fish is typically 3 ounces, while a serving of cheese might be 1 ounce.
• Caloric Measurement: Ounces are also used to measure calories and macronutrients in food, aiding in maintaining a balanced diet.
Retail and Grocery Shopping:
• Product Packaging: Many food items are packaged and sold in ounces. For instance, a pint of ice cream is labeled as 16 ounces, and a can of soda is usually 12 ounces.
• Bulk Purchases: Understanding ounce measurements helps consumers make informed decisions when buying bulk items, ensuring they get the best value for their money.
Conversion and Measurement
To accurately convert between different units involving ounces, it’s helpful to use a standard conversion formula. Here are some common conversions:
• Fluid Ounces to Milliliters: Multiply the number of fluid ounces by 29.57 to get the equivalent milliliters.
• Dry Ounces to Grams: Multiply the number of dry ounces by 28.35 to get the equivalent grams.
Quick Conversion Example:
• If you have 8 fluid ounces of water, you have
8 × 29.57 = 236.56 milliliters.
• If you have 5 dry ounces of flour, you have
5 × 28.35 = 141.755 grams.
An ounce is a versatile unit of measurement used in many aspects of daily life, from cooking and baking to nutrition and shopping. Understanding the differences between fluid ounces and dry ounces,
as well as their conversions, is essential for accuracy in measurements. Whether you're following a recipe, managing your diet, or making purchases, knowing how to measure in ounces will ensure you
achieve the best results.
How to Calculate Ounces in a Pint
Accurate measurement is essential in various aspects of daily life, from cooking and baking to brewing and shopping. Knowing how to calculate the number of ounces in a pint can help ensure precision
in your tasks. Let's break down the process and understand the nuances of converting pints to ounces.
The Basic Formula
In the United States, the conversion from pints to ounces is straightforward:
Ounces=Pints × 16
This formula is based on the fact that one US liquid pint is equal to 16 fluid ounces. This conversion is widely used in recipes, nutrition labels, and product packaging.
Step-by-Step Guide to Calculating Ounces in a Pint
Identify the Type of Pint:
• US Liquid Pint: Commonly used in cooking, baking, and beverage measurements.
• US Dry Pint: Used for dry ingredients like grains, fruits, and vegetables.
• UK Pint: Larger than the US pint, primarily used in the United Kingdom.
Use the Correct Conversion Factor:
• For a US liquid pint, multiply the number of pints by 16 to get the equivalent fluid ounces.
• For a US dry pint, multiply the number of pints by approximately 18.6 to get the equivalent dry ounces.
• For a UK pint, multiply the number of pints by 20 to get the equivalent fluid ounces.
Apply the Formula:
• Example 1: Converting 2 US liquid pints to ounces:
2 pints × 16 ounces per pint=32 ounces
• Example 2: Converting 1.5 UK pints to ounces:
1.5 pints × 20 ounces per pint = 30 ounces
• Example 3: Converting 3 US dry pints to ounces:
3 pints × 18.6 ounces per pint=55.8 ounces
Practical Examples
Cooking and Baking:
• Liquid Ingredients: If a recipe calls for 1 pint of milk, you need 16 fluid ounces of milk.
• Dry Ingredients: If you need a pint of strawberries, it will be approximately 18.6 dry ounces.
Brewing and Beverages:
• Beer Measurement: In the US, a pint of beer is 16 ounces, while in the UK, it's 20 ounces. This distinction is crucial for brewers and bartenders.
Grocery Shopping:
• Packaged Goods: Understanding these conversions helps when buying items sold by pint. For instance, a pint of ice cream in the US is 16 ounces.
Conversion Chart for Quick Reference
Pints (US Liquid) Fluid Ounces (US)
1 pint 16 ounces
2 pints 32 ounces
3 pints 48 ounces
4 pints 64 ounces
Pints (US Dry) Dry Ounces (US)
1 pint 18.6 ounces
2 pints 37.2 ounces
3 pints 55.8 ounces
4 pints 74.4 ounces
Pints (UK) Fluid Ounces (UK)
1 pint 20 ounces
2 pints 40 ounces
3 pints 60 ounces
4 pints 80 ounces
Additional Tips for Accurate Measurement
1. Use Measuring Tools: Always use appropriate measuring tools like liquid measuring cups for liquids and dry measuring cups for dry ingredients.
