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93 cosine, 345 definition of, 94 finding, 97 graph of, 95 Horizontal Line Test, 96 sine, 343, 345 tangent, 345 Inverse of a matrix, 602 finding an, 604 Inverse properties of logarithms, 230 333200_Index_SE.qxd 12/8/05 11:32 AM Page A216 A216 Index of natural logarithms, 234 of trigonometric functions, 347 Inverse trig... |
of-base formula, 239 natural, properties of, 234, 240, 278 inverse, 234 one-to-one, 234 power, 240, 278 product, 240, 278 quotient, 240, 278 properties of, 230, 240, 278 inverse, 230 one-to-one, 230 power, 240, 278 product, 240, 278 quotient, 240, 278 Logarithmic equation, solving, 246 Logarithmic function, 229 with ba... |
A7 of matrices, 592 scalar, 588 nth term of an arithmetic sequence, 654 recursion form, 654 of a geometric sequence, 664 of a sequence, finding a formula for, 678 Multiplicative identity of a real number, Number(s) A6 Multiplicative inverse, A5 for a matrix, 602 of a real number, A6 Multiplicity, 143 Multiplier effect... |
problem, 552 Optimization, 552 Order of a matrix, 572 on the real number line, A2 Ordered pair, 2 Ordered triple, 519 Orientation of a curve, 772 Origin, 2 of polar coordinate system, 779 of the real number line, A1 Index A217 symmetry, 18 Orthogonal vectors, 462 Outcome, 701 P Parabola, 128, 736, 793 axis of, 129, 73... |
ucible, A26 leading coefficient of, A23 like terms, A24 long division of, 153 prime, A26 prime factor, 174 standard form of, A23 synthetic division, 156 test intervals for, 144 Polynomial function, 128 real zeros of, 143 standard form, 142 test intervals, 197 of x with degree n, 128 Position equation, 525 Positive angl... |
completing the square, A49 by extracting square roots, A49 by factoring, A49 using Quadratic Formula, A49 using Square Root Principle, A49 Quadratic Formula, A49 Quadratic function, 128 standard form, 131 Quick tests for symmetry in polar coordinates, 787 Quotient difference, 46 of functions, 84 of two complex numbers... |
Relative minimum, 58 Remainder Theorem, 157, 213 Repeated zero, 143 Representation of matrices, 587 Resultant of vector addition, 449 Right triangle definitions of trigonometric functions, 301 hypotenuse, 301 opposite side, 301 right side of, 301 solving, 306 Rigid transformation, 78 Root(s) of a complex number, 475, ... |
of an absolute value inequality, A63 of an equation, 14, A46 extraneous, A48, A54 of an inequality, 541, A60 of a system of equations, 496 graphical interpretations, 510 of a system of inequalities, 543 Solution point, 14 Solution set, A60 Solving an absolute value inequality, A63 an equation, A46 exponential and loga... |
nth partial, 647 of powers of integers, 679 properties of, 646, 722 of square differences, 104 Sum and difference formulas, 400, 424 Sum and difference of same terms, A25 Sum or difference of two cubes, A27 Summary of a sequence, 642 variable, A5 Terminal point, 447 Terminal side of an angle, 282 Test of equations of ... |
, 347 key points, 322 intercepts, 322 maximum points, 322 minimum points, 322 product of, 407 reflection of, 324 right triangle definitions of, 301 secant, 295, 301 sine, 295, 301 square of, 407 tangent, 295, 301 unit circle definitions of, 295 Trigonometric identities cofunction identities, 374 even/odd identities, 37... |
angle, 282 of an ellipse, 744 Index A221 of a hyperbola, 753 of a parabola, 129, 133, 736 Vertical asymptote, 185 Vertical components of v, 452 Vertical line, 33 Vertical Line Test, 55 Vertical shift, 74 Vertical shrink, 78 Vertical stretch, 78 Volume, common formulas for, 7 W With replacement, 691 Without replacement... |
sc 2 u tan u u csc u u sec u cotu cot u secu sec u cscu csc u Sum and Difference Formulas sinu ± v sin u cos v ± cos u sin v cosu ± v cos u cos v sin u sin v tanu ± v tan u ± tan v 1 tan u tan v Double-Angle Formulas sin 2u 2 sin u cos u cos 2u cos2 u sin2 u tan 2u 2 tan u 1 tan2 u 2 cos2 u 1 1 2 sin2 u 2 Power-Reducin... |
a b Circle: Area r 2 Circumference 2r Sector of Circle: r2 2 Area s r in radians Circular Ring: Area R2 r2 2pw p average radius, w width of ring 333201_AP_BES.qxd 12/5/05 11:45 AM Page ES1 Linear Function f x mx b y (0, b) ( m( b −, 0 ( m( b −, 0 x f(x) = mx + b, m > 0 f(x) = mx + b, m < 0 GRAPHS OF PARENT FUNCTIONS A... |
for a < 0 for a < 0 a > 0, a < 0, relative maximum or vertex: 0, 0 x x 333201_AP_BES.qxd 12/5/05 11:45 AM Page ES2 Rational (Reciprocal) Function fx 1 x Exponential Function Logarithmic Function fx ax, a > 0, a 1 fx loga x, a > 0, a 1 y 3 2 1 f(x) = 1 x −1 1 2 3 x y f(x) = ax f(x) = a−x (0, 1) y 1 f(x) = loga x (1, 0)... |
