# Two-way frequency tables

## • Interpret a two-way table (S-ID.B.5). • Understand that the choices made when organizing data can lead to different conclusions (S-ID.B.5).

Sometimes, it is illuminating to categorize univariate data, especially when the categories might influence the values of the variable. For example, in health studies, participants are often categorized as smokers and non-smokers, or men and women.

1 Musical Preferences

WHAT: The 54 students in one of several middle school classrooms were asked two questions about musical preferences: “Do you like rock?” “Do you like rap?” The responses are summarized in a table. Students are asked several questions requiring them to understand and interpret the table, draw some conclusions, and explain them (MP3). This task introduces positive association and percentages based on the table.

WHY: The basic idea is for students to demonstrate that they know what it means for two variables to be associated: that if we knew someone were in one group (for example, they like rap), we now know more about their preferences for rock than if we knew nothing at all. This task returns to ideas about sample size and data collection from section 1 of this unit.

## External Resources

1 Two-Way Frequency Tables

#### Description

WHAT: This lesson allows students to understand two-way frequency tables based on data from their own class. It adds the ideas of joint, marginal and conditional frequencies (S-ID.B.5).

WHY: This is largely an opportunity for procedural fluency practice. Working with data about themselves and their peers is motivating.