Marginal and Conditional
Researchers looking at the relationship between the type of college attended
(public or private) and achievement gather the following data on 3265 people
who graduated from college in the same year. The variable “management
level” describes their job description 20 years after graduating from college.
a. Calculate the marginal distribution of management level in percents.
b. Find the conditional distribution of management level for each college type,
in percents.
c. Sketch the data from part (b) in a segmented bar graph and in a side-by-side
bar graph.
182
1756
1327
1769
1496
3265
a. Calculate the marginal distribution of management level in
percents.
182
High 
 5.6%
3265
1756
Medium 
 53.8%
3265
1327
Low 
 40.6%
3265
182
1756
1327
1769
1496
3265
b. Find the conditional distribution of management level for each
college type, in percents.
Public
High
Medium
Low
𝟕𝟓
=4.2 %
𝟏𝟕𝟔𝟗
𝟗𝟔𝟐
= 54.4 %
𝟏𝟕𝟔𝟗
𝟕𝟑𝟐
𝟏𝟕𝟔𝟗
= 41.4 %
Private
𝟏𝟎𝟕
𝟏𝟒𝟗𝟔
= 7.2 %
𝟕𝟗𝟒
𝟓𝟗𝟓
= 53.1 %
𝟓𝟗𝟓
𝟏𝟒𝟗𝟔
= 39.8 %
Public
Private
High
4.2 %
7.2 %
Medium
54.4 %
53.1 %
Low
41.4 %
39.8 %
c. Sketch the data from part (b) in a segmented bar graph and in
a side-by-side bar graph.
Public
Private
High
4.2 %
7.2 %
Medium
54.4 %
53.1 %
Low
41.4 %
39.8 %
c. Sketch the data from part (b) in a segmented bar graph and in
a side-by-side bar graph.
60
High
High
40
Low
10
Low
Public
Private
Low
Medium
Private
20
20
Public
40
30
Private
Med
Public
%
Med
Private
80
60
50
Public
100
High
Below is a graph showing the total number of Oscar
nominations for the four films that had PG or PG-13 ratings.
What’s wrong with the way the information is presented in this
graph?
Using similar figures to compare heights exaggerates
the differences between frequencies since people
(wrongly) tend to compare areas.
Class
Freq.
20-40
35
40-60
27
60-100
20
100-200 10
200 – 800 28