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Describing Distributions with Numbers

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Describing Distributions with Numbers W. H. Freeman Publishers - The Basic Practi... http://www.whfreeman.com/highschool/book.as... Preview this Book The Basic Practice of Statistics Request Exam Copy Third Edition David S. Moore (Purdue U.) Go To Companion Site Download Text chapters in .PDF format. You will need Adobe Acrobat Reader version 3.0 or above to view these June 2003, cloth, preview materials. (Additional instructions below.) 0-7167-9623-6 Exploring Data: Variables and Distributions Companion Site Chapter 1 - Picturing Distributions with Graphs (CH 01.pdf; 300KB) Summary Chapter 2 - Describing Distributions with Numbers (CH 02.pdf; 212KB) Features Chapter 3 - Normal Distributions (CH 03.pdf; 328KB) New to This Edition Exploring Data: Relationships Media Chapter 4 - Scatterplots and Correlation (CH 04.pdf; 300KB) Supplements Chapter 5 - Regression (CH 05.pdf; 212KB) Table of Chapter 6 - Two-Way Tables (CH 06.pdf; 328KB) Contents Preview Materials These copyrighted materials are for promotional purposes only. They may Other Titles by: not be sold, copied, or distributed. David S. Moore Download Instructions for Preview Materials in .PDF Format We recommend saving these files to your hard drive by following the instructions below. PC users 1. Right-click on a chapter link below 2. From the pop-up menu, select "Save Link", (if you are using Netscape) or "Save Target" (if you are using Internet Explorer) 3. In the "Save As" dialog box, select a location on your hard drive and rename the file, if you would like, then click "save".Note the name and location of the file so you can open it later. Macintosh users 1. Click and hold your mouse on a chapter link below 2. From the pop-up menu, select "Save Link As" (if you are using Netscape) or "Save Target As" (if you are using Internet Explorer) 3. In the "Save As" dialog box, select a location on your hard drive and rename the file, if you would like, then click "save". Note the name and location of the file so you can open it later. 1 of 2 05/03/04 19:56 P1: FBQ PB286A-01 PB286-Moore-V3.cls March 4, 2003 18:19 Exploring Data he first step in understanding data is to hear what the data say, to “let the statistics speak for themselves.” But numbers speak clearly only T when we help them speak by organizing, displaying, summarizing, and asking questions. That’s data analysis. The six chapters in Part I present the ideas and tools of statistical data analysis. They equip you with skills that are immediately useful whenever you deal with numbers. These chapters reflect the strong emphasis on exploring data that character- izes modern statistics. Although careful exploration of data is essential if we are to trust the results of inference, data analysis isn’t just preparation for inference. To think about inference, we carefully distinguish between the data we actually have and the larger universe we want conclusions about. The Bureau of Labor Statistics, for example, has data about employment in the 55,000 households contacted by its Current Population Survey. The bureau wants to draw conclu- sions about employment in all 110 million U.S. households. That’s a complex problem. From the viewpoint of data analysis, things are simpler. We want to explore and understand only the data in hand. The distinctions that inference requires don’t concern us in Chapters 1 to 6. What does concern us is a sys- tematic strategy for examining data and the tools that we use to carry out that strategy. Part of that strategy is to first look at one thing at a time and then at relation- ships. In Chapters 1, 2, and 3 you will study variables and their distributions. Chapters 4, 5, and 6 concern relationships among variables. 0 P1: FBQ PB286A-01 PB286-Moore-V3.cls March 4, 2003 18:19 PART I EXPLORING DATA:VARIABLES AND DISTRIBUTIONS Chapter 1 Picturing Distributions with Graphs Chapter 2 Describing Distributions with Numbers Chapter 3 The Normal Distributions EXPLORING DATA:RELATIONSHIPS Chapter 4 Scatterplots and Correlation Chapter 5 Regression Chapter 6 Two-Way Tables EXPLORING DATA REVIEW 1 P1: FBQ PB286A-01 PB286-Moore-V3.cls March 4, 2003 18:19 2 P1: FBQ PB286A-01 PB286-Moore-V3.cls March 4, 2003 18:19 CHAPTER 1 (Darrell Ingham/Allsport Concepts/Getty Images) In this chapter we cover... Picturing Distributions Individuals and variables Categorical variables: with Graphs pie charts and bar graphs Quantitative variables: histograms Interpreting histograms Quantitative variables: Statistics is the science of data. The volume of data available to us is over- stemplots whelming. Each March, for example, the Census Bureau collects economic and Time plots employment data from more than 200,000 people. From the bureau’s Web site you can choose to examine more than 300 items of data for each person (and more for households): child care assistance, child care support, hours worked, usual weekly earnings, and much more. The first step in dealing with such a flood of data is to organize our thinking about data. Individuals and variables Any set of data contains information about some group of individuals.Thein- formation is organized in variables. INDIVIDUALS AND VARIABLES Individuals are the objects described by a set of data. Individuals may be people, but they may also be animals or things. A variable is any characteristic of an individual. A variable can take different values for different individuals. 