# Lesson 2

Relative Frequency Tables

### Lesson Narrative

The mathematical purpose of this lesson is for students to create and interpret relative frequency tables. Students are introduced to relative frequency tables which are created by dividing each value in a two-way table by the total number of responses in the entire table, or the total number of responses in a row or a column. For example, there may be 33 students who list math as their favorite subject in grade 9. These 33 students may represent 7% of the entire school, 21% of 9th graders, or 31% of students in the school who listed math as their favorite subject.

The work of this lesson connects to previous work in which students created and interpreted two-way tables. The work of this lesson connects to upcoming work because students will use relative frequency tables to look for associations between categorical variables.

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

• Calculate values in relative frequency tables by row, by column, or by total.
• Create relative frequency tables based on information given in a two-way table or in everyday language.
• Interpret values (orally and in writing) in relative frequency tables.

### Student Facing

• Let’s find relative frequencies of categorical data.

### Student Facing

• I can calculate values in a relative frequency table and describe what the values mean in everyday language.

### Glossary Entries

• 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
• variable (statistics)

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