x) = sec x = 1 cos x 3 2 1 3 2 f(x) = cot x = 1 tan x y 3 2 1 − π x π 2π 3π 2π 2π −2 −3 x n, 1 1, 2 Domain: all Range: Period: No intercepts Vertical asymptotes: Odd function Origin symmetry x n Domain: all x n 2, 1 1, Range: 2 Period: y-intercept: Vertical asymptotes: 0, 1 x n 2 Even function y-axis symmetry x n Domai... |
____ 5. Variable ____ 6. Data ____ a) all students who attended the high school last year b) the cumulative GPA of one student who graduated from the high school last year c) 3.65, 2.80, 1.50, 3.90 d) a group of students who graduated from the high school last year, randomly selected e) the average cumulative GPA of st... |
all medical doctors who have been involved in one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit. Solution 1.4 The population is all medical doctors listed in the professional ... |
are examples of quantitative data. Quantitative data may be either discrete or continuous. All data that are the result of counting are called quantitative discrete data. These data take on only certain numerical values. If you count the number of phone calls you receive for each day of the week, you might get values ... |
), four different kinds of vegetable (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies). Name data sets that are quantitative discrete, quantitative continuous, and qualitative. Solution 1.7 A possible solution • One example of a quantita... |
collects information about the classification of her students as freshmen, sophomores, juniors, or seniors. The data she collects are summarized in the pie chart Figure 1.2. What type of data does this graph show? Figure 1.3 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 1 | Sa... |
and bar graphs. In a pie chart, categories of data are shown by wedges in a circle that represent the percent of individuals/items in each category. We use pie charts when we want to show parts of a whole. In a bar graph, the length of the bar for each category represents the number or percent of individuals in each c... |
1%.6% 1.0% 24.5% 22,044 out of 24,382 90.4% out of 100% Table 1.4 Ethnicity of Students at De Anza College Fall Term 2007 (Census Day) This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 1 | Sampling and Data 17 Figure 1.8 The following graph is the same as the previous graph but the... |
frequency distribution tables. Marginal distributions may be given as a fraction or decimal: For example, the total for men could be given as.6 or 3/5 since 30 / 50 =.6 = 3 / 5. Marginal distributions require bivariate data and only focus on one of the variables represented in the table. In other words, the reason 20 ... |
for your audience to ask questions and be prepared to answer them. Example 1.11 Suppose the guidance counselors at De Anza and Foothill need to make an oral presentation of the student data presented in Figures 1.5 and 1.6. Under what context should they choose to display the pie graph? When might they choose the bar ... |
names in a hat, shake the hat, close her eyes, and pick out three names. A more technological way is for Lisa to first list the last names of the members of her class together with a two-digit number, as in Table 1.7. ID Name ID Name ID Name 00 01 02 03 Anselmo Bautista Bayani 11 12 13 King Legeny Lisa 22 23 24 Roquer... |
1.7) The random numbers.94360 and.99832 do not contain appropriate two digit numbers. However the third random number,.14669, contains 14 (the fourth random number also contains 14), the fifth random number contains 05, and the seventh random number contains 04. The two-digit number 14 corresponds to Lundquist, 05 cor... |
of the four classes with those numbers are the cluster sample. So, unlike a stratified example, a cluster sample may not contain an equal number of randomly chosen students from each class. A type of sampling that is non-random is convenience sampling. Convenience sampling involves using results that are readily avail... |
, such as internet surveys, are often unreliable. • Sample size issues—: Samples that are too small may be unreliable. Larger samples are better, if possible. In some situations, having small samples is unavoidable and can still be used to draw conclusions. Examples include crash testing cars or medical testing for rar... |