2. Level Off Ingredients: When measuring dry ingredients, ensure to level off the top for an accurate measure.
3. Check Conversions: Double-check conversions, especially when using recipes from different countries or regions.
Calculating ounces in a pint is a fundamental skill that ensures precision in various tasks, from cooking to grocery shopping. By understanding the differences between US liquid pints, US dry pints,
and UK pints, and using the correct conversion formulas, you can achieve accurate measurements every time. This knowledge is invaluable for anyone looking to perfect their culinary skills or make
informed purchasing decisions.
Conversion Chart
Having a reliable conversion chart at your fingertips can be incredibly helpful in the kitchen, for brewing, or in any scenario where precise measurements are essential. Understanding how to convert
pints to ounces, whether you’re dealing with liquid or dry ingredients, ensures accuracy and consistency in your tasks. This section provides detailed conversion charts that you can refer to whenever
you need to convert pints to ounces.
Liquid Pints to Fluid Ounces Conversion Chart
For most everyday purposes in the United States, the conversion of pints to fluid ounces is straightforward: one US liquid pint equals 16 fluid ounces. This conversion is crucial for measuring
liquids accurately in recipes, beverages, and more.
Pints (US Liquid) Fluid Ounces (US)
1 pint 16 ounces
2 pints 32 ounces
3 pints 48 ounces
4 pints 64 ounces
5 pints 80 ounces
6 pints 96 ounces
7 pints 112 ounces
8 pints 128 ounces
9 pints 144 ounces
10 pints 160 ounces
This chart helps quickly convert larger quantities, making it easier to scale recipes up or down.
Dry Pints to Dry Ounces Conversion Chart
Dry ingredients require a different conversion. In the United States, one dry pint is approximately 18.6 ounces. This is important for measuring dry goods such as fruits, grains, and other solids.
Pints (US Dry) Dry Ounces (US)
1 pint 18.6 ounces
2 pints 37.2 ounces
3 pints 55.8 ounces
4 pints 74.4 ounces
5 pints 93 ounces
6 pints 111.6 ounces
7 pints 130.2 ounces
8 pints 148.8 ounces
9 pints 167.4 ounces
10 pints 186 ounces
Using this chart, you can ensure accuracy in recipes that call for dry ingredients.
UK Pints to Fluid Ounces Conversion Chart
For those using recipes or measurements from the United Kingdom, note that one UK pint is equivalent to 20 fluid ounces. This is a critical difference from the US pint and must be accounted for when
converting measurements.
Pints (UK) Fluid Ounces (UK)
1 pint 20 ounces
2 pints 40 ounces
3 pints 60 ounces
4 pints 80 ounces
5 pints 100 ounces
6 pints 120 ounces
7 pints 140 ounces
8 pints 160 ounces
9 pints 180 ounces
10 pints 200 ounces
Practical Applications
Cooking and Baking: Using the correct conversion ensures that recipes turn out as intended. For example, if a UK recipe calls for a pint of milk, you should use 20 fluid ounces if you're converting
to US measurements.
Brewing and Beverages: In the brewing industry, using the correct pint measurement is crucial. A pint of beer in the US is 16 ounces, whereas in the UK, it’s 20 ounces.
Everyday Measurements: Whether you’re buying groceries or following a recipe, knowing these conversions helps in making informed decisions. For instance, if you purchase a pint of blueberries, you
now know it’s roughly 18.6 dry ounces.
Conversion Formula Recap
To summarize the conversions:
• US Liquid Pint to Fluid Ounces: Multiply the number of pints by 16.
• US Dry Pint to Dry Ounces: Multiply the number of pints by 18.6.
• UK Pint to Fluid Ounces: Multiply the number of pints by 20.
Having a comprehensive conversion chart is invaluable for anyone who needs to convert between pints and ounces. Whether you are working with liquids or dry ingredients, or you are dealing with US or
UK measurements, this chart will ensure you get the conversions right every time. Accurate measurements lead to better results in cooking, baking, brewing, and beyond.
