Essentials of modern business statistics 3e anderson

Preface xvii About the Authors xxiiiStatistics in Practice: BusinessWeek 2 1.1 Applications in Business and Economics 3 Accounting 3Finance 4Marketing 4Production 4Economics 4 1.4 Descri

Entries in this tablegive the area under thecurve to the left of the

z value For example, for

z = –.85, the cumulative

probability is 1977

z

New Text

z .00 01 02 03 04 05 06 07 08 09

.0 5000 5040 5080 5120 5160 5199 5239 5279 5319 5359.1 5398 5438 5478 5517 5557 5596 5636 5675 5714 5753.2 5793 5832 5871 5910 5948 5987 6026 6064 6103 6141.3 6179 6217 6255 6293 6331 6368 6406 6443 6480 6517.4 6554 6591 6628 6664 6700 6736 6772 6808 6844 6879

.5 6915 6950 6985 7019 7054 7088 7123 7157 7190 7224.6 7257 7291 7324 7357 7389 7422 7454 7486 7517 7549.7 7580 7611 7642 7673 7704 7734 7764 7794 7823 7852.8 7881 7910 7939 7967 7995 8023 8051 8078 8106 8133.9 8159 8186 8212 8238 8264 8289 8315 8340 8365 8389

1.0 8413 8438 8461 8485 8508 8531 8554 8577 8599 86211.1 8643 8665 8686 8708 8729 8749 8770 8790 8810 88301.2 8849 8869 8888 8907 8925 8944 8962 8980 8997 90151.3 9032 9049 9066 9082 9099 9115 9131 9147 9162 91771.4 9192 9207 9222 9236 9251 9265 9279 9292 9306 9319

1.5 9332 9345 9357 9370 9382 9394 9406 9418 9429 94411.6 9452 9463 9474 9484 9495 9505 9515 9525 9535 95451.7 9554 9564 9573 9582 9591 9599 9608 9616 9625 96331.8 9641 9649 9656 9664 9671 9678 9686 9693 9699 97061.9 9713 9719 9726 9732 9738 9744 9750 9756 9761 9767

2.0 9772 9778 9783 9788 9793 9798 9803 9808 9812 98172.1 9821 9826 9830 9834 9838 9842 9846 9850 9854 98572.2 9861 9864 9868 9871 9875 9878 9881 9884 9887 98902.3 9893 9896 9898 9901 9904 9906 9909 9911 9913 99132.4 9918 9920 9922 9925 9927 9929 9931 9932 9934 9936

2.5 9938 9940 9941 9943 9945 9946 9948 9949 9951 99522.6 9953 9955 9956 9957 9959 9960 9961 9962 9963 99642.7 9965 9966 9967 9968 9969 9970 9971 9972 9973 99742.8 9974 9975 9976 9977 9977 9978 9979 9979 9980 99812.9 9981 9982 9982 9983 9984 9984 9985 9985 9986 9986

3.0 9986 9987 9987 9988 9988 9989 9989 9989 9990 9990

Cumulativeprobability Entries in the table

give the area under thecurve to the left of the

z value For example, for

z = 1.25, the cumulative

probability is 8944

David R Anderson University of Cincinnati

Dennis J Sweeney University of Cincinnati

Thomas A Williams Rochester Institute of Technology

MODERN BUSINESS

STATISTICS

MODERN BUSINESS

STATISTICS

MODERN BUSINESS

STATISTICS

MODERN BUSINESS

STATISTICS

MODERN BUSINESS

STATISTICS

MODERN BUSINESS

STATISTICS

MODERN BUSINESS

STATISTICS

MODERN BUSINESS

STATISTICS

MODERN BUSINESS

STATISTICS

ESSENTIALS OF MODERN BUSINESS

STATISTICS

ESSENTIALS OF

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Dedicated to Krista, Justin, Mark, and Colleen Mark, Linda, Brad, Tim, Scott, and Lisa

Cathy, David, and Kristin

Preface xvii About the Authors xxiii Chapter 1 Data and Statistics 1

Chapter 2 Descriptive Statistics: Tabular and Graphical

Presentations 30 Chapter 3 Descriptive Statistics: Numerical Measures 89 Chapter 4 Introduction to Probability 155

Chapter 5 Discrete Probability Distributions 200 Chapter 6 Continuous Probability Distributions 240 Chapter 7 Sampling and Sampling Distributions 271

Chapter 11 Comparisons Involving Proportions and a Test of

Independence 450 Chapter 12 Simple Linear Regression 484 Chapter 13 Multiple Regression 559 Chapter 14 Statistical Methods for Quality Control 609

Brief Contents

Appendix C Summation Notation 659 Appendix D Self-Test Solutions and Answers to Even-Numbered

Exercises 661

Index 697

Preface xvii About the Authors xxiii

Statistics in Practice: BusinessWeek 2 1.1 Applications in Business and Economics 3

Accounting 3Finance 4Marketing 4Production 4Economics 4

1.4 Descriptive Statistics 12 1.5 Statistical Inference 14 1.6 Statistical Analysis Using Microsoft Excel 15

Data Sets and Excel Worksheets 16Using Excel for Statistical Analysis 18

Summary 19 Glossary 20 Supplementary Exercises 21 Appendix 1.1 An Introduction to SWStat  27

Chapter 2 Descriptive Statistics: Tabular and Graphical

Statistics in Practice: Colgate-Palmolive Company 31 2.1 Summarizing Qualitative Data 32

Frequency Distribution 32Using Excel’s COUNTIF Function to Construct a Frequency Distribution 33Relative Frequency and Percent Frequency Distributions 34

Using Excel to Construct Relative Frequency and Percent FrequencyDistributions 35

Bar Graphs and Pie Charts 36Using Excel’s Chart Wizard to Construct Bar Graphs and Pie Charts 36

2.2 Summarizing Quantitative Data 41

Frequency Distribution 41Contents

Using Excel’s FREQUENCY Function to Construct a Frequency Distribution 43Relative Frequency and Percent Frequency Distributions 45

Histogram 45Using Excel’s Chart Wizard to Construct a Histogram 46Cumulative Distributions 48

Using Excel’s Histogram Tool to Construct a Frequency Distribution andHistogram 51

2.3 Exploratory Data Analysis: The Stem-and-Leaf Display 58 2.4 Crosstabulations and Scatter Diagrams 63

Crosstabulation 63Using Excel’s PivotTable Report to Construct a Crosstabulation 66Simpson’s Paradox 69

Scatter Diagram and Trendline 70Using Excel’s Chart Wizard to Construct a Scatter Diagram and a Trendline 72

Summary 78 Glossary 80 Key Formulas 80 Supplementary Exercises 81 Case Problem Pelican Stores 87

