Business Statistics For Dummies

411 Pages·2013·47.35 MB·English

by  Alan Anderson

Business
Statistics
by Alan Anderson, PhD
Business Statistics For Dummies®
Published by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com
Copyright © 2014 by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or
by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permit-
ted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permis-
sion of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions
Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, [phone], fax (201) 748-
6008, or online at http://www.wiley.com/go/permissions.
Trademarks: Wiley, For Dummies, the Dummies Man logo, Dummies.com, Making Everything Easier, and
related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc., and may not be
used without written permission. All other trademarks are the property of their respective owners. John
Wiley & Sons, Inc., is not associated with any product or vendor mentioned in this book.
LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: THE PUBLISHER AND THE AUTHOR MAKE NO
REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF
THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES, INCLUDING WITH-
OUT LIMITATION WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE
CREATED OR EXTENDED BY SALES OR PROMOTIONAL MATERIALS. THE ADVICE AND STRATEGIES
CONTAINED HEREIN MAY NOT BE SUITABLE FOR EVERY SITUATION. THIS WORK IS SOLD WITH THE
UNDERSTANDING THAT THE PUBLISHER IS NOT ENGAGED IN RENDERING LEGAL, ACCOUNTING, OR
OTHER PROFESSIONAL SERVICES. IF PROFESSIONAL ASSISTANCE IS REQUIRED, THE SERVICES OF
A COMPETENT PROFESSIONAL PERSON SHOULD BE SOUGHT. NEITHER THE PUBLISHER NOR THE
AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM. THE FACT THAT AN ORGANIZA-
TION OR WEBSITE IS REFERRED TO IN THIS WORK AS A CITATION AND/OR A POTENTIAL SOURCE
OF FURTHER INFORMATION DOES NOT MEAN THAT THE AUTHOR OR THE PUBLISHER ENDORSES
THE INFORMATION THE ORGANIZATION OR WEBSITE MAY PROVIDE OR RECOMMENDATIONS IT
MAY MAKE. FURTHER, READERS SHOULD BE AWARE THAT INTERNET WEBSITES LISTED IN THIS
WORK MAY HAVE CHANGED OR DISAPPEARED BETWEEN WHEN THIS WORK WAS WRITTEN AND
WHEN IT IS READ.
For general information on our other products and services, please contact our Customer Care
Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].
For technical support, please visit www.wiley.com/techsupport.
Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material
included with standard print versions of this book may not be included in e-books or in print-on-demand.
If this book refers to media such as a CD or DVD that is not included in the version you purchased, you
may download this material at http://booksupport.wiley.com. For more information about Wiley
products, visit www.wiley.com.
Library of Congress Control Number: 2013944875
ISBN 978-1-118-63069-3 (pbk); ISBN 978-1-118-78458-7 (ePub); ISBN 978-1-118-78449-5 (PDF)
Manufactured in the United States of America
10 9 8 7 6 5 4 3 2 1
Contents at a Glance
Introduction ................................................................ 1
Part I: Getting Started with Business Statistics .............. 5
Chapter 1: The Art and Science of Business Statistics .................................................7
Chapter 2: Pictures Tell the Story: Graphical Representations of Data ...................23
Chapter 3: Finding a Happy Medium: Identifying the Center of a Data Set ..............39
Chapter 4: Searching High and Low: Measuring Variation in a Data Set ..................55
Chapter 5: Measuring How Data Sets Are Related to Each Other .............................71
Part II: Probability Theory and Probability
Distributions ............................................................. 91
Chapter 6: Probability Theory: Measuring the Likelihood of Events ........................93
Chapter 7: Probability Distributions and Random Variables ..................................111
Chapter 8: The Binomial, Geometric, and Poisson Distributions ............................121
Chapter 9: The Uniform and Normal Distributions: So Many Possibilities! ...........139
Chapter 10: Sampling Techniques and Distributions ................................................165
Part III: Drawing Conclusions from Samples............... 185
Chapter 11: Confidence Intervals and the Student’s t-Distribution ........................187
Chapter 12: Testing Hypotheses about the Population Mean .................................201
Chapter 13: Testing Hypotheses about Multiple Population Means .......................233
Chapter 14: Testing Hypotheses about the Population Mean .................................251
Part IV: More Advanced Techniques:
Regression Analysis and Forecasting ......................... 281
Chapter 15: Simple Regression Analysis .....................................................................283
Chapter 16: Multiple Regression Analysis: Two or More
Independent Variables ...............................................................................................309
Chapter 17: Forecasting Techniques: Looking into the Future ................................327
Part V: The Part of Tens ........................................... 351
Chapter 18: Ten Common Errors That Arise in Statistical Analysis .......................353
Chapter 19: Ten Key Categories of Formulas for Business Statistics .....................361
Index ...................................................................... 373

Table of Contents
Introduction ................................................................. 1
About This Book ..............................................................................................1
Foolish Assumptions .......................................................................................2
Icons Used in This Book .................................................................................2
Beyond the Book .............................................................................................3
Where to Go from Here ...................................................................................3
Part I: Getting Started with Business Statistics .............. 5
