6th EDITION ELEMENTARY STATISTICS USING EXCEL 6th EDITION ELEMENTARY STATISTICS USING EXCEL MARIO F TRIOLA Special Contributions by Laura Iossi, Broward College www.freebookslides.com Director, Portfolio Management Deirdre Lynch Senior Portfolio Manager Suzy Bainbridge Portfolio Management Assistant Justin Billing Content Producer Peggy McMahon Managing Producer Karen Wernholm Manager, Courseware QA Mary Durnwald Manager, Content Development Robert Carroll Senior Producer Vicki Dreyfus Product Marketing Manager Tiffany Bitzel Field Marketing Manager Andrew Noble Product Marketing Assistant Jennifer Myers Senior Author Support/ Technology Specialist Joe Vetere Manager, Rights and Permissions Gina Cheselka Text and Cover Design, Illustrations Production Coordination, Composition Cenveo Publisher Services Cover Image: © Laura A Watt/Getty Images Field Marketing Assistant Erin Rush Copyright © 2018, 2014, 2010 by Pearson Education, Inc All Rights Reserved Printed in the United States of America This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise For information regarding permissions, request forms and the appropriate contacts within the Pearson Education Global Rights & Permissions department, please visit www.pearsoned.com/permissions/ Attributions of third party content appear on page 801, which constitutes an extension of this copyright page PEARSON, ALWAYS LEARNING, and MYSTATLAB are exclusive trademarks owned by Pearson Education, Inc or its affiliates in the U.S and>or other countries Unless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their respective owners and any references to third-party trademarks, logos or other trade dress are for demonstrative or descriptive purposes only Such 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FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF INFORMATION AVAILABLE FROM THE SERVICES THE DOCUMENTS AND RELATED GRAPHICS CONTAINED HERE IN COULD INCLUDE TECHNICAL INACCURACIES OR TYPOGRAPHICAL ERRORS CHANGES ARE PERIODICALLY ADDED TO THE INFORMATION HERE IN MICROSOFT AND >OR ITS RESPECTIVE SUPPLIERS MAY MAKE IMPROVEMENTS AND >OR CHANGES IN THE PRODUCT(S) AND >OR THE PROGRAM(S) DESCRIBED HERE IN AT ANY TIME PARTIAL SCREEN SHOTS MAY BE VIEWED IN FULL WITHIN THE SOFTWARE VERSION SPECIFIED Library of Congress Cataloging-in-Publication Data Names: Triola, Mario F Title: Elementary statistics using Microsoft Excel / Mario F Triola, Dutchess Community College Other titles: Elementary statistics using Excel Description: Sixth edition | Boston : Pearson, [2018] Identifiers: LCCN 2016016751| ISBN 9780134506623 (hardcover) | ISBN 0134506626 (hardcover) Subjects: LCSH: Statistics | Microsoft Excel (Computer file) Classification: LCC QA276.45.M53 T75 2018 | DDC 519.50285/554–dc23 LC record available at https://lccn.loc.gov/2016016751 Student Edition ISBN 13: 978-0-13-450662-3 ISBN 10: 0-13-450662-6 www.freebookslides.com To Ginny Marc, Dushana, and Marisa Scott, Anna, Siena, and Kaia www.freebookslides.com ABOUT THE AUTHOR Mario F Triola is a Professor Emeritus of Mathematics at Dutchess Community College, where he has taught statistics for over 30 years Marty is the author of Elementary Statistics 13th edition, Essentials of Statistics, 5th edition, Elementary Statistics Using the TI-83>84 Plus Calculator, 4th edition, and he is a co-author of Biostatistics for the Biological and Health Sciences, 2nd edition, Statistical Reasoning for Everyday Life, 5th edition, and Business Statistics Elementary Statistics is currently available as an International Edition, and it has been translated into several foreign languages Marty designed the original Statdisk statistical software, and he has written several manuals and workbooks for technology supporting statistics education He has been a speaker at many conferences and colleges Marty’s consulting work includes the design of casino slot machines and fishing rods He has worked with attorneys in determining probabilities in paternity lawsuits, analyzing data in medical malpractice lawsuits, identifying salary inequities based on gender, and analyzing disputed election results He has also used statistical methods in analyzing medical school surveys, and in analyzing survey results for the New York City Transit Authority Marty has testified as an expert witness in the New York State Supreme Court The Text and Academic Authors Association has awarded Marty a “Texty” for Excellence for his work on Elementary Statistics vii www.freebookslides.com CONTENTS INTRODUCTION TO STATISTICS EXPLORING DATA WITH TABLES AND GRAPHS 