Chapter 3 Descriptive Statistics: Numerical Measures 89

Statistics in Practice: Small Fry Design 90 3.1 Measures of Location 91

Mean 91Median 92Mode 93Using Excel to Compute the Mean, Median, and Mode 94Percentiles 95

Quartiles 96Using Excel’s Rank and Percentile Tool to Compute Percentiles and Quartiles 97

3.2 Measures of Variability 103

Range 104Interquartile Range 104Variance 105

Standard Deviation 106Using Excel to Compute the Sample Variance and Sample Standard Deviation 108

Coefficient of Variation 108Using Excel’s Descriptive Statistics Tool 108

3.3 Measures of Distribution Shape, Relative Location, and Detecting Outliers 113

Distribution Shape 113

z-Scores 115

Chebyshev’s Theorem 116Empirical Rule 116Detecting Outliers 117

3.4 Exploratory Data Analysis 120

Five-Number Summary 120Box Plot 121

3.5 Measures of Association Between Two Variables 125

Covariance 125

Interpretation of the Covariance 127

Correlation Coefficient 129

Interpretation of the Correlation Coefficient 130

Using Excel to Compute the Covariance and Correlation Coefficient 132

3.6 The Weighted Mean and Working with Grouped Data 135

Case Problem 1 Pelican Stores 149

Case Problem 2 National Health Care Association 150

Case Problem 3 Business Schools of Asia-Pacific 151

Appendix 3.1 Constructing a Box Plot Using SWStat ⴙ 151

Chapter 4 Introduction to Probability 155

Statistics in Practice: Morton International 156

4.1 Experiments, Counting Rules, and Assigning Probabilities 157

Counting Rules, Combinations, and Permutations 157

Assigning Probabilities 162

Probabilities for the KP&L Project 164

4.2 Events and Their Probabilities 167

4.3 Some Basic Relationships of Probability 171

Case Problem Hamilton County Judges 198

Chapter 5 Discrete Probability Distributions 200

Statistics in Practice: Citibank 201

5.1 Random Variables 201

Discrete Random Variables 202

Continuous Random Variables 203

5.2 Discrete Probability Distributions 204

5.3 Expected Value and Variance 210

5.4 Binomial Probability Distribution 215

A Binomial Experiment 216Martin Clothing Store Problem 216Using Excel to Compute Binomial Probabilities 221Expected Value and Variance for the Binomial Probability Distribution 223

5.5 Poisson Probability Distribution 226

An Example Involving Time Intervals 226

An Example Involving Length or Distance Intervals 227Using Excel to Compute Poisson Probabilities 228

5.6 Hypergeometric Probability Distribution 231

Using Excel to Compute Hypergeometric Probabilities 233

Summary 235 Glossary 235 Key Formulas 236 Supplementary Exercises 237

Chapter 6 Continuous Probability Distributions 240

Statistics in Practice: Procter & Gamble 241 6.1 Uniform Probability Distribution 242

Area as a Measure of Probability 243

6.2 Normal Probability Distribution 246

Normal Curve 246Standard Normal Probability Distribution 248Computing Probabilities for Any Normal Probability Distribution 253Grear Tire Company Problem 254

Using Excel to Compute Normal Probabilities 256

6.3 Exponential Probability Distribution 261

Computing Probabilities for the Exponential Distribution 262Relationship Between the Poisson and Exponential Distributions 263Using Excel to Compute Exponential Probabilities 263

Summary 266 Glossary 266 Key Formulas 266 Supplementary Exercises 267 Case Problem Specialty Toys 269

Statistics in Practice: MeadWestvaco Corporation 272 7.1 The Electronics Associates Sampling Problem 273 7.2 Simple Random Sampling 274

Sampling from a Finite Population 274Sampling from an Infinite Population 278

7.3 Point Estimation 280 7.4 Introduction to Sampling Distributions 283 7.5 Sampling Distribution of x¯ 286

Expected Value of x¯ 286 Standard Deviation of x¯ 287 Form of the Sampling Distribution of x¯ 288 Sampling Distribution of x¯ for the EAI Problem 290

Practical Value of the Sampling Distribution of x¯ 290

Relationship Between Sample Size and the Sampling Distribution of x¯ 292

7.6 Sampling Distribution of p¯ 296

Expected Value of p¯ 296

Standard Deviation of p¯ 297

Form of the Sampling Distribution of p¯ 297

Practical Value of the Sampling Distribution of p¯ 298

Statistics in Practice: Food Lion 309

8.1 Population Mean: σ Known 310

Margin of Error and the Interval Estimate 310

Using Excel 314

Practical Advice 316

8.2 Population Mean: σ Unknown 318

Margin of Error and the Interval Estimate 319

Using Excel 322

Practical Advice 323

Using a Small Sample 323

Summary of Interval Estimation Procedures 325

8.3 Determining the Sample Size 328

Case Problem 1 Bock Investment Services 343

Case Problem 2 Gulf Real Estate Properties 343

Case Problem 3 Metropolitan Research, Inc 346

Statistics in Practice: John Morrell & Company 348

9.1 Developing Null and Alternative Hypotheses 349

Testing Research Hypotheses 349

Testing the Validity of a Claim 349

Testing in Decision-Making Situations 350

Summary of Forms for Null and Alternative Hypotheses 350

9.2 Type I and Type II Errors 351 9.3 Population Mean: σ Known 354

One-Tailed Test 354Two-Tailed Test 360Using Excel 363Summary and Practical Advice 364Relationship Between Interval Estimation and Hypothesis Testing 366

9.4 Population Mean: σ Unknown 370

One-Tailed Test 371Two-Tailed Test 372Using Excel 374Summary and Practical Advice 376

9.5 Population Proportion 380

Using Excel 382Summary 384

Summary 386 Glossary 387 Key Formulas 387 Supplementary Exercises 388 Case Problem 1 Quality Associates, Inc 390 Case Problem 2 Unemployment Study 392

Statistics in Practice: Fisons Corporation 394 10.1 Inferences About the Difference Between Two Population Means:

σ1 andσ2 Known 395

Interval Estimation of µ1
µ2 395Using Excel to Construct a Confidence Interval 397Hypothesis Tests About µ1
µ2 399

Using Excel to Conduct a Hypothesis Test 401Practical Advice 403

10.2 Inferences About the Difference Between Two Population Means:

σ1 andσ2 Unknown 405

Interval Estimation of µ1
µ2 406Using Excel to Construct a Confidence Interval 407Hypothesis Tests About µ1
µ2 409

Using Excel to Conduct a Hypothesis Test 411Practical Advice 413

10.3 Inferences About the Difference Between Two Population Means: Matched Samples 417

Using Excel to Conduct a Hypothesis Test 419

10.4 Introduction to Analysis of Variance 424

Assumptions for Analysis of Variance 425Conceptual Overview 425

10.5 Analysis of Variance: Testing for the Equality of k Population Means 428

Between-Treatments Estimate of Population Variance 429Within-Treatments Estimate of Population Variance 430

