# 12. Interpret two-way tables for categorical data (C)

teaches Common Core State Standards CCSS.Math.Content.8.SP.A.4 http://corestandards.org/Math/Content/8/SP/A/4
teaches Common Core State Standards CCSS.Math.Practice.MP5 http://corestandards.org/Math/Practice/MP5

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Lesson objective: Understand that associations may be found in bivariate categorical data by looking at a two-way table.

Students bring prior knowledge of organizing and interpreting univariate categorical data from 1.MD.C.4. This prior knowledge is extended to bivariate categorical data as students find relative frequencies for a table. A conceptual challenge students may encounter is understanding that conditional frequencies do not use the grand total in the denominator of a percent.

The concept is developed through work with two-way tables, which helps to support finding relative frequencies and conditional frequencies.

This work helps students deepen their understanding of equivalence because relative frequencies can be represented as fractions, decimals, and percents.

Students engage in Mathematical Practice 5 (Use appropriate tools strategically) as they use relative frequencies and conditional frequencies to answer Paige's classmates' questions about her two-way table on eating breakfast and having energy at the end of the day.

Key vocabulary:

• association
• bivariate
• categorical data
• conditional frequency
• percent
• relative frequency
• two-way table
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