1-1 1-2 1-3 1-4 2-1 2-2 2-3 2-4 Statistical and Critical Thinking Types of Data 13 Collecting Sample Data 25 Introduction to Excel 35 49 Frequency Distributions for Organizing and Summarizing Data Histograms 62 Graphs That Enlighten and Graphs That Deceive 70 Scatterplots, Correlation, and Regression 83 51 DESCRIBING, EXPLORING, AND COMPARING DATA 3-1 3-2 3-3 Measures of Center 99 Measures of Variation 115 Measures of Relative Standing and Boxplots 130 PROBABILITY 4-1 4-2 4-3 4-4 4-5 151 Basic Concepts of Probability 153 Addition Rule and Multiplication Rule 167 Complements, Conditional Probability, and Bayes’ Theorem Counting 189 Probabilities Through Simulations (download only) 199 179 DISCRETE PROBABILITY DISTRIBUTIONS 5-1 5-2 5-3 Probability Distributions 208 Binomial Probability Distributions Poisson Probability Distributions 206 222 237 NORMAL PROBABILITY DISTRIBUTIONS 6-1 6-2 6-3 6-4 6-5 6-6 248 The Standard Normal Distribution 250 Real Applications of Normal Distributions 264 Sampling Distributions and Estimators 276 The Central Limit Theorem 287 Assessing Normality 299 Normal as Approximation to Binomial 307 ESTIMATING PARAMETERS AND DETERMINING SAMPLE SIZES 7-1 7-2 7-3 7-4 Estimating a Population Proportion 323 Estimating a Population Mean 341 Estimating a Population Standard Deviation or Variance Bootstrapping: Using Excel for Estimates 368 Basics of Hypothesis Testing 385 Testing a Claim About a Proportion 400 Testing a Claim About a Mean 414 Testing a Claim About a Standard Deviation or Variance INFERENCES FROM TWO SAMPLES 9-1 9-2 9-3 9-4 321 358 HYPOTHESIS TESTING 8-1 8-2 8-3 8-4 97 383 427 443 Two Proportions 445 Two Means: Independent Samples 458 Two Dependent Samples (Matched Pairs) 473 Two Variances or Standard Deviations 484 ix www.freebookslides.com 59 2-1 Frequency Distributions for Organizing and Summarizing Data 2-1 Basic Skills and Concepts Statistical Literacy and Critical Thinking McDonald’s Dinner Service Times Refer to the accompanying table summarizing service times (seconds) of McDonald’s dinners How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times? McDonald’s Dinner Service Times Refer to the accompanying frequency distribution What problem would be created by using classes of 60–120, 120–180, , 300–360? Relative Frequency Distribution Use percentages to construct the relative frequency dis- tribution corresponding to the accompanying frequency distribution for McDonald’s dinner service times What’s Wrong? Heights of adult males are known to have a normal distribution, as de- scribed in this section A researcher claims to have randomly selected adult males and measured their heights with the resulting relative frequency distribution as shown here Identify two major flaws with these results Table for Exercise McDonald’s Dinner Service Times Time (sec) Frequency 60–119 120–179 22 180–239 14 240–299 300–359 Table for Exercise Height (cm) Relative Frequency 130–144 23% In Exercises 5–8, identify the class width, class midpoints, and class boundaries for the given frequency distribution Also identify the number of individuals included in the summary The frequency distributions are based on real data from Appendix B 145–159 25% 160–174 22% 175–189 27% 190–204 28% Age (yr) of Best Actress When Oscar Was Won Frequency Age (yr) of Best Actor When Oscar Was Won Frequency 20–29 29 20–29 30–39 34 30–39 28 40–49 14 40–49 36 50–59 50–59 15 60–69 60–69 70–79 70–79 80–89 Blood Platelet Count of Males Frequency Blood Platelet Count of Females Frequency 0–99 100–199 25 100–199 51 200–299 92 200–299 90 300–399 28 300–399 10 400–499 400–499 500–599 500–599 600–699 In Exercises and 10, using a loose interpretation of the criteria for determining whether a frequency distribution is approximately a normal distribution, determine whether the given frequency distribution is approximately a normal distribution Give a brief explanation Normal Distributions Best Actresses Refer to the frequency distribution from Exercise 10 Best Actors Refer to the frequency distribution from Exercise www.freebookslides.com 60 CHAPTER Exploring Data with Tables and Graphs In Exercises 11–18, use the indicated data to construct the frequency distribution (The data for Exercises 13–16 can be downloaded at TriolaStats.com.) Constructing Frequency Distributions 11 Old Faithful Listed below are sorted duration times (seconds) of eruptions of the Old Faithful geyser in Yellowstone National Park Use these times to construct a frequency distribution Use a class width of 25 seconds and begin with a lower class limit of 125 seconds 125 203 205 221 225 229 233 233 235 236 236 237 238 238 239 240 240 240 240 241 241 242 242 242 243 243 244 245 245 245 245 246 246 248 248 248 249 249 250 251 252 253 253 255 255 256 257 258 262 264 12 Tornadoes Listed below are the F-scale intensities of recent tornadoes in the United States Construct a frequency distribution Do the intensities appear to have a normal distribution? 