Chapter 1: The Art and Science of Business Statistics . . . . . . . . . . . . . 7
Representing the Key Properties of Data .....................................................8
Analyzing data with graphs ..................................................................8
Defining properties and relationships
with numerical measures ..................................................................11
Probability: The Foundation of All Statistical Analysis ............................13
Random variables ................................................................................14
Probability distributions .....................................................................15
Using Sampling Techniques and Sampling Distributions .........................17
Statistical Inference: Drawing Conclusions from Data ..............................18
Confidence intervals ............................................................................18
Hypothesis testing ...............................................................................19
Simple regression analysis .................................................................20
Multiple regression analysis ...............................................................21
Forecasting techniques .......................................................................21
Chapter 2: Pictures Tell the Story: Graphical
Representations of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Analyzing the Distribution of Data by Class or Category .........................24
Frequency distributions for quantitative data .................................25
Frequency distribution for qualitative values ..................................29
Cumulative frequency distributions ..................................................30
Histograms: Getting a Picture of Frequency Distributions ......................31
Checking Out Other Useful Graphs .............................................................34
Line graphs: Showing the values of a data series ............................34
Pie charts: Showing the composition of a data set .........................35
Scatter plots: Showing the relationship
between two variables .....................................................................36
vi
Business Statistics For Dummies
Chapter 3: Finding a Happy Medium: Identifying the Center
of a Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Looking at Methods for Finding the Mean ..................................................40
Arithmetic mean ..................................................................................40
Geometric mean ...................................................................................42
Weighted mean.....................................................................................44
Getting to the Middle of Things: The Median of a Data Set ......................48
Comparing the Mean and Median ...............................................................49
Determining the relationship between mean and median .............50
Acknowledging the relative advantages and disadvantages
of the mean and median ..................................................................52
Discovering the Mode: The Most Frequently Repeated Element ............53
Chapter 4: Searching High and Low:
Measuring Variation in a Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Determining Variance and Standard Deviation .........................................55
Finding the sample variance...............................................................56
Finding the sample standard deviation ............................................57
Calculating population variance and standard deviation ..............61
Finding the Relative Position of Data ..........................................................64
Percentiles: Dividing everything into hundredths ..........................64
Quartiles: Dividing everything into fourths ......................................66
Interquartile range: Identifying the middle 50 percent ...................67
Measuring Relative Variation .......................................................................68
Coefficient of variation: The spread of a data set
relative to the mean .........................................................................69
Comparing the relative risks of two portfolios ................................70
Chapter 5: Measuring How Data Sets Are Related to Each Other . . . . 71
Understanding Covariance and Correlation ..............................................71
Sample covariance and correlation ...................................................73
Population covariance and correlation coefficient .........................77
Comparing correlation and covariance ............................................82
Interpreting the Correlation Coefficient .....................................................85
Showing the relationship between two variables ............................86
Application: Correlation and the benefits of diversification ..........88
Part II: Probability Theory and Probability
Distributions .............................................................. 91
Chapter 6: Probability Theory: Measuring
the Likelihood of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Working with Sets ..........................................................................................93
Membership ..........................................................................................94
Subset ....................................................................................................94
vii
Table of Contents
Union .....................................................................................................95
Intersection ...........................................................................................96
Complement .........................................................................................97
Betting on Uncertain Outcomes ..................................................................98
The sample space: Everything that can happen ..............................99
Event: One possible outcome .............................................................99