This segment aims to provide a detailed and user-friendly conversion chart, ensuring readers can easily convert pints to ounces in various contexts.
Practical Applications
Understanding how many ounces are in a pint is not just a theoretical exercise—it has numerous practical applications in everyday life. From cooking and baking to grocery shopping and brewing, this
knowledge is indispensable for accuracy and efficiency. Let's explore some real-world scenarios where knowing the conversion between pints and ounces can make a significant difference.
Cooking and Baking
Recipe Accuracy: When following a recipe, precise measurements are crucial for achieving the desired outcome. Many recipes, especially those from the United States, use pints and ounces to specify
ingredient quantities. Knowing that one US pint equals 16 fluid ounces ensures that you add the correct amount of liquids, whether you're making a soup, sauce, or beverage.
Baking Precision: Baking, in particular, requires exact measurements to ensure proper chemical reactions between ingredients. For instance, if a cake recipe calls for a pint of milk, you need to
measure out 16 fluid ounces to ensure the cake's texture and taste are just right. Similarly, if a recipe requires a pint of blueberries, knowing that this equals approximately 18.6 dry ounces helps
you measure the exact quantity needed.
Grocery Shopping
Product Quantities: Many packaged goods are sold in pint-sized containers. For example, a pint of ice cream in the US is typically 16 ounces. Understanding this conversion helps you compare prices
and quantities more effectively, ensuring you get the best value for your money.
Bulk Purchases: When buying bulk items like fruits, vegetables, or grains, knowing the dry pint measurement (18.6 ounces) helps you make informed decisions. If you're purchasing a pint of
strawberries, you'll know to expect about 18.6 ounces, which aids in planning and budgeting.
Brewing and Beverages
Beer and Alcohol: For beer enthusiasts and brewers, understanding pint measurements is essential. In the United States, a standard pint of beer is 16 ounces, while in the United Kingdom, it's 20
ounces. This difference is important for those who enjoy brewing their own beer or serving it. Accurate measurements ensure consistency and quality in the final product.
Cocktails and Mixology: In mixology, precise measurements of ingredients are crucial for creating balanced cocktails. Knowing that a pint of a liquid ingredient equals 16 fluid ounces helps
bartenders and cocktail enthusiasts measure ingredients accurately, ensuring the perfect blend of flavors.
Household and DIY Projects
Measuring Liquids: In various household tasks, from DIY projects to gardening, measuring liquids accurately is often necessary. For example, if a gardening guide suggests adding a pint of water to
your plants, you’ll know to measure out 16 fluid ounces.
Home Brewing: For those who brew their own beverages at home, understanding the conversion between pints and ounces is crucial. Whether you’re making kombucha, beer, or cider, precise measurements
ensure the quality and safety of your homemade brews.
Educational Purposes
Teaching Measurements: Educators can use the concept of pints and ounces to teach measurement conversions to students. Understanding these conversions helps students grasp the importance of accurate
measurements in various fields, including science, cooking, and engineering.
Scientific Experiments: In scientific experiments, precise measurements are vital for replicable results. Knowing how to convert pints to ounces ensures that liquid measurements in experiments are
accurate, which is essential for valid and reliable outcomes.
From the kitchen to the grocery store, from the brewery to the classroom, understanding how many ounces are in a pint has numerous practical applications. Whether you're cooking, baking, brewing, or
shopping, this knowledge helps you achieve accuracy and efficiency in your tasks. By mastering these conversions, you ensure that your measurements are precise, leading to better results in all your
FAQ: How many ounces in a pint?
How many ounces in a pint?
There are 16 fluid ounces in a US pint.
How many ounces are in a pint?
In the US, a pint contains 16 fluid ounces.
How many fluid ounces in a pint?
A US liquid pint has 16 fluid ounces.
How many ounces in a dry pint?
A US dry pint is approximately 18.6 ounces.
How many ounces is in a pint?
A pint in the US equals 16 fluid ounces.
How many fluid ounces are in a pint?
There are 16 fluid ounces in a US pint.
How many ounces in a half pint?
A half pint is 8 fluid ounces.
How many ounces in a pint of blueberries?
