 # Summarizing Bivariate Categorical Data

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Common Core For Algebra I

Examples, videos, and solutions to help Algebra I students learn how to summarize bivariate categorical data.

### New York State Common Core Math Algebra I, Module 2, Lesson 9

Worksheets for Algebra I, Module 2, Lesson 9 (pdf)

Student Outcomes

Students distinguish between categorical data and numerical data.

Students summarize data on two categorical variables collected from a sample using a two-way frequency table.

Lesson Summary

• Categorical data are data that take on values that are categories rather than numbers. Examples include male or female for the categorical variable of gender or the five superpower categories for the categorical variable of superpower qualities.
• A two-way frequency table is used to summarize bivariate categorical data.
• The number in a two-way frequency table at the intersection of a row and column of the response to two categorical variables represents a joint frequency.
• The total number of responses for each value of a categorical variable in the table represents the marginal frequency for that value.

Exit Ticket

1. A survey asked the question “How tall are you to the nearest inch?” A second question on this survey asked, “What sports do you play?” Indicate what type of data, numerical or categorical, would be collected from the first question? What type of data would be collected from the second question?

Another random sample of 100 surveys was selected. Jill had a copy of the frequency table that summarized these 100 surveys. Unfortunately, she spilled part of her lunch on the copy. The following summaries were still readable:

2. Help Jill recreate the table by determining the frequencies for cells (c), (e), (j), and (q).

3. Of the cells (c), (e), (j), and (q), which cells represent joint frequencies?

4. Of the cells (c), (e), (j), and (q), which cells represent marginal frequencies?

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