Computing probabilities of events ..................................................101
Looking at Types of Probabilities ..............................................................102
Unconditional (marginal) probabilities:
When events are independent ......................................................102
Joint probabilities: When two things happen at once ..................103
Conditional probabilities: When one event depends
on another .......................................................................................104
Determining independence of events..............................................105
Following the Rules: Computing Probabilities .........................................106
Addition rule .......................................................................................106
Complement rule ...............................................................................108
Multiplication rule .............................................................................109
Chapter 7: Probability Distributions and Random Variables . . . . . . .111
Defining the Role of the Random Variable ...............................................111
Assigning Probabilities to a Random Variable ........................................114
Calculating the probability distribution .........................................114
Visualizing probability distribution with a histogram ..................116
Characterizing a Probability Distribution with Moments ......................117
Understanding the summation operator (Σ) .................................117
Expected value ...................................................................................117
Variance and standard deviation .....................................................119
Chapter 8: The Binomial, Geometric,
and Poisson Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Looking at Two Possibilities with the Binomial Distribution ................122
Checking out the binomial distribution ..........................................122
Computing binomial probabilities ...................................................123
Moments of the binomial distribution ............................................127
Graphing the binomial distribution .................................................129
Determining the Probability of the Outcome That Occurs First:
Geometric Distribution ...........................................................................131
Computing geometric probabilities.................................................131
Moments of the geometric distribution ..........................................132
Graphing the geometric distribution ..............................................134
Keeping the Time: The Poisson Distribution ...........................................134
Computing Poisson probabilities ....................................................135
Graphing the Poisson distribution ..................................................137
viii
Business Statistics For Dummies
Chapter 9: The Uniform and Normal Distributions:
So Many Possibilities! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Comparing Discrete and Continuous Distributions ................................140
Working with the Uniform Distribution ....................................................142
Graphing the uniform distribution ..................................................143
Discovering moments of the uniform d istribution ........................144
Computing uniform probabilities ....................................................147
Understanding the Normal Distribution ...................................................150
Graphing the normal distribution ....................................................151
Getting to know the standard normal distribution .......................154
Computing standard normal probabilities .....................................154
Computing normal probabilities other than standard normal ....161
Chapter 10: Sampling Techniques and Distributions . . . . . . . . . . . . . 165
Sampling Techniques: Choosing Data from a Population ......................166
Probability sampling .........................................................................167
Nonprobability sampling ..................................................................172
Sampling Distributions ...............................................................................174
Portraying sampling distributions graphically ..............................175
Moments of a sampling distribution ...............................................178
The Central Limit Theorem ........................................................................179
Converting to a standard normal random variable ...................179
Part III: Drawing Conclusions from Samples ............... 185
Chapter 11: Confidence Intervals and
the Student’s t-Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Almost Normal: The Student’s t-Distribution ..........................................188
Properties of the t-distribution ........................................................188
Graphing the t-distribution ...............................................................190
Probabilities and the t-table .............................................................193
Point estimates vs. interval estimates ............................................194
Estimating confidence intervals for the population mean ...........195
Chapter 12: Testing Hypotheses about the Population Mean . . . . . . 201
Applying the Key Steps in Hypothesis Testing
for a Single Population Mean ..................................................................202
Writing the null hypothesis ..............................................................202
Coming up with an alternative hypothesis .....................................202
Choosing a level of significance .......................................................205
Computing the test statistic .............................................................207
Comparing the critical value(s) .......................................................208
Using the decision rule......................................................................216