Two-Way Tables

A two-way table lists the categories of one variable down the rows and the categories of another across the columns. Each cell holds the count of individuals who fall into that specific row category and that specific column category. Row and column totals, called marginal totals, sit at the edges, and the grand total sits in the corner. Because every individual lands in exactly one cell, the cells in a row must add up to that row's total, and the cells in a column must add up to that column's total. That structure is also how you find a missing cell: subtract the known cells from the total that contains them.

A single bar chart shows one variable alone. Two separate bar charts, one for each variable, can tell you the overall shape of each but cannot show whether the two variables move together. A two-way table keeps every individual's pair of values linked, so you can ask questions like whether sport preference differs by grade level, which no amount of separate charts can answer. This is why the table comes before the rules of probability later in the unit: the cells of a two-way table are literally joint counts, the rows and columns give you the building blocks for marginal and conditional probabilities, and comparing conditional frequencies across rows or columns is how you judge whether two variables are associated.

Two-way tables also set up simulation and probability work that follows, since a cell count divided by a total is just an empirical probability. Getting comfortable finding totals and missing cells here makes conditional probability and independence checks much easier later.