Transcript Slide 1

+ Do Now:
Mr. Buckley gathered some information on his class
and organized it in a table similar to the one below:
1) What individuals does this data set describe?
2) Identity each quantitative and each categorical variable.
3) Describe the distribution of ACT scores.
4) Could we infer from this set of data that students who prefer
math and science perform better on the ACT? Explain.
Student
Gender
ACT Score
Favorite Subject
GPA
James
M
34
Statistics
3.89
Jen
F
35
Biology
3.75
DeAnna
F
32
History
4.00
Jonathan
M
28
Literature
3.00
Doug
M
33
Algebra
2.89
Sharon
F
30
Spanish
3.25
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Check yourself!! Use your learning
objective sheet

Learning Target Check: Rank yourself on the following
objectives.

______ I can identify individuals and variables for a set of data

______ I can define categorical and quantitative variables

______ I can describe the distribution of a set of data

______ I can identify key characteristics of a set of data.
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Chapter 1: Exploring Data
Section 1.1
Analyzing Categorical Data
The Practice of Statistics, 4th edition - For AP*
STARNES, YATES, MOORE
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Chapter 1
Exploring Data
 Introduction:
Data Analysis: Making Sense of Data
 1.1
Analyzing Categorical Data
 1.2
Displaying Quantitative Data with Graphs
 1.3
Describing Quantitative Data with Numbers
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Section 1.1
Analyzing Categorical Data
Learning Objectives
After this section, you should be able to…

CONSTRUCT and INTERPRET bar graphs and pie charts

RECOGNIZE “good” and “bad” graphs

CONSTRUCT and INTERPRET two-way tables

DESCRIBE relationships between two categorical variables

ORGANIZE statistical problems


The values of a categorical variable are labels for the
different categories
The distribution of a categorical variable lists the count or
percent of individuals who fall into each category.
Example, page 8
Frequency Table
Format
Variable
Values
Relative Frequency Table
Count of
Stations
Format
Percent of
Stations
Adult Contemporary
1556
Adult Contemporary
Adult Standards
1196
Adult Standards
8.6
Contemporary Hit
4.1
Contemporary Hit
569
11.2
Country
2066
Country
14.9
News/Talk
2179
News/Talk
15.7
Oldies
1060
Oldies
Religious
2014
Religious
14.6
Rock
869
Rock
Count
6.3
Spanish Language
750
Other Formats
Total
1579
13838
7.7
Spanish Language
Percent
5.4
Other Formats
11.4
Total
99.9
Analyzing Categorical Data
Variables place individuals into one of
several groups or categories
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 Categorical
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categorical data
Frequency tables can be difficult to read. Sometimes
is is easier to analyze a distribution by displaying it
with a bar graph or pie chart.
Frequency Table
Format
Relative Frequency Table
Count of
Count of Stations
Stations
Format
Percent of
Percent of Stations
Stations
2500Adult Contemporary
1556
Adult Contemporary
2000Adult Standards
1196
Adult Standards
Contemporary Hit
1500
Country
1000
News/Talk
500Oldies
0Religious
Adult
11.2
Contemporary
Adult Standards
8.6
Contemporary hit
569
2066
11%
11%
Contemporary
Hit
5%
9%
Country
6%
2179
News/Talk
1060
Oldies
2014
8%
Religious
Country
14.9
4%
News/Talk
Oldies
15%
15%
16%
4.1
15.7
Religious 7.7
Rock
14.6
Rock
869
Rock
Spanish
6.3
Spanish Language
750
Spanish Language
Other
5.4
Other Formats
Total
1579
13838
Other Formats
11.4
Total
99.9
Analyzing Categorical Data
 Displaying
Good and Bad
Our eyes react to the area of the bars as well as
height. Be sure to make your bars equally wide.
Avoid the temptation to replace the bars with pictures
for greater appeal…this can be misleading!
Analyzing Categorical Data
Bar graphs compare several quantities by comparing
the heights of bars that represent those quantities.
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 Graphs:
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This ad for DIRECTV
has multiple problems.
How many can you
point out?
Pg. 10
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What type of graph would be
best to display this data?
Explain
When a dataset involves two categorical variables, we begin by
examining the counts or percents in various categories for one
of the variables.
Definition:
Two-way Table – describes two categorical
variables, organizing counts according to a row
variable and a column variable.
Example, p. 12
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance
96
98
194
Some chance, but probably not
426
286
712
A 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
What are the variables
described by this twoway table?
How many young
adults were surveyed?
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Tables and Marginal Distributions
Analyzing Categorical Data
 Two-Way
Definition:
The Marginal Distribution of one of the
categorical variables in a two-way table of
counts is the distribution of values of that
variable among all individuals described by the
table.
Note: Percents are often more informative than counts,
especially when comparing groups of different sizes.
To examine a marginal distribution,
1)Use the data in the table to calculate the marginal
distribution (in percents) of the row or column totals.
2)Make a graph to display the marginal distribution.
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Tables and Marginal Distributions
Analyzing Categorical Data
 Two-Way
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Tables and Marginal Distributions
Analyzing Categorical Data
 Two-Way
Example, p. 13
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance
96
98
194
Some chance, but probably not
426
286
712
A 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Chance of being wealthy by age 30
Percent
Almost no chance
194/4826 =
4.0%
Some chance
712/4826 =
14.8%
A 50-50 chance
1416/4826 =
29.3%
A good chance
1421/4826 =
29.4%
Almost certain
1083/4826 =
22.4%
Percent
Response
Examine the marginal
distribution of chance
of getting rich.
35
30
25
20
15
10
5
0
Almost none Some chance 50-50 chance Good chance
Survey Response
Almost
certain

