Learn on PengienVision, Mathematics, Grade 8Chapter 4: Investigate Bivariate Data

Lesson 5: Interpret Two-Way Relative Frequency Tables

In this Grade 8 enVision Mathematics lesson from Chapter 4, students learn how to construct and interpret two-way relative frequency tables by converting raw frequency counts into ratios, decimals, or percents. Students practice calculating joint and marginal relative frequencies and compare data across rows and columns to identify relationships between paired categorical variables. This lesson builds essential data literacy skills for analyzing real-world survey data involving two categories simultaneously.

Section 1

Two-Way Relative Frequency Tables

Property

A relative frequency refers to the ratio of the frequency of a particular realization of a bivariate categorical variable to the total number of observations.
In other words, a relative frequency is a number between 0 and 1 (inclusive), commonly represented by a fraction, decimal, or percent.

Examples

  • If 30 out of 75 surveyed students prefer science class, the relative frequency for this preference is 3075=0.40\frac{30}{75} = 0.40 or 40%.
  • A table shows 12 out of 60 people own a bicycle and live in the city. The relative frequency for this specific cell is 1260=0.20\frac{12}{60} = 0.20.

Section 2

Identifying associations using relative frequencies

Property

Relative frequencies in two-way tables can reveal associations between categorical variables.
When the relative frequencies for one variable differ significantly across categories of another variable, this suggests an association exists between the two variables.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Two-Way Relative Frequency Tables

Property

A relative frequency refers to the ratio of the frequency of a particular realization of a bivariate categorical variable to the total number of observations.
In other words, a relative frequency is a number between 0 and 1 (inclusive), commonly represented by a fraction, decimal, or percent.

Examples

  • If 30 out of 75 surveyed students prefer science class, the relative frequency for this preference is 3075=0.40\frac{30}{75} = 0.40 or 40%.
  • A table shows 12 out of 60 people own a bicycle and live in the city. The relative frequency for this specific cell is 1260=0.20\frac{12}{60} = 0.20.

Section 2

Identifying associations using relative frequencies

Property

Relative frequencies in two-way tables can reveal associations between categorical variables.
When the relative frequencies for one variable differ significantly across categories of another variable, this suggests an association exists between the two variables.

Examples