Comparing the Variance Estimates: The F Test 430

ANOVA Table 433Using Excel 433

Summary 439

Glossary 439

Key Formulas 440

Supplementary Exercises 442

Case Problem 1 Par, Inc 446

Case Problem 2 Wentworth Medical Center 447

Case Problem 3 Compensation for ID Professionals 448

Chapter 11 Comparisons Involving Proportions and a Test of

Statistics in Practice: United Way 451

11.1 Inferences About the Difference Between Two Population Proportions 452

Interval Estimation of p1
p2 452

Using Excel to Construct a Confidence Interval 454

Hypothesis Tests About p1
p2 456

Using Excel to Conduct a Hypothesis Test 457

11.2 Hypothesis Test for Proportions of a Multinomial Population 461

Using Excel to Conduct a Goodness of Fit Test 466

Case Problem A Bipartisan Agenda for Change 483

Statistics in Practice: Alliance Data Systems 485

12.1 Simple Linear Regression Model 486

Regression Model and Regression Equation 486

Estimated Regression Equation 487

12.2 Least Squares Method 489

Using Excel to Develop a Scatter Diagram and Compute the Estimated

Some Cautions About the Interpretation of Significance Tests 517

12.6 Excel’s Regression Tool 521

Using Excel’s Regression Tool for the Armand’s Pizza Parlors Problem 521Interpretation of Estimated Regression Equation Output 523

Interpretation of ANOVA Output 523

Interpretation of Regression Statistics Output 524

12.7 Using the Estimated Regression Equation for Estimation and Prediction 527

Point Estimation 527Interval Estimation 527

Confidence Interval Estimate of the Mean Value of y 527 Prediction Interval Estimate of an Individual Value of y 529

Using Excel to Develop Confidence and Prediction Interval Estimates 531

12.8 Residual Analysis: Validating Model Assumptions 535

Residual Plot Against x 536

Residual Plot Against 539Using Excel’s Regression Tool to Construct a Residual Plot 539

Summary 542 Glossary 543 Key Formulas 543 Supplementary Exercises 545 Case Problem 1 Spending and Student Achievement 551 Case Problem 2 U.S Department of Transportation 552 Case Problem 3 Alumni Giving 553

Case Problem 4 Major League Baseball Teams Values 555 Appendix 12.1 Regression Analysis with SWStat ⴙ 555

Statistics in Practice: International Paper 560 13.1 Multiple Regression Model 561

Regression Model and Regression Equation 561Estimated Multiple Regression Equation 561

13.2 Least Squares Method 562

An Example: Butler Trucking Company 563Using Excel’s Regression Tool to Develop the Estimated Multiple RegressionEquation 566

Note on Interpretation of Coefficients 567

13.3 Multiple Coefficient of Determination 572 13.4 Model Assumptions 575

13.5 Testing for Significance 577

Appendix 13.1 Multiple Regression Analysis with SWStat ⴙ 607

yˆ

Chapter 14 Statistical Methods for Quality Control 609

Statistics in Practice: Dow Chemical 610

14.1 Philosophies and Frameworks 611

Malcolm Baldrige National Quality Award 611

ISO 9000 612

Six Sigma 612

14.2 Statistical Process Control 614

Control Charts 615

Chart: Process Mean and Standard Deviation Known 616

Chart: Process Mean and Standard Deviation Unknown 618

KALI, Inc.: An Example of Acceptance Sampling 633

Computing the Probability of Accepting a Lot 633

Selecting an Acceptance Sampling Plan 635

Multiple Sampling Plans 637

Appendix D: Self-Test Solutions and Answers to Even-Numbered

The purpose of Essentials of Modern Business Statistics with Microsoft ® Excel is to give

students, primarily in the fields of business administration and economics, an introduction

to the field of statistics and its many applications The text is applications oriented and ten with the needs of the nonmathematician in mind; the mathematical prerequisite isknowledge of algebra

writ-Applications of data analysis and statistical methodology are an integral part of the ganization and presentation of the text material The discussion and development of eachtechnique is presented in an application setting, with the statistical results providing insights

or-to decisions and solutions or-to problems

Although the book is applications oriented, we have taken care to provide a soundmethodological development and to use notation that is generally accepted for the topic be-ing covered Hence, students will find that this text provides good preparation for the study

of more advanced material A bibliography to guide further study is included in an appendix

Use of Microsoft® Excel for Statistical Analysis

Essentials of Modern Business Statistics with Microsoft ® Excel is first and foremost a

sta-tistics textbook that emphasizes statistical concepts and applications But, since most tical problems are too large to be solved using hand calculations, some type of statisticalsoftware package is required to solve these problems There are several excellent statisticalpackages available today However, because most students and potential employers valuespreadsheet experience, many colleges and universities now use a spreadsheet package intheir statistics courses Microsoft Excel is the most widely used spreadsheet package in

prac-business as well as in colleges and universities We have written Essentials of Modern ness Statistics with Microsoft ® Excel especially for statistics courses in which Excel is used

Busi-as the software package

Excel has been integrated within each of the chapters and plays an integral part in ing an application orientation We assume that readers using this text are familiar with Excelbasics such as selecting cells, entering formulas, copying, and so on We build on that famil-iarity by showing how to use the appropriate Excel statistical functions and data analysis tools.The discussion of using Excel to perform a statistical procedure appears in a subsectionimmediately following the discussion of the statistical procedure We believe that this styleenables us to fully integrate the use of Excel throughout the text, but still maintain the pri-mary emphasis on the statistical methodology being discussed In each of these subsections,

provid-we use a standard format for setting up a worksheet for statistical analysis There are threeprimary tasks: Enter Data, Enter Functions and Formulas, and Apply Tools We believe aconsistent framework for applying Excel helps users to focus on the statistical methodol-ogy without getting bogged down in the details of using Excel

In presenting worksheet figures, we often use a nested approach in which the worksheetshown in the background of the figure displays the formulas and the worksheet shown inthe foreground shows the values computed using the formulas

Following is Figure 2.1 from the text, which is displayed to explain use of color in Excelfigures We use lavender to highlight the data from the sample (soft drink purchases in thisfigure) and green to highlight the cells containing Excel functions and formulas The greenPreface

A B C D E

1 Brand Purchased Soft Drink Frequency

2 Coke Classic Coke Classic =COUNTIF($A$2:$A$51,C2)

Changes in the Third Edition

We appreciate the acceptance and positive response to the previous editions of Essentials

of Modern Business Statistics with Microsoft Excel Accordingly, in making modifications

for this new edition, we have maintained the presentation style and readability of the vious editions The significant changes in the new edition are summarized here

pre-New Examples and Exercises Based on Real Data

We have added more than 200 new examples and exercises based on real data and recentreference sources of statistical information Using data pulled from sources also used by the

Wall Street Journal, USA Today, Fortune, Barron’s, and a variety of other sources, we draw

from actual studies to develop explanations and to create exercises that demonstrate manyuses of statistics in business and economics We believe that the use of real data helps gen-

FIGURE 2.1 FREQUENCY DISTRIBUTION FOR SOFT DRINK PURCHASES

CONSTRUCTED USING EXCEL’S COUNTIF FUNCTION

Note: Rows 11–44

are hidden.