, survey 100 hospitals across the state using simple random sampling. Example 1.12 A study is done to determine the average tuition that private high school students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the fall semester. What is the type of sampling in ea... |
these numbers. Record the three quiz scores in column one that correspond to these three numbers. d. Repeat for columns two through six. e. These 18 quiz scores are a stratified sample. 2. Create a cluster sample by picking two of the columns. Use the column numbers: one through six. a. Press MATH and arrow over to th... |
generate 50 random numbers and then picks students whose names correspond to the numbers. f. A student interviews classmates in his algebra class to determine how many pairs of jeans a student owns, on average. Solution 1.13 a. stratified b. cluster c. stratified d. systematic e. simple random f. convenience 1.13 Dete... |
second sample is a group of senior citizens who are, more than likely, taking courses for health and interest. The amount of money they spend on books is probably much less than the average parttime student. Both samples are biased. Also, in both cases, not all students have a chance to be in either sample. b. Since t... |
cans of beverage may contain more or less than 16 ounces of liquid. In one study, eight 16 ounce cans were measured and produced the following amount (in ounces) of beverage: 15.8, 16.1, 15.2, 14.8, 15.8, 15.9, 16.0, 15.5. Measurements of the amount of beverage in a 16-ounce can may vary because different people make ... |
called the number of observations) is important. The examples you have seen in this book so far have been small. Samples of only a few hundred observations, or even smaller, are sufficient for many purposes. In polling, samples that are from 1,200–1,500 observations are considered large enough and good enough if the s... |
content/col30309/1.8 Chapter 1 | Sampling and Data 29 is more helpful to leave an answer as an unreduced fraction. Levels of Measurement The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statis... |
°C exist and are colder than 0. Interval level data can be used in calculations, but one type of comparison cannot be done. 80 °C is not four times as hot as 20 °C (nor is 80 °F four times as hot as 20 °F). There is no meaning to the ratio of 80 to 20 (or four to one). Data that is measured using the ratio scale takes... |
or.15 or.30 or.10 or.05 3 20 5 20 3 20 6 20 2 20 1 20 Table 1.13 Frequency Table of Student Work Hours with Relative Frequencies The sum of the values in the relative frequency column of Table 1.13 is 20 20, or 1. Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumul... |
95 5 3 15 40 17 12 7 1 5 100 3 100 15 100 40 100 17 100 12 100 7 100 1 100 =.05 =.03 =.15 =.40 =.17 =.12 =.07 =.01 CUMULATIVE RELATIVE FREQUENCY.05.05 +.03 =.08.08 +.15 =.23.23 +.40 =.63.63 +.17 =.80.80 +.12 =.92.92 +.07 =.99.99 +.01 = 1.00 Total = 100 Total = 1.00 Table 1.15 Frequency Table of Soccer Player Height 32 ... |
. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 1 | Sampling and Data 33 1.15 Table 1.16 shows the amount, in inches, of annual rainfall in a sample of towns. Rainfall (Inches) Frequency Relative Frequency Cumulative Relative Frequency 2.95–4.97 4.97–6.99 6.99–9.01 9.01–11.03 1... |
relative frequency for the current row. Solution 1.17 a. 29 percent b. 36 percent c. 77 percent d. 87 e. quantitative continuous f. get rosters from each team and choose a simple random sample from each 1.17 From Table 1.16, find the number of towns that have rainfall between 2.95 and 9.01 inches. In your class, have ... |
18, not 19. Not all cumulative relative frequencies are correct. b. False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read 1052, 01579, 02105, 03684, 04737, 06316, 07368, 07895, 08421, 09474, 1.0000. c. d. 5 19 7 19, 12 19, 7 19 1.18 Tabl... |
2000 37,526 2001 37,862 2002 38,491 2003 38,477 Table 1.19 2004 38,444 2005 39,252 2006 38,648 2007 37,435 2008 34,172 2009 30,862 2010 30,296 2011 29,757 Total 653,782 Answer the following questions: a. What is the frequency of deaths measured from 2000 through 2004? b. What percentage of deaths occurred after 2006? ... |
among the groups. At this point the only difference between groups is the one imposed by the researcher. Different outcomes measured in the response variable, therefore, must be a direct result of the different treatments. In this way, an experiment can prove a cause-and-effect connection between the explanatory and r... |
