Joint, Marginal, and Conditional Relative Frequencies

A two-way table sorts people or things by two categorical variables at once, like grade level and whether they drive. Every cell, row total, and column total can turn into a percentage, but which total you divide by changes what question you're answering. Divide a single cell by the grand total and you get a joint relative frequency: the share of the whole group that falls into that exact combination. Divide a row total or column total by the grand total and you get a marginal relative frequency: the share of the whole group in just that one category, ignoring the other variable entirely. Divide a cell by its own row or column total instead of the grand total, and you get a conditional relative frequency: the share within one category that also falls into another.

The word 'of' tells you the denominator. 'Percent of all students' points to the grand total. 'Percent of seniors' points to the senior row or column total only. Mixing these up is the single most common error with two-way tables, so always ask what group you're taking a percentage out of before you divide.

This topic sets up everything after it: conditional relative frequencies are the bridge to conditional probability, and comparing conditional distributions across rows or columns is exactly how you check whether two variables are associated or independent.