AP Statistics
Categorical Data
Can be naturally formed (gender, ethnicity,
eye-color, etc).
 Can be formed by grouping quantitative
variables into classes (Old: 50+, Middleage: 30-49, Young: 15-29)
 Can be expressed as either counts or
percents.

Categorical Data



Data is often organized into two-way contingency tables.
Heart Attack
No Heart
Attack
Total
Aspirin
104
10,933
11,037
Placebo
189
10,845
11,034
Total
293
21,778
22,071
Values in red represent the marginal distributions.
22,071 is the grand total. Both marginal distributions add
up to the grand total.
Marginal Distributions


Relates to the total number of values that fall into any
one category. May also be calculated as a percent.
Example: Calculate the marginal distribution of the
medical occurrence (heart attack or not) in percent.
Medical
Occurrence
Heart Attack
No Heart Attack
Percent
1.33%
98.67%
293/22,071
21,778/22,071
Conditional Distribution

Recall the original distribution:

What percent of people who had heart attacks had
taken aspirin? (This is a conditional distribution
question.)
104/293 × 100 = 35.5%

Example





Myers-Briggs Personality Preference and Area of Study
Arts and
Sciences
Business
Allied
Health
Total
in
64
15
17
96
en
82
42
30
154
is
68
35
12
115
es
75
42
37
134
Total
289
134
96
519
“in” is “introvert/intuition (idealist)”.
“en” is “extrovert/intuition (idealist)”.
“is” is “introvert/sensing (realist)”.
“es” is “extrovert/sensing (realist)”.
Example Continued

Find the marginal distribution of personality preferences.
Personality
Preference
in
en
is
es
Percent
18.5%
29.67%
22.16%
25.8%
96/519
154/519
115/519
134/519
Example Continued
What percent of Allied Health majors have
“is” personalities?
 12/95 = 12.5%

Example Continued

What percent of each major have “is”
personalities?
Major
Arts and
Sciences
Business
Allied
Health
Percent
23.5%
26.1%
12.5%
68/289
35/134
12/96
Graphical Displays

Since the data is categorical, a bar graph can be used
for quick and easy interpretation.
Homework

Textbook: 4.51, 4.53-4.58, chapter 4
review