A pint of blueberries is roughly 18.6 ounces (dry).
How many ounces in a pint glass?
A standard US pint glass holds 16 fluid ounces.
How many ounces in a pint of sour cream?
A pint of sour cream contains 16 ounces.
How many ounces in a pint (UK)?
A UK pint has 20 fluid ounces.
How many ounces in a pint of ice cream?
A pint of ice cream is 16 fluid ounces.
How many ounces in half a pint?
Half a pint equals 8 fluid ounces.
How many ounces in a pint of tomatoes?
A pint of tomatoes is approximately 18.6 dry ounces.
How many ounces in a pint of beer?
A pint of beer in the US is 16 fluid ounces.
How many ounces in a pint of water?
A pint of water equals 16 fluid ounces.
How many ounces in a dry pint of blueberries?
A dry pint of blueberries is about 18.6 ounces.
How many dry ounces in a pint?
A US dry pint is approximately 18.6 ounces.
How many ounces are there in a pint?
There are 16 fluid ounces in a US pint.
How many ounces are in a half pint?
Half a pint is 8 fluid ounces.
How many ounces in a 1/2 pint?
A 1/2 pint is 8 ounces.
How many ounces are in a pint of blueberries?
A pint of blueberries is approximately 18.6 dry ounces.
How many ounces are in a half a pint?
A half a pint contains 8 ounces.
How many ounces in a half a pint?
There are 8 ounces in a half pint.
How many fluid ounces is in a pint?
A pint in the US contains 16 fluid ounces.
How many ounces are in a pint glass?
A US pint glass holds 16 fluid ounces.
How many ounces is in a half pint?
A half pint is 8 fluid ounces.
How many ounces in a pint of strawberries?
A pint of strawberries is about 18.6 dry ounces.
How many ounces in a pint of cherry tomatoes?
A pint of cherry tomatoes is approximately 18.6 ounces.
How many ounces in a pint jar?
A pint jar holds 16 fluid ounces.
How many ounces are in a pint of sour cream?
There are 16 ounces in a pint of sour cream.
How many fl ounces in a pint?
There are 16 fluid ounces in a US pint.
How many ounces of blueberries in a pint?
A pint of blueberries is about 18.6 dry ounces.
How many liquid ounces in a pint?
A US liquid pint equals 16 ounces.
How many ounces in a pint of milk?
A pint of milk is 16 fluid ounces.
How many ounces in a pint of liquor?
A pint of liquor is 16 fluid ounces.
How many ounces in a pint of raspberries?
A pint of raspberries is approximately 18.6 dry ounces.
How many ounces in a British pint?
A British pint is 20 fluid ounces.
How many ounces of sour cream in a pint?
There are 16 ounces of sour cream in a pint.
How many ounces in a pint of alcohol?
A pint of alcohol contains 16 fluid ounces.
How many ounces in a pint and a half?
A pint and a half is 24 fluid ounces.
How many ounces in a half pint of liquor?
A half pint of liquor is 8 fluid ounces.
How many ounces are in a pint of water?
A pint of water is 16 fluid ounces.
How many ounces in a pint of vodka?
A pint of vodka is 16 fluid ounces.
How many ounces in a pint of berries?
A pint of berries is about 18.6 dry ounces.
How many liquid ounces are in a pint?
A pint has 16 liquid ounces in the US.
How many ounces in a pint of whiskey?
A pint of whiskey is 16 fluid ounces.
How many ounces is in a pint of sour cream?
A pint of sour cream contains 16 ounces.
How many solid ounces in a pint?
A US dry pint is about 18.6 ounces.
How many ounces in a dry pint of tomatoes?
A dry pint of tomatoes is approximately 18.6 ounces.
How many ounces are in a pint of beer?
A pint of beer in the US is 16 fluid ounces.
How many ounces in a pint of oil?
A pint of oil is 16 fluid ounces.
How many ounces in a UK pint?
A UK pint has 20 fluid ounces.
How many ounces are in a 1/2 pint?
A 1/2 pint is 8 fluid ounces.
How many ounces are in a pint of liquor?
A pint of liquor is 16 fluid ounces.
How many ounces in a pint of cottage cheese?
