1.3 Representing a Categorical Variable with Tables

Frequency and Relative Frequency Tables

A frequency table lists the count of observations in each category of a categorical variable. A relative frequency table shows the proportion or percentage of the total in each category, found by dividing each frequency by the total number of observations. Relative frequencies let you compare groups of different sizes fairly.

Joint, Marginal, and Conditional Distributions

A two-way table organizes data on two categorical variables. Joint frequencies are counts in the interior cells; marginal frequencies are row/column totals. A marginal distribution shows percentages for one variable alone. A conditional distribution shows percentages for one variable given a specific value of the other, revealing possible associations.

Checking for Association

Two categorical variables are associated if the conditional distributions of one variable differ across categories of the other. If the distributions are roughly the same regardless of the condition, the variables are not associated (independent-like behavior). Comparing conditional distributions with bar graphs or percentages is the standard way to check this.

Key terms

Frequency table

A table showing the count of observations in each category of a categorical variable.

Relative frequency table

A table showing the proportion or percentage of observations in each category.

Joint frequency

A count in the interior cell of a two-way table representing a combination of two variable categories.

Marginal distribution

The distribution of a single variable, found using the row or column totals of a two-way table.

Conditional distribution

The distribution of one variable restricted to a specific category of another variable; used to check for association.

Try an AP-style question

What proportion of 12th graders like the new schedule?

1. 0.35
2. 0.636
3. 0.55
4. 0.70