surveys may be used. In an observational study, the researcher does not directly manipulate the independent variable. Instead, he or she takes recordings and measurements of naturally occurring phenomena. By sorting these data into control and experimental conditions, the relationship between the dependent and indepen... |
use blinding in this study? Solution 1.21 a. The explanatory variable is scent, and the response variable is the time it takes to complete the maze. b. There are two treatments: a floral-scented mask and an unscented mask. c. All subjects experienced both treatments. The order of treatments was randomly assigned so th... |
at Tilburg University in the Netherlands. Over the past two years, an extensive investigation involving three universities where Stapel has worked concluded that the psychologist is guilty of fraud on a colossal scale. Falsified data taints over 55 papers he authored and 10 Ph.D. dissertations that he supervised. Stap... |
the safety of all human subjects. For this reason, research institutions establish oversight committees known as Institutional Review Boards (IRB). All planned studies must be approved in advance by the IRB. Key protections that are mandated by law include the following: • Risks to participants must be minimized and r... |
ing retractions of study articles that have been proven fraudulent. A quick glance will show that the misuse of statistics is a bigger problem than most people realize. Vigilance against fraud requires knowledge. Learning the basic theory of statistics will empower you to analyze statistical studies critically. Example... |
as much as or more than Brand Y.” 1.5 | Data Collection Experiment 42 Chapter 1 | Sampling and Data 1.1 Data Collection Experiment Student Learning Outcomes • The student will demonstrate the systematic sampling technique. • The student will construct relative frequency tables. • The student will interpret results and... |
. __________ 2. __________ 7. __________ 12. __________ 3. __________ 8. __________ 13. __________ 4. __________ 9. __________ 14. __________ 5. __________ 10. __________ 15. __________ Table 1.23 A Systematic Sample Pick a systematic sample of 15 restaurants. 1. Describe your procedure. 2. Complete the table with your... |
cities. The number of restaurants will vary. 1. Describe your procedure. 2. Complete the table with your sample. 1. ________ 6. ________ 11. ________ 16. ________ 21. ________ 2. ________ 7. ________ 12. ________ 17. ________ 22. ________ 3. ________ 8. ________ 13. ________ 18. ________ 23. ________ 4. ________ 9. __... |
unit any individual or object to be measured explanatory variable the independent variable in an experiment; the value controlled by researchers frequency the number of times a value of the data occurs informed consent any human subject in a research study must be cognizant of any risks or costs associated with the st... |
selected for inclusion in a sample, that member is returned to the population for the selection of the next individual sampling without replacement a member of the population may be chosen for inclusion in a sample only once; if chosen, the member is not returned to the population before the next selection simple rand... |
, cluster sampling, and systematic sampling. Convenience sampling is a nonrandom method of choosing a sample that often produces biased data. Samples that contain different individuals result in different data. This is true even when the samples are well-chosen and representative of the population. When properly select... |
to the influence of the explanatory variable. “An ethics problem arises when you are considering an action that benefits you or some cause you support, hurts or reduces benefits to others, and violates some rule.”[4] Ethical violations in statistics are not always easy to spot. Professional 4. Gelman, A. (2013, May 1)... |
; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29 Determine what the key terms refer to in the example for Researcher A. 3. population 4. sample 5. parameter 6. statistic 7. variable This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 1 |... |
energy they produce (examples are 2.1, 5.0, 6.7). What type of data is that? g. What contributed to the large number of deaths in 2010? In 2004? Explain. h. If you were asked to present these data in an oral presentation, what type of graph would you choose to present and why? Explain what features you would point out... |
