# Lesson 3

Associations in Categorical Data

### Lesson Narrative

The mathematical purpose of this lesson is to recognize association among variables by analyzing relative frequency tables. Students learn that association between two variables means that the two variables are statistically related to each other. The work of this lesson connects to previous work because students created and interpreted relative frequency tables. The work of this lesson connects to upcoming work because students will learn about relationships between two numerical variables. When students create and analyze relative frequency tables to make decisions about associations between two variables, they are looking for and making use of structure (MP7).

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems (MP5). We recommend making technology available.

### Learning Goals

Teacher Facing

• Inspect patterns in relative frequency tables and two-way tables to determine if there is a possible association between two variables of interest.

### Student Facing

• Let’s look for relationships between categorical variables.

### Student Facing

• I can look for patterns in two-way tables and relative frequency tables to see if there is a possible association between two variables.

### Glossary Entries

• association

In statistics we say that there is an association between two variables if the two variables are statistically related to each other; if the value of one of the variables can be used to estimate the value of the other.

• categorical variable

A variable that takes on values which can be divided into groups or categories. For example, color is a categorical variable which can take on the values, red, blue, green, etc.

• relative frequency table

A version of a two-way table in which the value in each cell is divided by the total number of responses in the entire table or by the total number of responses in a row or a column.

The table illustrates the first type for the relationship between the condition of a textbook and its price for 120 of the books at a college bookstore.

$10 or less more than$10 but less than $30$30 or more
new 0.025 0.075 0.225
used 0.275 0.300 0.100
• two-way table

A way of organizing data from two categorical variables in order to investigate the association between them.

has a cell phone does not have a cell phone
10–12 years old 25 35
13–15 years old 38 12
16–18 years old 52 8
• variable (statistics)

A characteristic of individuals in a population that can take on different values

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