Algebra I: Lesson 5-3 (5073)
SAS® Curriculum Pathways®
Two-Variable Categorical Data: Lesson Summary with Examples
A two-way frequency table is a useful way to display data in order to examine the relationship between two
categorical variables. The rows represent the categories of one variable and the columns represent the categories
of the other variable. Each entry in this type of table represents a frequency count (how often an event occurs).
Marginal frequencies are the entries in the total row and column. Joint frequencies are the entries in the body of
the table.
A two-way relative frequency table displays the relative frequencies for each entry as compared to the total
number of observations.
A relative frequency table by row or by column compares data within a specific category, rather than against the
total number of observations.
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8/1/2012
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Algebra I: Lesson 5-3 (5073)
SAS® Curriculum Pathways®
Two-Way Frequency Table
A two-way frequency table is a table that displays data in order to examine the relationship between two
categorical variables.
The rows represent the categories of one variable and the columns represent the categories of the other
variable. Each entry in this type of table represents a frequency count (how often an event occurs).
The joint frequency refers to the entries in the body of a two-way frequency table. The marginal frequency
refers to the entries in the "total" row and the "total" column of a two-way frequency table.
joint frequencies
marginal frequencies
We can use the joint and marginal frequencies to analyze the data.
 Of those surveyed, 4 were females who drove to work.
 11 of those surveyed drove to work.
 10 of those surveyed were male.
 More men were surveyed than women.
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SAS® Curriculum Pathways®
Algebra I: Lesson 5-3 (5073)
Two-Way Relative Frequency Table
Two-variable categorical data can be displayed in a in a two-way relative frequency table where each entry
represents the frequency of an individual event relative to all observations in the table.
Ice Cream Survey 125 people were asked to name their favorite flavor of ice cream.
To display the data in a two-way relative frequency table, divide each table entry by 125, the total number
surveyed. The values can be expressed as ratios, decimals, or percentages.
Ratios
Decimals
Percentages
When interpreting a two-way relative frequency table, remember that each entry is being compared to the
total number of observations. It is common to use phrases like "What percent of the total…" or "Of the number
surveyed…" when interpreting relative frequencies. We may also look at each value as the intersection of two
categories.
For example, 12.8% of the people surveyed are men who prefer chocolate ice cream.
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Algebra I: Lesson 5-3 (5073)
SAS® Curriculum Pathways®
Relative Frequency by Row and by Column
Another way to look at data is to compare values within a specific category rather than against the total
number of observations. These tables display the relative frequency by row or by column where each entry
represents the frequency of an individual event relative to the total number of observations for the row or the
column. These two different types of relative frequency tables allow us to look at different relationships within
the data.
Favorite Activity Survey 100 adults were asked their favorite recreational activity: shopping, going to the
movies, or playing sports.
Relative Frequency Table by Row
To complete the relative frequency table by row, find the total number of observations for each row. Then
divide each row entry by the total number of observations for that row.
Identify the total number of observations for each row.
Divide all row entries by the total number of observations for the row.
Simplify.
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8/1/2012
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Algebra I: Lesson 5-3 (5073)
SAS® Curriculum Pathways®
Relative Frequency Table by Column
To complete the relative frequency table by column, find the total number of observations for each column.
Then divide each column entry by the total number of observations for that column.
When interpreting relative frequencies by row or column, keep in mind that each entry is being compared to
the total number of observations in its row or column. Therefore, it is common to use phrases that refer to the
subcategories, like "what percent of the men" or "of the group surveyed who like shopping", when interpreting
these relative frequencies.
Examples:

The statement, "Of those who preferred going to the movies, 38.1% were female" interprets the relative
frequency by column.

The statement, "62.5% of males that preferred playing sports" interprets the relative frequency by row.
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8/1/2012
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