in months) Frequency Relative Frequency Cumulative Relative Frequency.5–6.5 6.5–12.5 12.5–18.5 18.5–24.5 24.5–30.5 30.5–36.5 36.5–42.5 42.5–48.5 Table 1.31 Researcher A Survival Length (in months) Frequency Relative Frequency Cumulative Relative Frequency.5–6.5 6.5–12.5 12.5–18.5 18.5–24.5 24.5–30.5 30.5–36.5 36.5-45.5... |
if the population is the students in the school? 28. Would the sample size be large enough if the population is school-aged children and young adults in the United States? 29. Researcher A concludes that most students play video games between four and six hours each week. Researcher B concludes that most students play... |
5,000? 38. Is a sample of 500 volunteers a reliable measure for a population of 2,500? 39. A question on a survey reads: "Do you prefer the delicious taste of Brand X or the taste of Brand Y?" Is this a fair question? 40. Is a sample size of two representative of a population of five? 41. Is it possible for two experi... |
Explain your answers. a. driving time from New York to Florida b. departure time of a commuter train at rush hour c. distance from your house to school d. e. weight of a bag of rice at the store temperature of a refrigerator at any given time For each of the following eight exercises, identify: a. the population, b. t... |
, or qualitative), and give an example of the data. 57. number of tickets sold to a concert This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 1 | Sampling and Data 57 58. percent of body fat 59. favorite baseball team 60. time in line to buy groceries 61. number of students enrolle... |
five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is which of the following? a. cluster sampling b. c. d. convenience sampling stratified sampling simple random sampling 76. A study was done to determine the age, number of times per week, and the duration ... |
would use it for computer equipment. Also, 66 percent of those surveyed considered themselves relatively savvy computer users. a. Do you consider the sample size large enough for a study of this type? Why or why not? b. Based on your gut feeling, do you believe the percents accurately reflect the U.S. population for t... |
of the sample? c. Are these problems examples of sampling error or nonsampling error? d. During the same year, another pollster conducted a poll of 30,000 prospective voters. These researchers used a method they called quota sampling to obtain survey answers from specific subsets of the population. Quota sampling is a... |
take one or two courses? lastbaldeagle. Retrieved from http://www.youpolls.com/details.aspx?id=12328. 5. 6. Keeter, S., et al. (2006). Gauging the impact of growing nonresponse on estimates from a national RDD telephone survey. Public Opinion Quarterly, 70(5). Retrieved from http://hbanaszak.mjr.uw.edu.pl/TempTxt/Link... |
this statement: “47 percent of the people surveyed have lived in the United States for 5 years.” c. Fix the statement in b to make it correct. d. What fraction of the people surveyed have lived in the United States five or seven years? e. What fraction of the people surveyed have lived in the United States at most 12 ... |
relative frequency for CEOs younger than 55? e. Which graph shows the relative frequency and which shows the cumulative relative frequency? (a) Figure 1.13 (b) 62 Chapter 1 | Sampling and Data Use the following information to answer the next two exercises: Table 1.42 contains data on hurricanes that have made direct h... |
most complaints? Figure 1.15 94. An epidemiologist is studying the spread of the common cold among college students. He is interested in how the temperature of the dorm room correlates with the incidence of new infections. How can he design an observational study to answer this question? If he chooses to use surveys i... |
? Explain why or why not. Describe some possible sources of bias in this study, and how it might affect the results of the study. Give some suggestions about what could be done to improve the study. REFERENCES 1.1 Definitions of Statistics, Probability, and Key Terms The Data and Story Library. Retrieved from http://li... |
c.noaa.gov/gifs/table5.gif. ThoughtCo. Retrieved from https://www.thoughtco.com/levels-of-measurement-in-statistics-3126349. U.S. Census Bureau. Retrieved from https://www.census.gov/quickfacts/table/PST045216/00. Levels of measurement. Retrieved from https://www.cos.edu/Faculty/georgew/Tutorial/Data_Levels.htm. 1.4 Ex... |
