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The Practice of Statistics, 4th edition - For AP* STARNES, YATES, MOORE

Chapter 1: Exploring Data Introduction Data Analysis: Making Sense of Data

+ Chapter 1 Exploring Data

n  Introduction: Data Analysis: Making Sense of Data

n 1.1 Analyzing Categorical Data

n 1.2 Displaying Quantitative Data with Graphs

n 1.3 Describing Quantitative Data with Numbers

+ Introduction Data Analysis: Making Sense of Data

After this section, you should be able to…

ü  DEFINE “Individuals” and “Variables”

ü  DISTINGUISH between “Categorical” and “Quantitative” variables

ü  DEFINE “Distribution”

ü  DESCRIBE the idea behind “Inference”

Learning Objectives

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+Data A

nalysis

n Statistics is the science of data. n Data Analysis is the process of organizing,

displaying, summarizing, and asking questions about data.

Definitions:

Individuals – objects (people, animals, things) described by a set of data Variable - any characteristic of an individual

Categorical Variable (aka qualitative variable) – places an individual into one of several groups or categories.

Quantitative Variable (aka numerical variable) – takes numerical values for which it makes sense to find an average.

+Data A

nalysis n  AP EXAM TIP If you learn to distinguish categorical from

quantitative variables now, it will pay big rewards later. The type of data determines what kinds of graphs and which numerical summaries are appropriate. You will be expected to analyze categorical and quantitative data effectively on the AP exam.

n  Not every variable that takes number values is quantitative. Zip code is one example. Although zip codes are numbers, it doesn’t make sense to talk about the average zip code. In fact, zip codes place individuals (people or dwellings) into categories based on location. Some variables—such as gender, race, and occupation—are categorical by nature. Other categorical variables are created by grouping values of a quantitative variable into classes. For instance, we could classify people in a data set by age: 0–9, 10–19, 20–29, and so on.

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PROBLEM: (a) Who are the individuals in this data set? (b) What variables were measured? Identify each as categorical or quantitative. In what units were the quantitative variables measured? (c) Describe the individual in the highlighted row.

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Solution to Example

(a) The individuals are the 10 randomly selected Canadian students. (b) The eight variables measured are province where student lives (categorical), gender (categorical), number of languages spoken (quantitative, in whole numbers), dominant hand (categorical), height (quantitative, in centimeters), wrist circumference (quantitative, in millimeters), preferred communication method (categorical), and travel time to school (quantitative, in minutes). (c) This student lives in Ontario, is male, speaks three languages, is left-handed, is 150 cm tall (about 59 inches), has a wrist circumference of 100 mm (about 4 inches), prefers to communicate via Internet chat, and travels 10 minutes to get to school.

+Data A

nalysis n A variable generally takes on many different values.

In data analysis, we are interested in how often a variable takes on each value.

Definition:

Distribution – tells us what values a variable takes and how often it takes those values

2009 Fuel Economy Guide

MODEL MPG

1

2

3

4

5

6

7

8

9

Acura RL 22

Audi A6 Quattro 23

Bentley Arnage 14

BMW 5281 28

Buick Lacrosse 28

Cadillac CTS 25

Chevrolet Malibu 33

Chrysler Sebring 30

Dodge Avenger 30

2009 Fuel Economy GuideMODEL MPG <new>

9

10

11

12

13

14

15

16

17

Dodge Avenger 30

Hyundai Elantra 33

Jaguar XF 25

Kia Optima 32

Lexus GS 350 26

Lincolon MKZ 28

Mazda 6 29

Mercedes-Benz E350 24

Mercury Milan 29

2009 Fuel Economy Guide

MODEL MPG <new>

16

17

18

19

20

21

22

23

24

Mercedes-Benz E350 24

Mercury Milan 29

Mitsubishi Galant 27

Nissan Maxima 26

Rolls Royce Phantom 18

Saturn Aura 33

Toyota Camry 31

Volkswagen Passat 29

Volvo S80 25

MPG14 16 18 20 22 24 26 28 30 32 34

2009 Fuel Economy Guide Dot Plot

Variable of Interest: MPG

Dotplot of MPG Distribution

Example

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MPG14 16 18 20 22 24 26 28 30 32 34

2009 Fuel Economy Guide Dot Plot

2009 Fuel Economy GuideMODEL MPG <new>

9

10

11

12

13

14

15

16

17

Dodge Avenger 30

Hyundai Elantra 33

Jaguar XF 25

Kia Optima 32

Lexus GS 350 26

Lincolon MKZ 28

Mazda 6 29

Mercedes-Benz E350 24

Mercury Milan 29

2009 Fuel Economy Guide

MODEL MPG <new>

16

17

18

19

20

21

22

23

24

Mercedes-Benz E350 24

Mercury Milan 29

Mitsubishi Galant 27

Nissan Maxima 26

Rolls Royce Phantom 18

Saturn Aura 33

Toyota Camry 31

Volkswagen Passat 29

Volvo S80 25

2009 Fuel Economy Guide

MODEL MPG

1

2

3

4

5

6

7

8

9

Acura RL 22

Audi A6 Quattro 23

Bentley Arnage 14

BMW 5281 28

Buick Lacrosse 28

Cadillac CTS 25

Chevrolet Malibu 33

Chrysler Sebring 30

Dodge Avenger 30

Add numerical summaries

Data A

nalysis

Examine each variable by itself.

Then study relationships among

the variables. Start with a graph or

graphs

How to Explore Data

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+Data A

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From Data Analysis to Inference

Population

Sample

Collect data from a representative Sample...

Perform Data Analysis, keeping probability in mind…

Make an Inference about the Population.

Inference- drawing conclusions about a population based on information from a sample. When inferring, one must always take into account the idea of probability (you’ll learn more about this in later chapters).

CHECK YOUR UNDERSTANDING

Jake is a car buff who wants to find out more about the vehicles that students at his school drive. He gets permission to go to the student parking lot and record some data. Later, he does some research about each model of car on the Internet. Finally, Jake makes a spreadsheet that includes each car’s model, year, color, number of cylinders, gas mileage, weight, and whether it has a navigation system. 1. Who are the individuals in Jake’s study?

2. What variables did Jake measure? Identify each as categorical or quantitative.

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+ Introduction Data Analysis: Making Sense of Data

In this section, we learned that…

ü  A dataset contains information on individuals.

ü  For each individual, data give values for one or more variables.

ü  Variables can be categorical or quantitative.

ü  The distribution of a variable describes what values it takes and how often it takes them.

ü  Inference is the process of making a conclusion about a population based on a sample set of data.

Summary

+ Looking Ahead…

We’ll learn how to analyze categorical data.

ü Bar Graphs ü Pie Charts ü Two-Way Tables ü Conditional Distributions

We’ll also learn how to organize a statistical problem.

In the next Section…