1 Brand Purchased Soft Drink Frequency

erate more student interest in the material and enables the student to learn about both thestatistical methodology and its application.

New Case Problems

We have added several new case problems to this edition, bringing the total number of caseproblems in the text to 21 The new case problems appear in the chapters on descriptive sta-tistics, probability distributions, and regression analysis These case problems provide stu-dents with the opportunity to analyze somewhat larger data sets and prepare managerialreports based on the results of the analysis

New Statistics in Practice

Each chapter begins with a Statistics in Practice article that describes an application of thestatistical methodology to be covered in the chapter Statistics in Practice have been pro-vided by practitioners at companies such as Colgate-Palmolive, Citibank, Procter & Gamble,Monsanto, and others This edition includes two new Statistics in Practice: Food Lion(Chapter 8) and John Morrell & Company (Chapter 9)

New Materials for Microsoft Excel

All Excel materials have been updated to be consistent with Microsoft Excel 2003, and twooptions have been added to enhance learning and extend the use of Excel

• EasyStat: Digital Tutor for Microsoft ® Excel, Version 2 This online tutorial will

make it easier for students to learn how to use Excel to perform statistical sis In each digital video, one of the textbook authors demonstrates how Excel can

analy-be used to perform a particular statistical procedure Students may purchase an

online subscription for the Excel version of EasyStat Digital Tutor at http://asw swlearning.com.

• Coverage of Excel Add-in SWStatⴙ, Version 2 SWStat is now covered in the

appendixes of relevant chapters, giving you the option of incorporating this Excel

add-in in your course SWStat V.2 may be bundled with the text.

Features and Pedagogy

Anderson, Sweeney, and Williams have continued many of the features that appeared in thesecond edition Some of the important ones are noted here

Methods Exercises and Applications Exercises

The end-of-section exercises are split into two parts: Methods and Applications The ods exercises require users to use the formulas and make computations The Applicationsexercises require students to apply the chapter material in real-world situations Thus, stu-dents focus on the computational “nuts and bolts” and then move on to the subtleties of sta-tistical applications and the interpretation of the statistical output

Meth-Self-Test Exercises

Some exercises are identified as self-test exercises Completely worked-out solutions forthese exercises are provided in an appendix at the end of the book Students can attempt theself-text exercises and immediately check the solutions to evaluate their understanding ofthe concepts presented in the chapter

Margin Annotations and Notes & Comments

Margin annotations that highlight key points and provide additional insights for the studentare a key feature of this text These annotations, which appear in the margins, are designed

to provide emphasis and enhance understanding of the terms and concepts being presented

in the text

At the end of many sections, we provide “Notes & Comments” designed to give thereader additional insights about the statistical methodology and its application These notesinclude warnings about limitations of the methodology, recommendations for application,brief descriptions of technical considerations, and other matters

Data Files Accompany the Text

Approximately 200 data files are available on the Student CD packaged with new copies ofthe text Data sets for all case problems, as well as data sets and worksheets for larger ex-ercises, are included

Get Choice and Flexibility with ThomsonNOW™

You envisioned it, we developed it Designed by instructors and students for instructors and

students, ThomsonNOW for ASW’s Essentials of Modern Business Statistics is the most

re-liable, flexible, and easy-to-use online suite of services and resources With efficient andimmediate paths to success, ThomsonNOW delivers the results you expect ThomsonNOWwill be available in the fall of 2006

• Personalized learning plans For every chapter, personalized learning plans allow

students to focus on what they still need to learn and to select the activities that bestmatch their learning styles (such as the relevant EasyStat tutorials, animations, step-by-step problem demonstrations, and text pages)

• More study options Students can choose how they read the textbook—via

inte-grated digital eBook or by reading the print version

Ancillary Learning Materials for Students

• A Student CD is packaged free with each new text It provides Excel worksheets

for all text examples, exercises and Case problems, and a PredInt add-in with rections for computing confidence and predication intervals in regression analysis

di-If necessary, the Student CD may be purchased at the text’s website

• The Study Guide (ISBN 0-324-31279-2) prepared by John Loucks of St

Ed-ward’s University, will provide the student with significant supplementary studymaterials For each chapter, it contains key concepts, review materials, exampleproblems worked out in full detail, exercises with answers, and self-test questionswith answers

• EasyStat Digital Tutor for Microsoft ® Excel, Version 2 These online tutorials

make it easier than ever for students to learn how to use Excel to perform statistical

analysis For more information, visit http://easystat.swlearning.com.

Special thanks are owed to our associates from business and industry who supplied the tistics in Practice” features We recognize them individually by a credit line in each of the ar-ticles Finally, we are also indebted to our senior acquisitions editor Charles McCormick, Jr.,our senior developmental editor Alice Denny, our senior production editor Deanna Quinn,our technology project editor Kelly Reid, our senior marketing manager Larry Qualls, andothers at Thomson Business and Economics for their editorial counsel and support during thepreparation of this text

“Sta-David R Anderson Dennis J Sweeney Thomas A Williams

David R Anderson. David R Anderson is Professor of Quantitative Analysis in the lege of Business Administration at the University of Cincinnati Born in Grand Forks, NorthDakota, he earned his B.S., M.S., and Ph.D degrees from Purdue University Professor An-derson has served as Head of the Department of Quantitative Analysis and Operations Man-agement and as Associate Dean of the College of Business Administration In addition, hewas the coordinator of the College’s first Executive Program.