0 1 0 1 1 1 0 0 0 1 0 0 0 13 Burger King Lunch Service Times Refer to Data Set 25 “Fast Food” and use the drive- through service times for Burger King lunches Begin with a lower class limit of 70 seconds and use a class width of 40 seconds 14 Burger King Dinner Service Times Refer to Data Set 25 “Fast Food” and use the drive- through service times for Burger King dinners Begin with a lower class limit of 30 seconds and use a class width of 40 seconds 15 Wendy’s Lunch Service Times Refer to Data Set 25 “Fast Food” and use the drive- through service times for Wendy’s lunches Begin with a lower class limit of 70 seconds and use a class width of 80 seconds Does the distribution appear to be a normal distribution? 16 Wendy’s Dinner Service Times Refer to Data Set 25 “Fast Food” and use the drive- through service times for Wendy’s dinners Begin with a lower class limit of 30 seconds and use a class width of 40 seconds Using a loose interpretation of a normal distribution, does this distribution appear to be a normal distribution? 17 Analysis of Last Digits Heights of statistics students were obtained by the author as part of an experiment conducted for class The last digits of those heights are listed below Construct a frequency distribution with 10 classes Based on the distribution, the heights appear to be reported or actually measured? What you know about the accuracy of the results? 0 5 0 5 0 5 0 5 1 5 3 8 18 Analysis of Last Digits Weights of respondents were recorded as part of the California Health Interview Survey The last digits of weights from 50 randomly selected respondents are listed below Construct a frequency distribution with 10 classes Based on the distribution, the weights appear to be reported or actually measured? What you know about the accuracy of the results? 5 5 0 0 0 5 0 0 0 5 0 In Exercises 19 and 20, construct the relative frequency distributions and answer the given questions Relative Frequencies for Comparisons 19 Oscar Winners Construct one table (similar to Table 2-9 on page 58) that includes relative frequencies based on the frequency distributions from Exercises and 6, and then compare the ages of Oscar-winning actresses and actors Are there notable differences? 20 Blood Platelet Counts Construct one table (similar to Table 2-9 on page 58) that includes relative frequencies based on the frequency distributions from Exercises and 8, and then compare them Are there notable differences? www.freebookslides.com 2-1 Frequency Distributions for Organizing and Summarizing Data In Exercises 21 and 22, construct the cumulative frequency distribution that corresponds to the frequency distribution in the exercise indicated Cumulative Frequency Distributions 21 Exercise (Age of Best Actress When Oscar Was Won) 22 Exercise (Age of Best Actor When Oscar Was Won) In Exercises 23 and 24, use the given categorical data to construct the relative frequency distribution Categorical Data 23 Clinical Trial When XELJANZ (tofacitinib) was administered as part of a clinical trial for this rheumatoid arthritis treatment, 1336 subjects were given mg doses of the drug, and here are the numbers of adverse reactions: 57 had headaches, 21 had hypertension, 60 had upper respiratory tract infections, 51 had nasopharyngitis, and 53 had diarrhea Does any one of these adverse reactions appear to be much more common than the others? (Hint: Find the relative frequencies using only the adverse reactions, not the total number of treated subjects.) 24 Births Natural births randomly selected from four hospitals in New York State occurred on the days of the week (in the order of Monday through Sunday) with these frequencies: 52, 66, 72, 57, 57, 43, 53 Does it appear that such births occur on the days of the week with equal frequency? Exercises 25–28 involve large sets of data, so Excel should be used Complete lists of the data are not included in Appendix B, but they can be downloaded from the website TriolaStats.com Use the indicated data and construct the frequency distribution Large Data Sets 25 Systolic Blood Pressure Use the systolic blood pressures of the 300 subjects included in Data Set “Body Data.” Use a class width of 20 mm Hg and begin with a lower class limit of 80 mm Hg Does the frequency distribution appear to be a normal distribution? 