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The standard deviation can help you calculate the spread of data. There are different equations to use if are calculating the standard deviation of a sample or of a population. | https://openstax.org/books/introductory-statistics-2e/pages/2-chapter-review |
The Standard Deviation allows us to compare individual data or classes to the data set mean numerically. | https://openstax.org/books/introductory-statistics-2e/pages/2-chapter-review |
s=ââ(xâx¯)2nâ1ââ(xâx¯)2nâ1ors=ââf(xâx¯)2nâ1ââf(xâx¯)2nâ1is the formula for calculating the standard deviation of a sample. To calculate the standard deviation of a population, we would use the population mean,μ, and the formulaÏ=ââ(xâμ)2Nââ(xâμ)2NorÏ=ââf(xâμ)2... | https://openstax.org/books/introductory-statistics-2e/pages/2-chapter-review |
i=(k100)(n+1)i=(k100)(n+1) | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
wherei= the ranking or position of a data value, | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
k= the kth percentile, | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
n= total number of data. | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
Expression for finding the percentile of a data value:(x+0.5yn)(x+0.5yn)(100) | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
wherex= the number of values counting from the bottom of the data list up to but not including the data value for which you want to find the percentile, | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
y= the number of data values equal to the data value for which you want to find the percentile, | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
n= total number of data | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
μ=âfmâfμ=âfmâfWheref= interval frequencies andm= interval midpoints. | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
sx=âfm2nâx¯2sx=âfm2nâx¯2wheresx=sample standard deviationx¯= sample meansx=sample standard deviationx¯= sample mean | https://openstax.org/books/introductory-statistics-2e/pages/2-formula-review |
Box plot : a graph that gives a quick picture of the middle 50% of the data | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
First Quartile : the value that is the median of the of the lower half of the ordered data set | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Frequency : the number of times a value of the data occurs | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Frequency Polygon : looks like a line graph but uses intervals to display ranges of large amounts of data | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Frequency Table : a data representation in which grouped data is displayed along with the corresponding frequencies | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Histogram : a graphical representation inx-yform of the distribution of data in a data set;xrepresents the data andyrepresents the frequency, or relative frequency. The graph consists of contiguous rectangles. | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Interquartile Range : orIQR, is the range of the middle 50 percent of the data values; theIQRis found by subtracting the first quartile from the third quartile. | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Interval : also called a class interval; an interval represents a range of data and is used when displaying large data sets | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Mean : a number that measures the central tendency of the data; a common name for mean is 'average.' The term 'mean' is a shortened form of 'arithmetic mean.' By definition, the mean for a sample (denoted byx¯x¯) isx¯=Sum of all values in the sampleNumber of values in the samplex¯=Sum of all values in the sampleNum... | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Median : a number that separates ordered data into halves; half the values are the same number or smaller than the median and half the values are the same number or larger than the median. The median may or may not be part of the data. | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Midpoint : the mean of an interval in a frequency table | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Mode : the value that appears most frequently in a set of data | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Outlier : an observation that does not fit the rest of the data | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Paired Data Set : two data sets that have a one to one relationship so that:both data sets are the same size, andeach data point in one data set is matched with exactly one point from the other set. | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Percentile : a number that divides ordered data into hundredths; percentiles may or may not be part of the data. The median of the data is the second quartile and the 50thpercentile. The first and third quartiles are the 25thand the 75thpercentiles, respectively. | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Quartiles : the numbers that separate the data into quarters; quartiles may or may not be part of the data. The second quartile is the median of the data. | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Relative Frequency : the ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Skewed : used to describe data that is not symmetrical; when the right side of a graph looks âchopped offâ compared the left side, we say it is âskewed to the left.â When the left side of the graph looks âchopped offâ compared to the right side, we say the data is âskewed to the right.â Alternatively: w... | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Standard Deviation : a number that is equal to the square root of the variance and measures how far data values are from their mean; notation:sfor sample standard deviation and Ï for population standard deviation. | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