Col-At the University of Cincinnati, Professor Anderson has taught introductory statisticsfor business students as well as graduate-level courses in regression analysis, multivariateanalysis, and management science He has also taught statistical courses at the Department

of Labor in Washington, D.C He has been honored with nominations and awards for cellence in teaching and excellence in service to student organizations

ex-Professor Anderson has coauthored 10 textbooks in the areas of statistics, managementscience, linear programming, and production and operations management He is an activeconsultant in the field of sampling and statistical methods

Dennis J Sweeney. Dennis J Sweeney is Professor of Quantitative Analysis and Founder

of the Center for Productivity Improvement at the University of Cincinnati Born in DesMoines, Iowa, he earned a B.S.B.A degree from Drake University and his M.B.A andD.B.A degrees from Indiana University where he was an NDEA Fellow During 1978–79,Professor Sweeney worked in the management science group at Procter & Gamble; during1981–82, he was a visiting professor at Duke University Professor Sweeney served as Head

of the Department of Quantitative Analysis and as Associate Dean of the College of ness Administration at the University of Cincinnati

Busi-Professor Sweeney has published more than 30 articles and monographs in the area ofmanagement science and statistics The National Science Foundation, IBM, Procter &Gamble, Federated Department Stores, Kroger, and Cincinnati Gas & Electric have funded

his research, which has been published in Management Science, Operations Research, Mathematical Programming, Decision Sciences, and other journals.

Professor Sweeney has coauthored 10 textbooks in the areas of statistics, managementscience, linear programming, and production and operations management

Thomas A Williams. Thomas A Williams is Professor of Management Science in theCollege of Business at Rochester Institute of Technology Born in Elmira, New York, heearned his B.S degree at Clarkson University He did his graduate work at Rensselaer Poly-technic Institute, where he received his M.S and Ph.D degrees

Before joining the College of Business at RIT, Professor Williams served for sevenyears as a faculty member in the College of Business Administration at the University ofCincinnati, where he developed the undergraduate program in Information Systems andthen served as its coordinator At RIT, he was the first chairman of the Decision SciencesDepartment He teaches courses in management science and statistics, as well as graduatecourses in regression and decision analysis

Professor Williams is the coauthor of 11 textbooks in the areas of management science,statistics, production and operations management, and mathematics He has been a consul-

tant for numerous Fortune 500 companies and has worked on projects ranging from the use

of data analysis to the development of large-scale regression models

About the Authors

Data and Statistics

1.3 DATA SOURCESExisting SourcesStatistical StudiesData Acquisition Errors

1.4 DESCRIPTIVE STATISTICS

1.5 STATISTICAL INFERENCE

1.6 STATISTICAL ANALYSISUSING MICROSOFT EXCELData Sets and Excel WorksheetsUsing Excel for StatisticalAnalysis

With a global circulation of more than 1 million, BusinessWeek

is the most widely read business magazine in the world More

than 200 dedicated reporters and editors in 26 bureaus

world-wide deliver a variety of articles of interest to the business and

economic community Along with feature articles on current

topics, the magazine contains regular sections on International

Business, Economic Analysis, Information Processing, and

Sci-ence & Technology Information in the feature articles and the

regular sections helps readers stay abreast of current

develop-ments and assess the impact of those developdevelop-ments on business

and economic conditions

Most issues of BusinessWeek provide an in-depth report on

a topic of current interest Often, the in-depth reports contain

sta-tistical facts and summaries that help the reader understand the

business and economic information For example, the

Decem-ber 6, 2004, issue included a special report on the pricing of

goods made in China; the January 3, 2005, issue provided

infor-mation about where to invest in 2005; and the April 4, 2005, issue

provided an overview of the BusinessWeek 50, a diverse group

of top-performing companies In addition, the weekly

Business-Week Investor provides statistics about the state of the economy,

including production indexes, stock prices, mutual funds, and

in-terest rates

BusinessWeek also uses statistics and statistical information

in managing its own business For example, an annual survey of

subscribers helps the company learn about subscriber

demo-graphics, reading habits, likely purchases, lifestyles, and so on

BusinessWeek managers use statistical summaries from the

sur-vey to provide better services to subscribers and advertisers One

recent North American subscriber survey indicated that 90% of

BusinessWeek subscribers use a personal computer at home and that 64% of BusinessWeek subscribers are involved with com- puter purchases at work Such statistics alert BusinessWeek man-

agers to subscriber interest in articles about new developments

in computers The results of the survey are also made available

to potential advertisers The high percentage of subscribers ing personal computers at home and the high percentage of sub-scribers involved with computer purchases at work would be anincentive for a computer manufacturer to consider advertising in

us-BusinessWeek.

In this chapter, we discuss the types of data available for tistical analysis and describe how the data are obtained We in-troduce descriptive statistics and statistical inference as ways ofconverting data into meaningful and easily interpreted statisticalinformation

sta-BusinessWeek uses statistical facts and summaries

in many of its articles © Terri Miller/ E-VisualCommunications, Inc

BUSINESSWEEK*

NEW YORK, NEW YORK

*The authors are indebted to Charlene Trentham, Research Manager at

BusinessWeek, for providing this Statistics in Practice.

Frequently, we see the following kinds of statements in newspaper and magazine articles:

• A Jupiter Media survey found that 31% of adult males spend 10 or more hours a

week watching television For adult women, it was 26% (The Wall Street Journal,

January 26, 2004)

• General Motors, the leader in automotive cash rebates, provided an average cash

in-centive of $4300 per vehicle during 2003 (USA Today, January 23, 2004).

1.1 Applications in Business and Economics 3

• More than 40% of Marriott International managers work their way up through the

ranks (Fortune, January 20, 2003).

• Employees in management and finance had a median annual salary of $49,712 for

2003 (The World Almanac, 2004).

• Genentech was rated number 1 in Fortune’s “100 Best Companies to Work For”.Genentech’s average annual pay for salaried and hourly workers respectively was

$69,425 and $47,817 (Fortune, January 23, 2006).

• The New York Yankees have the highest payroll in major league baseball In 2003,

the team payroll was $152,749,814 with a median of $4,575,000 per player (USA Today, September 1, 2003).

• The Dow Jones Industrial Average closed at 10,960 on January 13, 2006 (The Wall Street Journal, January 14, 2006).

The numerical facts in the preceding statements (31%; 26%; $4300; 40%; $49,712;

$69,425; $47,817; $152,749,814; $4,575,000; and 10,960) are called statistics Thus, in

every-day usage, the term statistics refers to numerical facts However, the field, or subject, of

sta-tistics involves much more than numerical facts In a broad sense, statisticsis the art andscience of collecting, analyzing, presenting, and interpreting data Particularly in business andeconomics, the information provided by collecting, analyzing, presenting, and interpretingdata gives managers and decision makers a better understanding of the business and economicenvironment and thus enables them to make more informed and better decisions In this text,

we emphasize the use of statistics for business and economic decision making

Chapter 1 begins with some illustrations of the applications of statistics in business and

economics In Section 1.2 we define the term data and introduce the concept of a data set This section also introduces key terms such as variables and observations, discusses the

difference between quantitative and qualitative data, and illustrates the uses of sectional and time series data Section 1.3 discusses how data can be obtained from exist-ing sources or through survey and experimental studies designed to obtain new data Theimportant role that the Internet now plays in obtaining data is also highlighted The uses ofdata in developing descriptive statistics and in making statistical inferences are described

cross-in Sections 1.4 and 1.5

In today’s global business and economic environment, anyone can access vast amounts ofstatistical information The most successful managers and decision makers understand theinformation and know how to use it effectively In this section, we provide examples thatillustrate some of the uses of statistics in business and economics

