Two-Way Tables

A two-way table sorts data by two categories at once: one runs across the columns, the other down the rows. Each inner cell is a count of items that match both labels — its row label and its column label. The totals sit in the margins: a Total column on the right adds up each row, a Total row along the bottom adds up each column.

Suppose we ask every pupil in a class whether they walk, take the bus, or come by car, and we split that by boys and girls. One category (travel) goes across, the other (boys/girls) goes down:

	Walk	Bus	Car	Total
Boys	8	5	2	15
Girls	6	7	2	15
Total	14	12	4	30

Read across the boys' row: 8 + 5 + 2 = 15. Read down the walk column: 8 + 6 = 14. The grand total in the bottom-right corner, 30, is reached either way — across the margins (15 + 15) or along them (14 + 12 + 4) — because every pupil is counted in exactly one cell.

One category labels the rows, another labels the columns; each inner cell counts items matching both.
Every row adds to its row total and every column adds to its column total, written in the margins.
A missing cell is its row (or column) total minus the other cells in that line.
The bottom-right corner is the grand total — the size of the whole data set.
Read a probability as a cell divided by the grand total: P = \dfrac{\text{cell}}{\text{grand total}}.