55
STAT 100A
Chapter 3: Describing Bivariate Data
Sections 3.1-3.2: Bivariate Data & Graphs for Qualitative Variables
Sometimes the data that are collected consist of
observations for two variables on the same
experimental unit. Special techniques that can be
used in describing these variables will help you
identify possible relationships between them.
Bivariate Data Sets
qualitative, qualitative
qualitative, quantitative
quantitative, quantitative
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Side-by-Side Bar Graph
A side-by-side bar graph is used to compare two or
more sets of qualitative data.
Note: Data sets should always be compared by using relative
frequencies, because different sample or population sizes make
comparisons using frequencies difficult.
Example: In a class survey, Penn State statistics students
were asked, “Regarding your weight, do you think you are:
About right? Overweight? Underweight?” The following
graph displays the results by sex.
female
male
about right overweight underweight
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
perception
relative frequency
Gender and Perception of Weigh t
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Side-by-Side Pie Charts
Side-by-side pie charts are used to compare two or
more sets of qualitative data.
Example: The color distributions for two snacksize
bags of M&M’s candies, one plain and one peanut,
are displayed first in a contingency table and then in
side-by-side pie charts.
Brown Yellow Red Orange Green Blue
Plain 15 14 12 4 5 6
Peanut 6 2 2 3 3 5
Peanut Plain Brown
Yellow
Red
Orange
Green
Blue
Category
Blue
23.8%
Green
14.3%
Orange
14.3%
Red
9.5%
Yellow
9.5%
Brown
28.6%
Blue
10.7%
Green
8.9%
Orange
7.1%
Red
21.4% Yellow
25.0%
Brown
26.8%
Panel variable: Type
Pie Chart of Color by Ty pe of M&M's
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STAT 100A
Section 3.3: Scatterplots for Two Quantitative Variables
To determine whether a linear relationship between y
and x is plausible, it is helpful to plot the sample data
in a scatterplot.
scatterplot – shows the relationship between two
quantitative variables measured on the same
experimental units with one variable’s values plotted
along the vertical axis and the other along the
horizontal axis. Each experimental unit in the data
appears as the point in the plot fixed by the values of
both variables for that experimental unit.