Accounting

Public accounting firms use statistical sampling procedures when conducting audits fortheir clients For instance, suppose an accounting firm wants to determine whether theamount of accounts receivable shown on a client’s balance sheet fairly represents the ac-tual amount of accounts receivable Usually the large number of individual accounts re-ceivable makes reviewing and validating every account too time-consuming and expensive

As common practice in such situations, the audit staff selects a subset of the accountscalled a sample After reviewing the accuracy of the sampled accounts, the auditors draw aconclusion as to whether the accounts receivable amount shown on the client’s balancesheet is acceptable

Financial analysts use a variety of statistical information to guide their investment mendations In the case of stocks, the analysts review a variety of financial data includingprice/earnings ratios and dividend yields By comparing the information for an individualstock with information about the stock market averages, a financial analyst can begin todraw a conclusion as to whether an individual stock is over- or underpriced For example,

recom-Barron’s (September 12, 2005) reported that the average price/earnings ratio for the 30 stocks

in the Dow Jones Industrial Average was 16.5 JPMorgan showed a price/earnings ratio of11.8 In this case, the statistical information on price/earnings ratios indicated a lower price

in comparison to earnings for JPMorgan than the average for the Dow Jones stocks fore, a financial analyst might conclude that JPMorgan was underpriced This and otherinformation about JPMorgan would help the analyst make a buy, sell, or hold recommen-dation for the stock

There-Marketing

Electronic scanners at retail checkout counters collect data for a variety of marketing search applications For example, data suppliers such as ACNielsen and Information Re-sources, Inc., purchase point-of-sale scanner data from grocery stores, process the data, andthen sell statistical summaries of the data to manufacturers Manufacturers spend hundreds

re-of thousands re-of dollars per product category to obtain this type re-of scanner data turers also purchase data and statistical summaries on promotional activities such as spe-cial pricing and the use of in-store displays Brand managers can review the scannerstatistics and the promotional activity statistics to gain a better understanding of the rela-tionship between promotional activities and sales Such analyses often prove helpful in es-tablishing future marketing strategies for the various products

Manufac-Production

Today’s emphasis on quality makes quality control an important application of statistics

in production A variety of statistical quality control charts are used to monitor the

out-put of a production process In particular, an x-bar chart can be used to monitor the average

output Suppose, for example, that a machine fills containers with 12 ounces of a soft drink.Periodically, a production worker selects a sample of containers and computes the average

number of ounces in the sample This average, or x-bar value, is plotted on an x-bar chart A

plotted value above the chart’s upper control limit indicates overfilling, and a plotted valuebelow the chart’s lower control limit indicates underfilling The process is termed “in con-

trol” and allowed to continue as long as the plotted x-bar values fall between the chart’s per and lower control limits Properly interpreted, an x-bar chart can help determine when

up-adjustments are necessary to correct a production process

Economics

Economists frequently provide forecasts about the future of the economy or some aspect of

it They use a variety of statistical information in making such forecasts For instance, inforecasting inflation rates, economists use statistical information on such indicators as the Producer Price Index, the unemployment rate, and manufacturing capacity utilization.Often these statistical indicators are entered into computerized forecasting models that pre-dict inflation rates

1.2 Data 5

Applications of statistics such as those described in this section are an integral part ofthis text Such examples provide an overview of the breadth of statistical applications Tosupplement these examples, practitioners in the fields of business and economics providedchapter-opening Statistics in Practice articles that introduce the material covered in eachchapter The Statistics in Practice applications show the importance of statistics in a widevariety of business and economic situations

1.2 Data

Dataare the facts and figures collected, analyzed, and summarized for presentation and terpretation All the data collected in a particular study are referred to as the data setfor thestudy Table 1.1 shows a data set containing information for 25 companies that are part ofthe S&P 500 The S&P 500 is made up of 500 companies selected by Standard & Poor’s.These companies account for 76% of the market capitalization of all U.S stocks Thesestocks are closely followed by investors and Wall Street analysts

in-Earnings Share per

BusinessWeek Price Share Company Exchange Ticker Rank ($) ($)

Source: BusinessWeek (April 4, 2005).

TABLE 1.1 DATA SET FOR 25 S&P 500 COMPANIES

file

CD

BWS&P

Elements, Variables, and Observations

Elementsare the entities on which data are collected For the data set in Table 1.1, each dividual company’s stock is an element; the element names appear in the first column With

in-25 stocks, the data set contains in-25 elements

Avariableis a characteristic of interest for the elements The data set in Table 1.1 cludes the following five variables:

in-• Exchange: Where the stock is traded—N (New York Stock Exchange) and NQ

(Nasdaq National Market)

• Ticker Symbol: The abbreviation used to identify the stock on the exchange

listing

• BusinessWeek Rank: A number from 1 to 500 that is a measure of company strength

• Share Price ($): The closing price (February 28, 2005)

• Earnings per Share ($): The earnings per share for the most recent 12 months

Measurements collected on each variable for every element in a study provide the data.The set of measurements obtained for a particular element is called an observation Refer-ring to Table 1.1, we see that the set of measurements for the first observation (Abbott Lab-oratories) is N, ABT, 90, 46, and 2.02 The set of measurements for the second observation(Altria Group) is N, MO, 148, 66, and 4.57, and so on A data set with 25 elements contains

25 observations

Scales of Measurement

Data collection requires one of the following scales of measurement: nominal, ordinal,interval, or ratio The scale of measurement determines the amount of information con-tained in the data and indicates the most appropriate data summarization and statisticalanalyses

When the data for a variable consist of labels or names used to identify an attribute ofthe element, the scale of measurement is considered a nominal scale For example, refer-ring to the data in Table 1.1, we see that the scale of measurement for the exchange variable

is nominal because N and NQ are labels used to identify where the company’s stock is traded

In cases where the scale of measurement is nominal, a numeric code as well as nonnumericlabels may be used For example, to facilitate data collection and to prepare the data for en-try into a computer database, we might use a numeric code by letting 1 denote the New YorkStock Exchange and 2 denote the Nasdaq National Market In this case the numeric values

1 and 2 provide the labels used to identify where the stock is traded The scale of ment is nominal even though the data appear as numeric values

measure-The scale of measurement for a variable is called an ordinal scale if the data hibit the properties of nominal data and the order or rank of the data is meaningful Forexample, Eastside Automotive sends customers a questionnaire designed to obtain data

ex-on the quality of its automotive repair service Each customer provides a repair servicerating of excellent, good, or poor Because the data obtained are the labels— excellent,good, or poor—the data have the properties of nominal data In addition, the data can beranked, or ordered, with respect to the service quality Data recorded as excellent indi-cate the best service, followed by good and then poor Thus, the scale of measurement

is ordinal Note that the ordinal data can also be recorded using a numeric code For

example, the BusinessWeek rank for the data in Table 1.1 is ordinal data It provides a rank from 1 to 500 based on BusinessWeek’s assessment of the company’s strength.