3 P1: FBQ PB286A-01 PB286-Moore-V3.cls March 4, 2003 18:19 r 4 CHAPTER 1 Picturing Distributions with Graphs A college’s student data base, for example, includes data about every cur- rently enrolled student. The students are the individuals described by the data set. For each individual, the data contain the values of variables such as date of birth, gender (female or male), choice of major, and grade point average. In practice, any set of data is accompanied by background information that helps us understand the data. When you plan a statistical study or explore data from someone else’s work, ask yourself the following questions: 1. Who? What individuals do the data describe? How many individuals appear in the data? 2. What? How many variables do the data contain? What are the exact definitions of these variables? In what units of measurement is each variable recorded? Weights, for example, might be recorded in pounds, Are data artistic? in thousands of pounds, or in kilograms. David Galenson, an economist 3. Why? What purpose do the data have? Do we hope to answer some at the University of Chicago, specific questions? Do we want to draw conclusions about individuals uses data and statistical other than the ones we actually have data for? Are the variables suitable analysis to study innovation among painters from the for the intended purpose? nineteenth century to the Some variables, like gender and college major, simply place individuals into present. Economics journals categories. Others, like height and grade point average, take numerical values publish his work. Art history for which we can do arithmetic. It makes sense to give an average income for a journals send it back unread.“Fundamentally company’s employees, but it does not make sense to give an “average” gender. antagonistic to the way We can, however, count the numbers of female and male employees and do humanists do their work,” said arithmetic with these counts. the chair of art history at Chicago. If you are a student of the humanities, reading this CATEGORICAL AND QUANTITATIVE VARIABLES statistics text may help you start a new wave in your field. A categorical variable places an individual into one of several groups or categories. A quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense. The distribution of a variable tells us what values it takes and how often it takes these values. EXAMPLE 1.1 A professor’s data set Here is part of the data set in which a professor records information about student performance in a course: P1: FBQ PB286A-01 PB286-Moore-V3.cls March 4, 2003 18:19 Individuals and variables 5 The individuals described are the students. Each row records data on one individual. Each column contains the values of one variable for all the individuals. In addition to the student’s name, there are 7 variables. School and major are categorical vari- ables. Scores on homework, the midterm, and the final exam and the total score are quantitative. Grade is recorded as a category (A, B, and so on), but each grade also corresponds to a quantitative score (A = 4, B = 3, and so on) that is used to calculate student grade point averages. Most data tables follow this format—each row is an individual, and each col- umn is a variable. This data set appears in a spreadsheet program that has rows and spreadsheet columns ready for your use. Spreadsheets are commonly used to enter and transmit data and to do simple calculations such as adding homework, midterm, and final scores to get total points. APPLYYOURKNOWLEDGE 1.1 Fuel economy. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2002 model motor vehicles: Make and Vehicle Transmission Number of City Highway model type type cylinders MPG MPG · · · Acura NSX Two-seater Automatic 6 17 24 Audi A4 Compact Manual 4 22 31 Buick Century Midsize Automatic 6 20 29 Dodge Ram 1500 Standard pickup truck Automatic 8 15 20 · · · (a) What are the individuals in this data set? (b) For each individual, what variables are given? Which of these variables are categorical and which are quantitative? 1.2 A medical study.
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