26 Diastolic Blood Pressure Use the diastolic blood pressures of the 300 subjects included in Data Set “Body Data.” Use a class width of 15 mm Hg and begin with a lower class limit of 40 mm Hg Does the frequency distribution appear to be a normal distribution? 27 Earthquake Magnitudes Use the magnitudes of the 600 earthquakes included in Data Set 21 “Earthquakes.” Use a class width of 0.5 and begin with a lower class limit of 1.00 Does the frequency distribution appear to be a normal distribution? 28 Earthquake Depths Use the depths (km) of the 600 earthquakes included in Data Set 21 “Earthquakes.” Use a class width of 10.0 km and begin with a lower class limit of 0.0 km Does the frequency distribution appear to be a normal distribution? 2-1 Beyond the Basics 29 Interpreting Effects of Outliers Refer to Data Set 30 “Aluminum Cans” in Appendix B for the axial loads of aluminum cans that are 0.0111 in thick An axial load is the force at which the top of a can collapses The load of 504 lb is an outlier because it is very far away from all of the other values Construct a frequency distribution that includes the value of 504 lb, and then construct another frequency distribution with the value of 504 lb excluded In both cases, start the first class at 200 lb and use a class width of 20 lb State a generalization about the effect of an outlier on a frequency distribution 61 www.freebookslides.com 62 CHAPTER Exploring Data with Tables and Graphs 2-2 Histograms PART Basic Concepts of Histograms Key Concept While a frequency distribution is a useful tool for summarizing data and investigating the distribution of data, an even better tool is a histogram, which is a graph that is easier to interpret than a table of numbers DEFINITION A histogram is a graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data) The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies The heights of the bars correspond to frequency values Important Uses of a Histogram ■ Visually displays the shape of the distribution of the data ■ Shows the location of the center of the data ■ Shows the spread of the data ■ Identifies outliers A histogram is basically a graph of a frequency distribution For example, Figure 2-2 shows the histogram corresponding to the frequency distribution given in Table 2-2 on page 51 Class frequencies should be used for the vertical scale and that scale should be labeled as in Figure 2-2 There is no universal agreement on the procedure for selecting which values are used for the bar locations along the horizontal scale, but it is common to use class boundaries (as shown in Figure 2-2) or class midpoints or class limits or something else It is often easier for us mere mortals to use class midpoints for the horizontal scale Histograms can be generated using Excel Relative Frequency Histogram A relative frequency histogram has the same shape and horizontal scale as a histogram, but the vertical scale uses relative frequencies (as percentages or proportions) instead of actual frequencies Figure 2-3 is the relative frequency histogram corresponding to Figure 2-2 FIGURE 2-2 Histogram of McDonald’s Drive-Through Lunch Service Times (seconds) FIGURE 2-3 Relative Frequency Histogram of McDonald’s Drive-Through Lunch Service Times (seconds) www.freebookslides.com 2-2 Histograms Critical Thinking: Interpreting Histograms Even though creating histograms is more fun than human beings should be allowed to have, the ultimate objective is to understand characteristics of the data Explore the data by analyzing the histogram to see what can be learned about “CVDOT”: the center of the data, the variation (which will be discussed at length in Section 3-2), the shape of the distribution, whether there are any outliers (values far away from the other values), and time (whether there is any change in the characteristics of the data over time) Examining Figure 2-2, we see that the histogram is centered around 160 sec or 170 sec, the values vary from around 75 sec to 325 sec, and the distribution is very roughly bell-shaped There aren’t any outliers, and any changes in time are irrelevant for these data Common Distribution Shapes The histograms shown in Figure 2-4 depict four common distribution shapes FIGURE 2-4 (a) (b) (c) (d) Common Distributions Normal Distribution When graphed as a histogram, a normal distribution has a “bell” shape similar to the one superimposed in Figure 2-5 Many statistical methods require