1.2 Data 7

The scale of measurement for a variable becomes an interval scaleif the data show theproperties of ordinal data and the interval between values is expressed in terms of a fixedunit of measure Interval data are always numeric Scholastic Aptitude Test (SAT) scoresare an example of interval-scaled data For example, three students with SAT scores of 1120,

1050, and 970 can be ranked or ordered in terms of best performance to poorest formance In addition, the differences between the scores are meaningful For instance,student 1 scored 1120
1050  70 points more than student 2, while student 2 scored

per-1050
970  80 points more than student 3

The scale of measurement for a variable is a ratio scaleif the data have all the erties of interval data and the ratio of two values is meaningful Variables such as dis-tance, height, weight, and time use the ratio scale of measurement This scale requires that

prop-a zero vprop-alue be included to indicprop-ate thprop-at nothing exists for the vprop-ariprop-able prop-at the zero point.For example, consider the cost of an automobile A zero value for the cost would indicatethat the automobile has no cost and is free In addition, if we compare the cost of $30,000for one automobile to the cost of $15,000 for a second automobile, the ratio propertyshows that the first automobile is $30,000/$15,000 2 times, or twice, the cost of the sec-ond automobile

Qualitative and Quantitative Data

Data can also be classified as either qualitative or quantitative Qualitative dataincludelabels or names used to identify an attribute of each element Qualitative data use either thenominal or ordinal scale of measurement and may be nonnumeric or numeric Quantita- tive datarequire numeric values that indicate how much or how many Quantitative dataare obtained using either the interval or ratio scale of measurement

Aqualitative variableis a variable with qualitative data, and a quantitative variableis

a variable with quantitative data The statistical analysis appropriate for a particular variabledepends upon whether the variable is qualitative or quantitative If the variable is qualitative,the statistical analysis is rather limited We can summarize qualitative data by counting thenumber of observations in each qualitative category or by computing the proportion of theobservations in each qualitative category However, even when the qualitative data use anumeric code, arithmetic operations such as addition, subtraction, multiplication, and divi-sion do not provide meaningful results Section 2.1 discusses ways for summarizing quali-tative data

On the other hand, arithmetic operations often provide meaningful results for a tative variable For example, for a quantitative variable, the data may be added and then di-vided by the number of observations to compute the average value This average is usuallymeaningful and easily interpreted In general, more alternatives for statistical analysis arepossible when the data are quantitative Section 2.2 and Chapter 3 provide ways of sum-marizing quantitative data

quanti-Cross-Sectional and Time Series Data

For purposes of statistical analysis, distinguishing between cross-sectional data and timeseries data is important Cross-sectional dataare data collected at the same or approxi-mately the same point in time The data in Table 1.1 are cross-sectional because they de-scribe the five variables for the 25 S&P 500 companies at the same point in time Time series dataare data collected over several time periods For example, Figure 1.1 provides

a graph of the U.S city average price per gallon for unleaded regular gasoline The graph showsgasoline prices in a fairly stable band between $1.80 and $2.00 from May, 2004, through

Qualitative data are

often referred to as

categorical data.

The statistical method

appropriate for

summarizing data depends

upon whether the data are

qualitative or quantitative.

NOTES AND COMMENTS

1 An observation is the set of measurements

ob-tained for each element in a data set Hence, thenumber of observations is always the same as thenumber of elements The number of measure-ments obtained for each element equals the num-ber of variables Hence, the total number of dataitems can be determined by multiplying the num-ber of observations by the number of variables

2 Quantitative data may be discrete or

continu-ous Quantitative data that measure how many(e.g., number of calls received in 5 minutes) arediscrete Quantitative data that measure howmuch (e.g., weight or time) are continuous be-cause no separation occurs between the possi-ble data values

February, 2005 After that they become very volatile They rise significantly culminating with

a sharp spike in September, 2005 After that, they ease sharply Most of the statistical methodspresented in this text apply to cross-sectional rather than time series data

2004 Jun Jul Aug Sep Oct Nov Dec2005

FIGURE 1.1 U.S CITY AVERAGE PRICE PER GALLON FOR CONVENTIONAL

REGULAR GASOLINE

Source: U.S Energy Information Administration, January, 2006.

1.3 Data Sources 9

Source Some of the Data Typically Available

Employee records Name, address, social security number, salary, number of vacation days,

num-ber of sick days, and bonusProduction records Part or product number, quantity produced, direct labor cost, and materials costInventory records Part or product number, number of units on hand, reorder level, economic

order quantity, and discount scheduleSales records Product number, sales volume, sales volume by region, and sales volume by

customer typeCredit records Customer name, address, phone number, credit limit, and accounts receivable

balanceCustomer profile Age, gender, income level, household size, address, and preferences

TABLE 1.2 EXAMPLES OF DATA AVAILABLE FROM INTERNAL COMPANY RECORDS

nel records Other internal records contain data on sales, advertising expenditures, tion costs, inventory levels, and production quantities Most companies also maintain de-tailed data about their customers Table 1.2 shows some of the data commonly available frominternal company records

distribu-Organizations that specialize in collecting and maintaining data make available stantial amounts of business and economic data Companies access these external datasources through leasing arrangements or by purchase Dun & Bradstreet, Bloomberg, andDow Jones & Company are three firms that provide extensive business database services

sub-to clients ACNielsen and Information Resources, Inc., built successful businesses ing and processing data that they sell to advertisers and product manufacturers

collect-Data are also available from a variety of industry associations and special interest ganizations The Travel Industry Association of America maintains travel-related informa-tion such as the number of tourists and travel expenditures by states Such data would be ofinterest to firms and individuals in the travel industry The Graduate Management Admis-sion Council maintains data on test scores, student characteristics, and graduate manage-ment education programs Most of the data from these types of sources are available toqualified users at a modest cost

or-The Internet continues to grow as an important source of data and statistical tion Almost all companies maintain Web sites that provide general information about thecompany as well as data on sales, number of employees, number of products, productprices, and product specifications In addition, a number of companies now specialize inmaking information available over the Internet As a result, one can obtain access to stockquotes, meal prices at restaurants, salary data, and an almost infinite variety of information.Government agencies are another important source of existing data For instance, the U.S.Department of Labor maintains considerable data on employment rates, wage rates, size of thelabor force, and union membership Table 1.3 lists selected governmental agencies and some ofthe data they provide Most government agencies that collect and process data also make the re-sults available through a Web site For instance, the U.S Census Bureau has a wealth of data atits Web site, www.census.gov Figure 1.2 shows the homepage for the U.S Census Bureau