A pint of cottage cheese is 16 ounces.
How many ounces of blueberries are in a pint?
A pint of blueberries is roughly 18.6 dry ounces.
How many ounces in a pint of blackberries?
A pint of blackberries is about 18.6 dry ounces.
How many ounces in a solid pint?
A solid pint in the US is approximately 18.6 ounces.
How many fluid ounces are there in a pint?
There are 16 fluid ounces in a US pint.
How many ounces in a pint and a half?
A pint and a half equals 24 fluid ounces.
How many ounces of ice cream in a pint?
A pint of ice cream is 16 ounces.
How many ounces is in a pint of blueberries?
A pint of blueberries is about 18.6 dry ounces.
How many ounces is there in a pint?
There are 16 fluid ounces in a pint.
How many fluid ounces in a half pint?
A half pint is 8 fluid ounces.
How many ounces of cherry tomatoes in a pint?
A pint of cherry tomatoes is approximately 18.6 dry ounces.
How many ounces in a half pint of vodka?
A half pint of vodka is 8 fluid ounces.
How many ounces are in a pint jar?
A pint jar holds 16 fluid ounces.
How many ounces in a quarter pint?
A quarter pint is 4 fluid ounces.
How many ounces in a pint of heavy cream?
A pint of heavy cream contains 16 fluid ounces.
How many ounces in a cup, pint, quart, gallon?
1 cup is 8 ounces, 1 pint is 16 ounces, 1 quart is 32 ounces, and 1 gallon is 128 ounces.
How many ounces are in a pint of cherry tomatoes?
A pint of cherry tomatoes is approximately 18.6 dry ounces.
How many ounces in a pint of fruit?
A pint of fruit generally measures about 18.6 dry ounces.
How many ounces in a pint glass of beer?
A standard US pint glass of beer holds 16 fluid ounces.
How many ounces of raspberries in a pint?
A pint of raspberries is about 18.6 dry ounces.
How many ounces in a pint of grape tomatoes?
A pint of grape tomatoes is roughly 18.6 dry ounces.
How many ounces in a 1 pint?
A 1 pint in the US is 16 fluid ounces.
How many ounces of tomatoes in a pint?
A pint of tomatoes is about 18.6 dry ounces.
How many ounces in a pint solid?
A solid pint in the US is roughly 18.6 dry ounces.
How many ounces in a pint mason jar?
A pint mason jar holds 16 fluid ounces.
How many ounces in a US pint?
A US pint contains 16 fluid ounces.
How many ounces blueberries in a pint?
A pint of blueberries is about 18.6 dry ounces.
How many ounces is in a dry pint?
A dry pint in the US measures about 18.6 ounces.
How many fl ounces are in a pint?
There are 16 fluid ounces in a US pint.
How many ounces are in a pint of strawberries?
A pint of strawberries is roughly 18.6 dry ounces.
How many ounces in a beer pint?
A beer pint in the US is 16 fluid ounces.
How many ounces in a Ben and Jerry's pint?
A Ben and Jerry's pint contains 16 fluid ounces of ice cream.
Thomas M. A.
A literature-lover by design and qualification, Thomas loves exploring different aspects of software and writing about the same.
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A filter is a circuit that removes or "filters out" frequency components in a specific range. In other words, it separates the frequency spectrum of the signal into frequency components that will
pass and frequency components that will be blocked.
Let us assume that we have an audio signal composed of a perfect 5 kHz sine wave. We know what a sine wave looks like in the time domain, and in the frequency domain we can only see a frequency
“spike” of 5 kHz. Now let us suppose that we activate a 500 kHz oscillator to introduce high frequency noise into the audio signal. The signal seen on the oscilloscope is still just a sequence of
voltages, with a value at each moment, but the signal will look different because its time domain changes must now reflect the 5 kHz sine wave and high-frequency noise fluctuations. However, in the
frequency domain, sine waves and noise are separate frequency components that exist simultaneously in the one signal. Sine waves and noise occupy different parts of the signal's frequency domain
representation (as shown in the figure below), which means that we can filter out noise by directing the signal through circuits that pass low frequencies and block high frequencies.
EMI Filter Solutions' Provider: ACSOON
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