that sample data come from a population having a distribution that is approximately a normal distribution, and we can often use a histogram to judge whether this requirement is satisfied There are more advanced and less subjective methods for determining whether the distribution is a normal distribution Normal quantile plots are very helpful for assessing normality: see Part of this section 63 www.freebookslides.com 64 CHAPTER Exploring Data with Tables and Graphs Go Figure 2.5 quintillion bytes: Amount of data that we generated last year (A quintillion is followed by 18 zeroes.) FIGURE 2-5 Bell-Shaped Distribution of Arm Circumferences Because this histogram is roughly bell-shaped, we say that the data have a normal distribution (A more rigorous definition will be given in Chapter 6.) Uniform Distribution The different possible values occur with approximately the same frequency, so the heights of the bars in the histogram are approximately uniform, as in Figure 2-4(b) Figure 2-4(b) depicts outcomes of digits from state lotteries Skewness Remembering Skewness: Skewed Left: Resembles toes on left foot Skewed Right: Resembles toes on right foot A distribution of data is skewed if it is not symmetric and extends more to one side than to the other Data skewed to the right (also called positively skewed) have a longer right tail, as in Figure 2-4(c) Annual incomes of adult Americans are positively skewed Data skewed to the left (also called negatively skewed) have a longer left tail, as in Figure 2-4(d) Life span data in humans are skewed to the left (Here’s a mnemonic for remembering skewness: A distribution skewed to the right resembles the toes on your right foot, and one skewed to the left resembles the toes on your left foot.) Distributions skewed to the right are more common than those skewed to the left because it’s often easier to get exceptionally large values than values that are exceptionally small With annual incomes, for example, it’s impossible to get values below zero, but there are a few people who earn millions or billions of dollars in a year Annual incomes therefore tend to be skewed to the right Using Excel for Histograms Excel and XLSTAT can be used to quickly and easily construct histograms Instructions for both methods are provided To generate a histogram, first enter or open the data set For example, download the Appendix B data sets for Excel from TriolaStats.com and open the Excel workbook 25 - Fast Food.xlsx to obtain the 50 McDonald’s lunch drive-through service times listed in Table 2-1 Using XLSTAT to Generate Histograms Click the XLSTAT tab in the Ribbon (If XLSTAT is not available, it must be installed using the procedure in Section 1-4 on page 42.) Click the somewhat creepy-looking Visualizing Data button, and then select Histograms from the dropdown menu The Histograms dialog box now appears First enter the data range in the Data box For example, in 25 - Fast Food.xlsx the data (including sample label) are listed in cells through 51 of column A Select the cells that include the data or enter the input range of A1:A51 www.freebookslides.com 2-2 Histograms Next select Data type In this example, select Discrete, since lunch service times are whole numbers only If you are not sure of the data type, revisit Section 1-2 for a description of continuous and discrete data types Check (✔) the Sample labels box if the first cell of the data range includes the name (or label) of the data instead of a data value Uncheck the box if the first cell includes a data value instead of a label Select Sheet to display the histogram on a new worksheet Select Range and specify a cell to display the histogram on the current worksheet XLSTAT will automatically define class boundaries To define your own class boundaries, first enter all of the desired class boundaries in a single column on the spreadsheet These must be entered in ascending order, starting with the lower class boundary of the first class followed by the upper class boundaries of all classes (74.5, 124.5, 174.5, 224.5, 274.5, 324.5 in this example) If the Sample labels box is checked in Step 5, be sure to also include a label for the class boundaries data Click the Options tab, select User Defined, and select the cells that include the user-defined class boundaries (and data label if applicable) Click the Charts tab and confirm that the Histograms box is checked and the Bars option is selected Select Frequency in the Ordinate of the histograms box To generate a relative frequency histogram, simply select Relative Frequency instead Click