FIGURE 1.2 U.S CENSUS BUREAU HOMEPAGE

Government Agency Some of the Data Available

Census Bureau Population data, number of households, and household

Federal Reserve Board Data on the money supply, installment credit, exchange rates,

http://www.federalreserve.gov and discount ratesOffice of Management and Budget Data on revenue, expenditures, and debt of the federal

http://www.whitehouse.gov/omb governmentDepartment of Commerce Data on business activity, value of shipments by industry, level

http://www.doc.gov of profits by industry, and growing and declining industriesBureau of Labor Statistics Consumer spending, hourly earnings, unemployment rate,

http://www.bls.gov safety records, and international statistics

TABLE 1.3 EXAMPLES OF DATA AVAILABLE FROM SELECTED GOVERNMENT AGENCIES

1.3 Data Sources 11

In an experimental study, a variable of interest is first identified Then one or more othervariables are identified and controlled so that data can be obtained about how they influencethe variable of interest For example, a pharmaceutical firm might be interested in conducting

an experiment to learn about how a new drug affects blood pressure Blood pressure is thevariable of interest in the study The dosage level of the new drug is another variable that ishoped to have a causal effect on blood pressure To obtain data about the effect of the newdrug, researchers select a sample of individuals The dosage level of the new drug is con-trolled, as different groups of individuals are given different dosage levels Before and afterdata on blood pressure are collected for each group Statistical analysis of the experimen-tal data can help determine how the new drug affects blood pressure

Nonexperimental, or observational, statistical studies make no attempt to control thevariables of interest A survey is perhaps the most common type of observational study Forinstance, in a personal interview survey, research questions are first identified Then a ques-tionnaire is designed and administered to a sample of individuals Some restaurants use ob-servational studies to obtain data about their customers’ opinions of the quality of food,service, atmosphere, and so on A questionnaire used by the Lobster Pot Restaurant in Red-ington Shores, Florida, is shown in Figure 1.3 Note that the customers completing the ques-tionnaire are asked to provide ratings for five variables: food quality, friendliness of service,promptness of service, cleanliness, and management The response categories of excellent,

Studies of smokers and

nonsmokers are

observational studies

because researchers do

not determine or control

who will smoke and who

will not smoke.

FIGURE 1.3 CUSTOMER OPINION QUESTIONNAIRE USED BY THE LOBSTER POT

RESTAURANT, REDINGTON SHORES, FLORIDA

We are happy you stopped by the Lobster Pot Restaurant and want tomake sure you will come back So, if you have a little time, we will really appreciate

it if you will fill out this card Your comments and suggestions are extremely important to us Thank you!

What prompted your visit to us?

The largest experimental

statistical study ever

conducted is believed to be

the 1954 Public Health

Service experiment for

the Salk polio vaccine.

Nearly 2 million children

in grades 1, 2, and 3 were

selected from throughout

the United States.

good, satisfactory, and unsatisfactory provide ordinal data that enable Lobster Pot’s agers to assess the quality of the restaurant’s operation.

man-Managers wanting to use data and statistical analyses as aids to decision making must

be aware of the time and cost required to obtain the data The use of existing data sources

is desirable when data must be obtained in a relatively short period of time If importantdata are not readily available from an existing source, the additional time and cost involved

in obtaining the data must be taken into account In all cases, the decision maker shouldconsider the contribution of the statistical analysis to the decision-making process The cost

of data acquisition and the subsequent statistical analysis should not exceed the savings erated by using the information to make a better decision

gen-Data Acquisition Errors

Managers should always be aware of the possibility of data errors in statistical studies.Using erroneous data can be worse than not using any data at all An error in data acquisi-tion occurs whenever the data value obtained is not equal to the true or actual value thatwould be obtained with a correct procedure Such errors can occur in a number of ways.For example, an interviewer might make a recording error, such as a transposition in writingthe age of a 24-year-old person as 42, or the person answering an interview question mightmisinterpret the question and provide an incorrect response

Experienced data analysts take great care in collecting and recording data to ensure thaterrors are not made Special procedures can be used to check for internal consistency of thedata For instance, such procedures would indicate that the analyst should review the accu-racy of data for a respondent shown to be 22 years of age but reporting 20 years of workexperience Data analysts also review data with unusually large and small values, calledoutliers, which are candidates for possible data errors In Chapter 3 we present some of themethods statisticians use to identify outliers

Errors often occur during data acquisition Blindly using any data that happen to beavailable or using data that were acquired with little care can result in misleading informa-tion and bad decisions Thus, taking steps to acquire accurate data can help ensure reliableand valuable decision-making information

Most of the statistical information in newspapers, magazines, company reports, and otherpublications consists of data that are summarized and presented in a form that is easy forthe reader to understand Such summaries of data, which may be tabular, graphical, or nu-merical, are referred to as descriptive statistics

Refer again to the data set in Table 1.1 showing data on 25 S&P 500 companies ods of descriptive statistics can be used to provide summaries of the information in this data set For example, a tabular summary of the data for the qualitative variable Exchange isshown in Table 1.4 A graphical summary of the same data, called a bar graph, is shown inFigure 1.4 These types of tabular and graphical summaries generally make the data easier

Meth-to interpret Referring Meth-to Table 1.4 and Figure 1.4, we can see easily that the majority of thestocks in the data set are traded on the New York Stock Exchange On a percentage basis,80% are traded on the New York Stock Exchange and 20% are traded on the Nasdaq Na-tional Market

1.4 Descriptive Statistics 13

Percent Exchange Frequency Frequency

FIGURE 1.4 BAR GRAPH FOR THE EXCHANGE VARIABLE

A graphical summary of the data for the quantitative variable Share Price for the S&Pstocks, called a histogram, is provided in Figure 1.5 The histogram makes it easy to seethat the share prices range from $0 to $100, with the highest concentrations between $20and $60

In addition to tabular and graphical displays, numerical descriptive statistics are used

to summarize data The most common numerical descriptive statistic is the average, ormean Using the data on the variable Earnings per Share for the S&P stocks in Table 1.1,

we can compute the average by adding the earnings per share for all 25 stocks and dividingthe sum by 25 Doing so provides an average earnings per share of $2.49 This averagedemonstrates a measure of the central tendency, or central location, of the data for thatvariable

In a number of fields, interest continues to grow in statistical methods that can be usedfor developing and presenting descriptive statistics Chapters 2 and 3 devote attention to thetabular, graphical, and numerical methods of descriptive statistics