CHAPTER 1 Exploring Data€¦ · CHAPTER 1 Exploring Data Introduction Data Analysis: Making Sense...

The Practice of Statistics, 5th Edition

Starnes, Tabor, Yates, Moore

Bedford Freeman Worth Publishers

CHAPTER 1Exploring Data

Introduction

Data Analysis:

Making Sense of Data

The Practice of Statistics, 5th Edition 2

Hiring Discrimination Activity

An airline has just finished training 25 pilots – 15 male and 10 female – to

become captains. Unfortunately, only eight captain positions are available right

now. Airline managers announce that they will use a lottery to determine which

pilots will fill the available positions. The names of all 25 pilots will be written on

identical slips of paper. The slips will be placed in a hat, mixed thoroughly, and

drawn out one at a time until all eight captains have been identified.

A day later, managers announce the results of the lottery. Of the 8 captains

chosen, 5 are female and 3 are male. Some of the male pilots who weren’t

selected suspect that the lottery was not carried out fairly. One of these pilots

asks your statistics class for advice about whether to file a grievance with the

pilots’ union.

The key questions in this possible discrimination seems to be: Is it plausible

(believable) that these results happened just by chance? To find out, you and

your classmates will simulate the lottery process that airline managers said

they used.



1. Simulate the number of female pilots randomly selected.

a. Mix the slips of paper thoroughly. Without looking, remove 8 slips from the

cup. Count the number of female pilots selected.

b. Shuffle the cards. Without looking, remove 8 cards. Count the number of

female pilots selected.

c. Numbers 1 -15 to represent male pilots. Numbers 16 – 25 represent female

pilots. Generate random numbers with the following command.

Math, left arrow, 5, “1,25,20”, ), enter

Use the first non-repeated numbers to count the number of female

pilots selected.

2. Please perform simulation “b” three times for each person in the group

each. Record the number of female pilots in each of the trials on the

dotplot.



3. Does it seem believable that airline managers carried out a fair lottery?

What advice would you give the male pilot who contacted you?

4. Would your advice change if the lottery had chosen 6 female (and 2

male) pilots? What about 7 female pilots? Explain.

0 1 2 3 4 5 6 7 8

Number of Female Pilots Selected

Learning Objectives

After this section, you should be able to:


✓ IDENTIFY the individuals and variables in a set of data

✓ CLASSIFY variables as categorical or quantitative

Data Analysis: Making Sense of Data


Data Analysis

Statistics is the science of data.

Data Analysis is the process of organizing, displaying, summarizing,

and asking questions about data.

Individuals

✓ objects described by a set of data

Variable

✓ any characteristic of an individual

Categorical Variable

✓ places an individual into

one of several groups or

categories.

Quantitative Variable

✓ takes numerical values for

which it makes sense to find

an average.


A variable generally takes on many different values.

• We are interested in how often a variable takes on each value.

Distribution

✓ tells us what values a variable takes and how often

it takes those values.

Variable of Interest:

MPG

Dotplot of MPG

Distribution

Data Analysis


Examine each variable

by itself.

Then study relationships

among the variables.

Start with a graph

or graphs

How to Explore Data

Add numerical

summaries


US Census Data

Here is information about 10 randomly selected U.S. residents from a

recent census, imported using Fathom software.

StateNumber of Family

Members Age Gender Marital status Total

Income ($)Travel time to

work (min)

Kentucky 2 61 Female Married 21,000 20

Florida 6 27 Female Married 21,300 20

Wisconsin 2 27 Male Married 30,000 5

California 4 33 Female Married 26,000 10

Michigan 3 49 Female Married 15,100 25

Virginia 3 26 Female Married 25,000 15

Pennsylvania 4 44 Male Married 43,000 10

Virginia 4 22 Male Single 3,000 0

California 1 30 Male Single 40,000 15

New York 4 34 Female Separated 30,000 40

a. Who are the individuals in this data

set?

b. What variables are measured? Identify

each as categorical or quantitative.

c. Describe the individual in the first row.

a. The individuals are the ten randomly selected U.S.

residents from the recent Census

b. Cat.: State, gender, marital status. Quant.: number of

family members, age, income, travel time

c. This individual is a 61 year old married female from

Kentucky. She has two members in her household,

has a total income of $21,000, and drives 20 minutes

to work.


Population

Sample

Collect data from a

representative

Sample...

Perform Data

Analysis, keeping

probability in

mind…

Make an Inference

about the

Population.

From Data Analysis to Inference

Section Summary

In this section, we learned that…


✓ A dataset contains information on individuals.

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

✓ Variables can be categorical or quantitative.

✓ The distribution of a variable describes what values it takes and

how often it takes them.

✓ Inference is the process of making a conclusion about a

population based on a sample set of data.

Data Analysis: Making Sense of Data


HOMEWORK

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