Marginal distributions tell us nothing about the relationship
between two variables.
Definition:
A Conditional Distribution of a variable
describes the values of that variable among
individuals who have a specific value of another
variable.
To examine or compare conditional distributions,
1)Select the row(s) or column(s) of interest.
2)Use the data in the table to calculate the conditional
distribution (in percents) of the row(s) or column(s).
3)Make a graph to display the conditional distribution.
• Use a side-by-side bar graph or segmented bar
graph to compare distributions.
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Between Categorical Variables
Analyzing Categorical Data
 Relationships
Example, p. 15
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance
96
98
194
Some chance, but probably not
426
286
712
A 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Calculate the conditional
distribution of opinion
among males.
Examine the relationship
between gender and
opinion.
Chance
ofofbeing
being
byage
age
Chance
age
30
Chanceof
being wealthy
wealthy by
3030
Response
Male
Female
100%
Almost no chance
98/2459 =
4.0%
96/2367 =
4.1%
90%
286/2459 =
11.6%
426/2367 =
18.0%
720/2459 =
29.3%
696/2367 =
29.4%
758/2459 =
30.8%
663/2367 =
28.0%
597/2459 =
24.3%
486/2367 =
20.5%
A 50-50 chance
A good chance
Almost certain
80%
3570%
35
3060%
30
2550%
25
20
20
1540%
15
1030%
10
55
0020%
Percent
Percent
Some chance
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Tables and Conditional Distributions
Analyzing Categorical Data
 Two-Way
Almost certain
Good chance
Male
50-50 chance
Ma
Some
50-50
Good
Almost no Some
chance50-50
chance Good
chance
10%Almost
0%
chance
chance
chance
Males
chance
chance
Females
OpinionOpinion
Opinion
Fem
Almost
Almost
Some chance
certain
certain
Almost no chan

As you learn more about statistics, you will be asked to solve
more complex problems.

Here is a four-step process you can follow.
How to Organize a Statistical Problem: A Four-Step Process
State: What’s the question that you’re trying to answer?
Plan: How will you go about answering the question? What
statistical techniques does this problem call for?
Do: Make graphs and carry out needed calculations.
Conclude: Give your practical conclusion in the setting of the
real-world problem.
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a Statistical Problem
Analyzing Categorical Data
 Organizing

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Using the 4-Step Process
State: What is the relationship between gender and responses

Plan:

Do:

Conclude:
Percent
to the question “What do you think are the chances you will
have much more than a middle-classChance
income
at wealthy
age 30?”
of being
by age 30
35
30
25
20
15
10
5
0
Males
Fema
Almost no
chance
Some
chance
50-50
chance
Good
chance
Opinion
Pg. 18
Almost
certain
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Section 1.1
Analyzing Categorical Data
Summary
In this section, we learned that…

The distribution of a categorical variable lists the categories and gives
the count or percent of individuals that fall into each category.

Pie charts and bar graphs display the distribution of a categorical
variable.

A two-way table of counts organizes data about two categorical
variables.

The row-totals and column-totals in a two-way table give the marginal
distributions of the two individual variables.

There are two sets of conditional distributions for a two-way table.
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Section 1.1
Analyzing Categorical Data
Summary, continued
In this section, we learned that…

We can use a side-by-side bar graph or a segmented bar graph
to display conditional distributions.

To describe the association between the row and column variables,
compare an appropriate set of conditional distributions.

Even a strong association between two categorical variables can be
influenced by other variables lurking in the background.

You can organize many problems using the four steps state, plan,
do, and conclude.
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Looking Ahead…
In the next Section…
We’ll learn how to display quantitative data.
Dotplots
Stemplots
Histograms
We’ll also learn how to describe and compare
distributions of quantitative data.