S. Geological Survey. Retrieved from http://earthquake.usgs.gov/earthquakes/eqarchives/year/. SOLUTIONS 1 soccer = 12/40 = ; basketball = 20/40 = ; lacrosse = 8/40 = 0.2 2 women who play soccer = 8/20 = ; women who play basketball = 8/20 = ; women who play lacrosse = 4/20 = ; 3 patients with the virus 5 The average len... |
each researcher’s data are clearly distinguishable. The numbers and the scale should be legible and clear when the bar graph is displayed. 32 There is not enough information given to judge if either one is correct or incorrect. 34 The software program seems to work because the second study shows that more patients imp... |
children who take ski or snowboard lessons b. a group of these children c. d. the population mean age of children who take their first snowboard lesson the sample mean age of children who take their first snowboard lesson e. X = the age of one child who takes his or her first ski or snowboard lesson f. values for X, s... |
. qualitative b. quantitative discrete c. quantitative discrete d. qualitative 81 Causality: The fact that two variables are related does not guarantee that one variable is influencing the other. We cannot assume that crime rate impacts education level or that education level impacts crime rate. Confounding: There are ... |
the airlines. The airlines shown with the greatest number of complaints are the ones with the most passengers. You must consider the appropriateness of methods for presenting data; in this case displaying totals is misleading. 94 He can observe a population of 100 college students on campus. He can collect data about ... |
organized. (credit: William Greeson) Introduction By the end of this chapter, the student should be able to do the following: Chapter Objectives • Display data graphically and interpret the following graphs: stem-and-leaf plots, line graphs, bar graphs, frequency polygons, time series graphs, histograms, box plots, an... |
. Our emphasis will be on histograms and box plots. NOTE This book contains instructions for constructing a histogram and a box plot for the TI-83+ and TI-84 calculators. The Texas Instruments (TI) website (http://education.ti.com/educationportal/sites/US/sectionHome/ support.html) provides additional instructions for ... |
, scores for the last 30 games were as follows (smallest to largest): 32, 32, 33, 34, 38, 40, 42, 42, 43, 44, 46, 47, 47, 48, 48, 48, 49, 50, 50, 51, 52, 52, 52, 53, 54, 56, 57, 57, 60, 61 Construct a stemplot for the data. The stemplot is a quick way to graph data and gives an exact picture of the data. You want to lo... |
.5, 3.8, 4.4, 4.8, 4.9, 5.2, 5.5, 5.7, 5.8, 8.0 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 2 | Descriptive Statistics 75 Example 2.3 A side-by-side stem-and-leaf plot allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of l... |
to the right of the stem. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 2 | Descriptive Statistics 77 2.3 The table shows the number of wins and losses a sports team has had in 42 seasons. Create a side-by-side stemand-leaf plot of these wins and losses. Losses Wins Year Losse... |
consist of bars that are separated from each other. The bars can be rectangles, or they can be rectangular boxes, used in three-dimensional plots, and they can be vertical or horizontal. The bar graph shown in Example 2.5 has age- This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter ... |
.6% 1.1% 59.2% 1.7% This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 2 | Descriptive Statistics 81 Solution 2.6 Figure 2.4 2.6 Park City is broken down into six voting districts. The table shows the percentage of the total registered voter population that lives in each district as... |
can readily display large data sets. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 2 | Descriptive Statistics 83 A histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is more or less a number line, labeled ... |
. 60, 60.5, 61, 61, 61.5, 63.5, 63.5, 63.5, 64, 64, 64, 64, 64, 64, 64, 64.5, 64.5, 64.5, 64.5, 64.5, 64.5, 64.5, 64.5, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67.5, 67.5, 67.5, 67.5, 67.5, 67.5, 67.5, 68, ... |
. For example, if there are 150 values of data, take the square root of 150 and round to 12 bars or intervals. 84 Chapter 2 | Descriptive Statistics The boundaries are as follows: • 59.95 • 59.95 + 2 = 61.95 • 61.95 + 2 = 63.95 • 63.95 + 2 = 65.95 • 65.95 + 2 = 67.95 • 67.95 + 2 = 69.95 • 69.95 + 2 = 71.95 • 71.95 + 2 ... |