OK and the histogram will be displayed as shown on the next page The histogram with default class boundaries is on the left and the histogram with user defined class boundaries (matching Figure 2-2) is on the right 65 www.freebookslides.com 66 CHAPTER Exploring Data with Tables and Graphs XLSTAT: Default class boundaries XLSTAT: User defined class boundaries XLSTAT: Relative Frequency Histogram Using Excel to Generate Histograms To generate a histogram using Excel (instead of XLSTAT), follow the same steps listed under Using Excel to Construct a Frequency Distribution on page 53, but in Step 3c, click the box labeled Chart Output (and confirm the Pareto box is not checked) before clicking OK Remember, this procedure uses a process called binning, and Excel’s bins (classes) are based on upper class limits www.freebookslides.com 2-2 Histograms PART 67 Assessing Normality with Normal Quantile Plots Some really important methods presented in later chapters have a requirement that sample data must be from a population having a normal distribution Histograms can be helpful in determining whether the normality requirement is satisfied, but they are not very helpful with small data sets Section 6-5 discusses methods for assessing normality—that is, determining whether the sample data are from a normally distributed population Section 6-5 includes a procedure for constructing normal quantile plots, which are easy to generate using technology such as XLSTAT Interpretation of a normal quantile plot is based on the following criteria: Criteria for Assessing Normality with a Normal Quantile Plot Normal Distribution: The population distribution is normal if the pattern of the points in the normal quantile plot is reasonably close to a straight line, and the points not show some systematic pattern that is not a straight-line pattern Not a Normal Distribution: The population distribution is not normal if the normal quantile plot has either or both of these two conditions: • The points not lie reasonably close to a straight-line pattern • The points show some systematic pattern that is not a straight-line pattern The following are examples of normal quantile plots Procedures for creating such plots are described in Section 6-5 Normal Distribution: The points are reasonably close to a straight-line pattern, and there is no other systematic pattern that is not a straight-line pattern Not a Normal Distribution: The points not lie reasonably close to a straight line Not a Normal Distribution: The points show a systematic pattern that is not a straight-line pattern 2-2 Basic Skills and Concepts Statistical Literacy and Critical Thinking Heights Heights of adult males are normally distributed If a large sample of heights of adult males is randomly selected and the heights are illustrated in a histogram, what is the shape of that histogram? More Heights The population of heights of adult males is normally distributed If we obtain a voluntary response sample of 5000 of those heights, will a histogram of the sample heights be bell-shaped? Blood Platelet Counts Listed below are blood platelet counts (1000 cells/mL) randomly selected from adults in the United States Why does it not make sense to construct a histogram for this data set? 191 286 263 193 193 215 162 646 250 386 www.freebookslides.com 68 CHAPTER Exploring Data with Tables and Graphs Blood Platelet Counts If we collect a sample of blood platelet counts much larger than the sample included with Exercise 3, and if our sample includes a single outlier, how will that outlier appear in a histogram? In Exercises 5–8, answer the questions by referring to the following histogram, which depicts the weights (grams) of all quarters listed in Data Set 29 “Coin Weights” in Appendix B (Grams are actually units of mass and the values shown on the horizontal scale are rounded.) Interpreting a Histogram Sample Size What is the approximate number of quarters depicted in the three bars farthest to the left? Class Width and Class Limits Give the approximate values of the class width, and the lower and upper class limits of the class depicted in the bar farthest to the left Relative Frequency Histogram How would the shape of the histogram change if the ver- tical scale uses relative frequencies expressed in percentages instead of the actual frequency counts as shown here? Gap What is a reasonable explanation for the gap between the quarters with weights be- tween 5.5 grams and 5.8 grams and the group of quarters with weights between 6.0 grams and 6.4 grams? (Hint: Refer to the columns of quarters in Data Set 29 “Coin Weights” in Appendix B.) Constructing Histograms In Exercises 9–16, construct the histograms and answer the given questions Old Faithful Use the frequency distribution from Exercise 11 in Section 2-1 on page 59 to construct a histogram Does it appear to be the graph of data from a population with a normal distribution? 