Variance : mean of the squared deviations from the mean, or the square of the standard deviation; for a set of data, a deviation can be represented asxâx¯x¯wherexis a value of the data andx¯x¯is the sample mean. The sample variance is equal to the sum of the squares of the deviations divided by the difference of ... | https://openstax.org/books/introductory-statistics-2e/pages/2-key-terms |
In this module we learned the basic terminology of probability. The set of all possible outcomes of an experiment is called the sample space. Events are subsets of the sample space, and they are assigned a probability that is a number between zero and one, inclusive. | https://openstax.org/books/introductory-statistics-2e/pages/3-chapter-review |
Two eventsAandBare independent if the knowledge that one occurred does not affect the chance the other occurs. If two events are not independent, then we say that they are dependent. | https://openstax.org/books/introductory-statistics-2e/pages/3-chapter-review |
In sampling with replacement, each member of a population is replaced after it is picked, so that member has the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member of a population may be chosen only once, and the events are considere... | https://openstax.org/books/introductory-statistics-2e/pages/3-chapter-review |
The multiplication rule and the addition rule are used for computing the probability ofAandB, as well as the probability ofAorBfor two given eventsA,Bdefined on the sample space. In sampling with replacement each member of a population is replaced after it is picked, so that member has the possibility of being chosen m... | https://openstax.org/books/introductory-statistics-2e/pages/3-chapter-review |
There are several tools you can use to help organize and sort data when calculating probabilities. Contingency tables help display data and are particularly useful when calculating probabilites that have multiple dependent variables. | https://openstax.org/books/introductory-statistics-2e/pages/3-chapter-review |
A tree diagram use branches to show the different outcomes of experiments and makes complex probability questions easy to visualize. | https://openstax.org/books/introductory-statistics-2e/pages/3-chapter-review |
A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample spaceStogether with circles or ovals. The circles or ovals represent events. A Venn diagram is especially helpful for visualizing the OR event, the AND event, and the complement of an eve... | https://openstax.org/books/introductory-statistics-2e/pages/3-chapter-review |
AandBare events | https://openstax.org/books/introductory-statistics-2e/pages/3-formula-review |
P(S) = 1 whereSis the sample space | https://openstax.org/books/introductory-statistics-2e/pages/3-formula-review |
0 â¤P(A) ⤠1 | https://openstax.org/books/introductory-statistics-2e/pages/3-formula-review |
P(A|B) =P(AANDB)P(B)P(AANDB)P(B) | https://openstax.org/books/introductory-statistics-2e/pages/3-formula-review |
IfAandBare independent,P(AANDB) =P(A)P(B),P(A|B) =P(A) andP(B|A) =P(B). | https://openstax.org/books/introductory-statistics-2e/pages/3-formula-review |
IfAandBare mutually exclusive,P(AORB) =P(A) +P(B) andP(AANDB) = 0. | https://openstax.org/books/introductory-statistics-2e/pages/3-formula-review |
The multiplication rule:P(AANDB) =P(A|B)P(B) | https://openstax.org/books/introductory-statistics-2e/pages/3-formula-review |
The addition rule:P(AORB) =P(A) +P(B) -P(AANDB) | https://openstax.org/books/introductory-statistics-2e/pages/3-formula-review |
AND Event : An outcome is in the eventAANDBif the outcome is in bothAANDBat the same time. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Complement Event : The complement of eventAconsists of all outcomes that are NOT inA. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Conditional Probability : the likelihood that an event will occur given that another event has already occurred | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Conditional Probability ofAGIVENB : P(A|B) is the probability that eventAwill occur given that the eventBhas already occurred. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Conditional Probability of One Event Given Another Event : P(A|B) is the probability that eventAwill occur given that the eventBhas already occurred. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
contingency table : the method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; the table provides an easy way to calculate conditional probabilities. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Dependent Events : If two events are NOT independent, then we say that they are dependent. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Equally Likely : Each outcome of an experiment has the same probability. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Event : a subset of the set of all outcomes of an experiment; the set of all outcomes of an experiment is called asample spaceand is usually denoted byS. An event is an arbitrary subset inS. It can contain one outcome, two outcomes, no outcomes (empty subset), the entire sample space, and the like. Standard notations f... | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Experiment : a planned activity carried out under controlled conditions | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Independent Events : The occurrence of one event has no effect on the probability of the occurrence of another event. EventsAandBare independent if one of the following is true:P(A|B) =P(A)P(B|A) =P(B)P(AANDB) =P(A)P(B) | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Mutually Exclusive : Two events are mutually exclusive if the probability that they both happen at the same time is zero. If eventsAandBare mutually exclusive, thenP(AANDB) = 0. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Or Event : An outcome is in the eventAORBif the outcome is inAor is inBor is in bothAandB. | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Outcome : a particular result of an experiment | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Probability : a number between zero and one, inclusive, that gives the likelihood that a specific event will occur; the foundation of statistics is given by the following 3 axioms (by A.N. Kolmogorov, 1930âs): LetSdenote the sample space andAandBare two events inS. Then:0 â¤P(A) ⤠1IfAandBare any two mutually excl... | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Sample Space : the set of all possible outcomes of an experiment | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Tree Diagram : the useful visual representation of a sample space and events in the form of a âtreeâ with branches marked by possible outcomes together with associated probabilities (frequencies, relative frequencies) | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
