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Statistics Demystified STAN GIBILISCO McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-147104-9 The material in this eBook also appears in the print version of this title: 0-07-143118-7. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. 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DOI: 10.1036/0071431187 For more information about this title, click here For more information about this title, click here CONTENTS Preface xi Acknowledgments xiii PART 1: STATISTICAL CONCEPTS 1 CHAPTER 1 Background Math 3 Sets 3 Relations and Functions 7 Numbers 12 One-Variable Equations 17 Simple Graphs 20 Tweaks, Trends, and Correlation 25 Quiz 32 CHAPTER 2 Learning the Jargon 35 Experiments and Variables 35 Populations and Samples 38 vii viii CONTENTS Distributions 41 More Definitions 47 Quiz 60 CHAPTER 3 Basics of Probability 63 The Probability Fallacy 63 Key Definitions 65 Properties of Outcomes 70 Permutations and Combinations 79 The Density Function 82 Two Common Distributions 86 Quiz 91 CHAPTER 4 Descriptive Measures 94 Percentiles 94 Quartiles and Deciles 102 Intervals by Element Quantity 106 Fixed Intervals 111 Other Specifications 117 Quiz 121 Test: Part One 125 CONTENTS ix PART 2: STATISTICS IN ACTION 141 CHAPTER 5 Sampling and Estimation 143 Source Data and Sampling Frames 143 Random Sampling 148 Estimation 155 Confidence Intervals 161 Quiz 169 CHAPTER 6 Hypotheses, Prediction, and Regression 171 Assumptions and Testing 171 What’s the Forecast? 178 Regression 185 Quiz 196 CHAPTER 7 Correlation, Causation, Order, and Chaos 200 Correlation Principles 200 Causes and Effects 208 Chaos, Bounds, and Randomness 215 Quiz 230 CHAPTER 8 Some Practical Problems 234 Frequency Distributions 234 Variance and Standard Deviation 244 x CONTENTS Probability 249 Data Intervals 254 Sampling and Estimation 260 Hypotheses, Prediction, and Regression 264 Correlation and Causation 268 Quiz 271 Test: Part Two 276 Final Exam 296 Answers to Quiz, Test, and Exam Questions 326 Suggested Additional References 329 Index 331 PREFACE This book is for people who want to learn or review the basic concepts and definitionsinstatisticsandprobabilityatthehigh-schoollevel.Itcanserveas asupplementaltextinaclassroom,tutored,orhome-schoolingenvironment. Itshouldbeusefulforcareerchangerswhoneedtorefreshtheirknowledge.I recommend that you start at the beginning of this book and go straight through. Many students have a hard time with statistics. This is a preparatory text that can get you ready for a standard course in statistics. If you’ve had trouble with other statistics books because they’re too difficult, or because you find yourself performing calculations without any idea of what you’re really doing, this book should help you. This book contains numerous practice quiz, test, and exam questions. They resemble the sorts of questions found in standardized tests. There is a short quiz at the end of every chapter. The quizzes are ‘‘open-book.’’ You may (and should) refer to the chapter texts when taking them. When you think you’re ready, take the quiz, write down your answers, and then give your list of answers to a friend. Have the friend tell you your score, but not which questions you got wrong. The answers are listed in the back of the book. Stick with a chapter until you get most of the answers correct. This book is divided into two multi-chapter parts, followed by part tests. Take these tests when you’re done with the respective parts and have taken all the chapter quizzes. The part tests are ‘‘closed-book,’’ but the questions are easier than those in the quizzes. A satisfactory score is 75% or more correct. Again, answers are in the back of the book. Thereisafinalexamattheendofthiscourse.Itcontainsquestionsdrawn uniformly from all the chapters in the book. Take it when you have finished bothparts,bothparttests,andallofthechapterquizzes.Asatisfactoryscore isatleast75%correctanswers.Withtheparttestsandthefinalexam,aswith thequizzes,haveafriendtellyouyourscorewithoutlettingyouknowwhich xi Copyright © 2004 by The McGraw-Hill Companies, Inc. Click here for terms of use. xii PREFACE questions you missed. That way, you will not subconsciously memorize the answers.Youcanchecktoseewhereyourknowledgeisstrongandwhereitis not. I recommend that you complete one chapter every couple of weeks. An hour or two daily ought to be enough time for this. When you’re done with the course, you can use this book, with its comprehensive index, as a perma- nent reference. Suggestions for future editions are welcome. STANGIBILISCO ACKNOWLEDGMENTS Illustrations in this book were generated with CorelDRAW. Some of the clip art is courtesy of Corel Corporation. I extend thanks to Steve Sloat and Tony Boutelle, who helped with the technical evaluation of the manuscript. xiii Copyright © 2004 by The McGraw-Hill Companies, Inc. Click here for terms of use. PART ONE Statistical Concepts Copyright © 2004 by The McGraw-Hill Companies, Inc. Click here for terms of use.
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