10 Tornadoes Use the frequency distribution from Exercise 12 in Section 2-1 on page 59 to construct a histogram Does the histogram appear to be skewed? If so, identify the type of skewness 11 Burger King Lunch Service Times Use the frequency distribution from Exercise 13 in Section 2-1 on page 60 to construct a histogram Does the histogram appear to be skewed? If so, identify the type of skewness 12 Burger King Dinner Service Times Use the frequency distribution from Exercise 14 in Section 2-1 on page 60 to construct a histogram Using a strict interpretation of the criteria for being a normal distribution, does the histogram appear to depict data from a population with a normal distribution? 13 Wendy’s Lunch Service Times Use the frequency distribution from Exercise 15 in Section 2-1 on page 60 to construct a histogram Does the histogram appear to be skewed? If so, identify the type of skewness www.freebookslides.com 2-2 Histograms 14 Wendy’s Dinner Service Times Use the frequency distribution from Exercise 16 in Section 2-1 on page 60 to construct a histogram In using a strict interpretation of the criteria for being a normal distribution, does the histogram appear to depict data from a population with a normal distribution? 15 Analysis of Last Digits Use the frequency distribution from Exercise 17 in Section 2-1 on page 60 to construct a histogram What can be concluded from the distribution of the digits? Specifically, the heights appear to be reported or actually measured? 16 Analysis of Last Digits Use the frequency distribution from Exercise 18 in Section 2-1 on page 60 to construct a histogram What can be concluded from the distribution of the digits? Specifically, the heights appear to be reported or actually measured? 2-2 Beyond the Basics 17 Back-to-Back Relative Frequency Histograms When using histograms to com- pare two data sets, it is sometimes difficult to make comparisons by looking back and forth between the two histograms A back-to-back relative frequency histogram has a format that makes the comparison much easier Instead of frequencies, we should use relative frequencies (percentages or proportions) so that the comparisons are not difficult when there are different sample sizes Use the relative frequency distributions of the ages of Oscarwinning actresses and actors from Exercise 19 in Section 2-1 on page 60, and complete the back-to-back relative frequency histograms shown below Then use the result to compare the two data sets Age 50% 40% 30% 20% 10% 0% 89.5 79.5 69.5 59.5 49.5 39.5 29.5 19.5 Actresses 0% 10% 20% 30% 40% 50% Actors 18 Interpreting Normal Quantile Plots Which of the following normal quantile plots appear to represent data from a population having a normal distribution? Explain a b c d 69 www.freebookslides.com 70 CHAPTER Exploring Data with Tables and Graphs 2-3 Graphs That Enlighten and Graphs That Deceive Key Concept Section 2-2 introduced the histogram, and this section introduces other common graphs that foster understanding of data We also discuss some graphs that are deceptive because they create impressions about data that are somehow misleading or wrong The era of charming and primitive hand-drawn graphs has passed, and technology now provides us with powerful tools for generating a wide variety of graphs Here we go Graphs That Enlighten Dotplots A dotplot consists of a graph of quantitative data in which each data value is plotted as a point (or dot) above a horizontal scale of values Dots representing equal values are stacked Features of a Dotplot ■ Displays the shape of the distribution of data ■ It is usually possible to recreate the original list of data values EXAMPLE Dotplot of Pulse Rates of Males Figure 2-6 shows a dotplot of the pulse rates (beats per minute) of males from Data Set “Body Data” in Appendix B The two stacked dots above the position at 50 indicate that two of the pulse rates are 50 (In this dotplot, the horizontal scale allows even numbers only, but the original pulse rates are all even numbers.) FIGURE 2-6 Dotplot of Pulse Rates of Males YOUR TURN Do Exercise “Pulse Rates.” Stemplots A stemplot (or stem-and-leaf plot) represents quantitative data by separating each value into two parts: the