Venn Diagram : the visual representation of a sample space and events in the form of circles or ovals showing their intersections | https://openstax.org/books/introductory-statistics-2e/pages/3-key-terms |
The characteristics of a probability distribution function (PDF) for a discrete random variable are as follows: | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
Each probability is between zero and one, inclusive (inclusivemeans to include zero and one). | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
The sum of the probabilities is one. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
The expected value, or mean, of a discrete random variable predicts the long-term results of a statistical experiment that has been repeated many times. The standard deviation of a probability distribution is used to measure the variability of possible outcomes. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
A statistical experiment can be classified as a binomial experiment if the following conditions are met: | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
There are a fixed number of trials,n. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
There are only two possible outcomes, called "success" and, "failure" for each trial. The letterpdenotes the probability of a success on one trial andqdenotes the probability of a failure on one trial. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
Thentrials are independent and are repeated using identical conditions. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
The outcomes of a binomial experiment fit a binomial probability distribution. The random variableX= the number of successes obtained in thenindependent trials. The mean ofXcan be calculated using the formulaμ=np, and the standard deviation is given by the formula Ï =npqnpq. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
There are three characteristics of a geometric experiment: | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
There are one or more Bernoulli trials with all failures except the last one, which is a success. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
In theory, the number of trials could go on forever. There must be at least one trial. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
The probability,p, of a success and the probability,q, of a failure are the same for each trial. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
In a geometric experiment, define the discrete random variableXas the number of independent trials until the first success. We say that X has a geometric distribution and writeX~G(p) wherepis the probability of success in a single trial. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
The mean of the geometric distributionX~G(p) isμ=1p1pand the standard deviation isÏ(1âp)p2Ï(1âp)p2=1p(1pâ1)1p(1pâ1). | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
Ahypergeometric experimentis a statistical experiment with the following properties: | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
You take samples from two groups. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
You are concerned with a group of interest, called the first group. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
You sample without replacement from the combined groups. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
Each pick is not independent, since sampling is without replacement. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
You are not dealing with Bernoulli Trials. | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
The outcomes of a hypergeometric experiment fit a hypergeometric probability distribution. The random variableX= the number of items from the group of interest. The distribution ofXis denotedX~H(r,b,n), wherer= the size of the group of interest (first group),b= the size of the second group, andn= the size of the chosen... | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
APoisson probability distributionof a discrete random variable gives the probability of a number of events occurring in a fixed interval of time or space, if these events happen at a known average rate and independently of the time since the last event. The Poisson distribution may be used to approximate the binomial, ... | https://openstax.org/books/introductory-statistics-2e/pages/4-chapter-review |
Mean or Expected Value:μ=ââxâXxP(x)μ=ââxâXxP(x) | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
Standard Deviation:Ï=ââxâX(xâμ)2P(x)Ï=ââxâX(xâμ)2P(x) | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
X~B(n,p) means that the discrete random variableXhas a binomial probability distribution withntrials and probability of successp. | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
X= the number of successes innindependent trials | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
n= the number of independent trials | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
Xtakes on the valuesx= 0, 1, 2, 3, ...,n | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
p= the probability of a success for any trial | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
q= the probability of a failure for any trial | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
p+q= 1 | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
q= 1 âp | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
The mean ofXisμ=np. The standard deviation ofXisÏ=npqnpq. | https://openstax.org/books/introductory-statistics-2e/pages/4-formula-review |
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