Use six bars on the histogram. 9, 9, 9.5, 9.5, 10, 10, 10, 10, 10, 10, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 12, 12, 12, 12, 12, 12, 12, 12.5, 12.5, 12.5, 12.5, 14 Example 2.10 The following data are the number of b... |
able to determine what is appropriate and reasonable. The following histogram displays the number of books on the x-axis and the frequency on the y-axis. 86 Chapter 2 | Descriptive Statistics Figure 2.6 Go to Appendix G. There are calculator instructions for entering data and for creating a customized histogram. Creat... |
Create a histogram and clearly label the endpoints of the intervals. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 2 | Descriptive Statistics 87 Example 2.11 Using this data set, construct a histogram. Number of Hours My Classmates Spent Playing Video Games on Weekends 9.95 19... |
2.12 A frequency polygon was constructed from the frequency table below. Frequency Distribution for Calculus Final Test Scores Lower Bound Upper Bound Frequency Cumulative Frequency 49.5 59.5 69.5 79.5 89.5 Table 2.17 59.5 69.5 79.5 89.5 99.5 5 10 30 40 15 5 15 45 85 100 This OpenStax book is available for free at htt... |
15 45 85 100 Frequency Distribution for Calculus Final Grades Lower Bound Upper Bound Frequency Cumulative Frequency 49.5 59.5 69.5 79.5 89.5 Table 2.20 59.5 69.5 79.5 89.5 99.5 10 10 30 45 5 10 20 50 95 100 Figure 2.9 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 2 | Descript... |
8 201.5 202.5 202.9 203.5 2007 202.416 203.499 205.352 206.686 207.949 208.352 208.299 2008 211.080 211.693 213.528 214.823 216.632 218.815 219.964 2009 211.143 212.193 212.709 213.240 213.856 215.693 215.351 2010 216.687 216.741 217.631 218.009 218.178 217.965 218.011 2011 220.223 221.309 223.467 224.906 225.964 225.7... |
,409 541,990 542,045 528,631 522,247 474,579 5,681,664 5,790,761 5,826,394 5,737,615 5,828,697 5,656,839 5,299,563 Uses of a Time Series Graph Time series graphs are important tools in various applications of statistics. When a researcher records values of the same variable over an extended period of time, it is someti... |
be one of the observed values. It is 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. For example, consider the following data: 1, 11.5, 6, 7.2, 4, 8, 9, 10, 6.8, 8.3, 2, 2, 10, 1 Ordered from smallest t... |
half, we can see that we have an odd number of values in the lower half. Thus, the median of the lower half, or the first quartile ( Q1 ) will be the middle value, or 2. Using the same procedure, we can see that the median of the upper half, or the third quartile ( Q3 ) will be the middle value of the upper half, or 9... |
IQR = 649,000 – 308,750 = 340,250 (1.5)(IQR) = (1.5)(340,250) = 510,375 Q1 – (1.5)(IQR) = 308,750 – 510,375 = –201,625 Q3 + (1.5)(IQR) = 649,000 + 510,375 = 1,159,375 No house price is less than –201,625. However, 5,500,000 is more than 1,159,375. Therefore, 5,500,000 is a potential outlier. 2.15 For the 11 salaries, ... |
is 14 values. There are 14 values less than the 28th percentile. They include the two 4s, the five 5s, and the seven 6s. The 28th percentile is between the last six and the first seven. The 28th percentile is 6.5. Find the median. Look again at the Cumulative Relative Frequency column and find.52. The median is the 50... |
nine in the table (between the 40th and 41st values). Therefore, we need to take the mean of the 40th an 41st values. The 80th percentile = 8 + 9 2 = 8.5. b. The 90th percentile will be the 45th data value (location is 0.90(50) = 45), and the 45th data value is nine. c. Q1 is also the 25th percentile. The 25th percent... |
57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77 a. Find the 70th percentile. b. Find the 83rd percentile. Solution 2.18 a. b. k = 70 i = the index n = 29 i = k 100 (n + 1) = ( 70 100 k = 83rd percentile i = the index n = 29 i = k 100 (n + 1) = ( 83 100 )(29 + 1) = 21. This equation tells us that i, or the position of t... |
, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77 a. Find the percentile for 58. b. Find the percentile for 25. Solution 2.19 a. Counting from the bottom of the list, there are 18 data values less than 58. There is one value of 58. x = 18 and y = 1. x +.5y n (100) = 18 +.5(1) 29 (100) = 63.80. Fifty-eight is... |
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