stem (such as the leftmost digit) and the leaf (such as the rightmost digit) Better stemplots are often obtained by first rounding the original data values Also, stemplots can be expanded to include more rows and can be condensed to include fewer rows, as in Exercise 21 “Expanded Stemplots” Features of a Stemplot ■ Shows the shape of the distribution of the data ■ Retains the original data values ■ The sample data are sorted (arranged in order) www.freebookslides.com www.freebookslides.com 72 CHAPTER Exploring Data with Tables and Graphs Florence Nightingale Florence Nightingale (1820–1910) is known to many as the founder of the nursing profession, but she also saved thousands of lives by using statistics When she encountered an unsanitary and undersupplied hospital, she improved those conditions and then used statistics to convince others of the need for more widespread medical reform She developed original graphs to illustrate that during the Crimean War, more soldiers died as a result of unsanitary conditions than were killed in combat Florence Nightingale pioneered the use of social statistics as well as graphics techniques Select Sheet to display the stemplot on a new worksheet Select Range and specify a cell to display the stemplot on the current worksheet Click the Options tab and confirm that the Charts box is checked Click the Charts (1) tab and confirm that the Stem-and-leaf-plots box is checked Click OK and the stemplot will be displayed as shown below XLSTAT Time-Series Graph A time-series graph is a graph of time-series data, which are quantitative data that have been collected at different points in time, such as monthly or yearly Feature of a Time-Series Graph ■ Reveals information about trends over time EXAMPLE Time-Series Graph of Fatalities of Law Enforcement Officers The time-series graph shown in Figure 2-7 depicts the yearly number of fatalities of law enforcement officers in the United States See that a spike occurred in 2001, the year of the September 11, 2001, terrorist attacks Except for the data from 2001, there appears to be a slight downward trend FIGURE 2-7 Time-Series Graph of Law Enforcement Fatalities YOUR TURN Do Exercise “Gender Pay Gap.” www.freebookslides.com 2-3 Graphs That Enlighten and Graphs That Deceive Using Excel to Create Time-Series Graphs Creating time-series graphs in Excel is simple and requires only a few steps The procedure for creating time-series graphs is very similar to that for creating other types of charts in Excel, including pie charts and bar charts The following steps provide basic instructions for creating a chart in Excel Enter the data values in a column of the spreadsheet Select the cells that contain the data to be used in the chart by clicking the top cell in the data column and, while holding the touchpad>mouse button down, dragging the cursor to the bottom cell in the data column Click the Insert tab in the Ribbon, and then click Line in the Charts section of the Ribbon Select the Line or Line with Markers graph type The graph will appear with default formatting The line graph can be edited for improved appearance a Change the layout of the graph by clicking the Quick Layout button in the Ribbon b Right-click the axis and select Format Axis to adjust axis options and formatting c Right-click any data point and use Format Data Series to adjust line and marker formatting Bar Graphs A bar graph uses bars of equal width to show frequencies of categories of categorical (or qualitative) data The bars may or may not be separated by small gaps Feature of a Bar Graph ■ Shows the relative distribution of categorical data so that it is easier to compare the different categories Using Excel to Create Bar Graphs Creating bar graphs in Excel is simple and requires only a few steps The procedure for creating bar graphs is very similar to the procedure for creating time-series graphs and other types of charts in Excel continued 73 ... TABLES 11 -1 11- 2 ANALYSIS OF VARIANCE 12 -1 One-Way ANOVA 12 -2 Two-Way ANOVA 607 609 624 NONPARAMETRIC TESTS 13 -1 13-2 13 -3 13 -4 13 -5 13 -6 13 -7 572 Goodness-of-Fit 574 Contingency Tables 586 6 41 Basics... 484 ix www.freebookslides.com x Contents 10 11 12 13 14 15 APPENDIX A APPENDIX B APPENDIX C APPENDIX D CORRELATION AND REGRESSION 10 -1 10-2 10 -3 10 -4 10 -5 Correlation 504 Regression 523 Prediction... choosing and using the best features of Excel and the appropriate add-in Which Version of Excel? Excel instructions are given for Excel 2 016 , Excel 2 013 , Excel 2 010 , and Excel for Mac 2 011 These versions