Two-Way Tables

An ordinary table sorts things one way. A two-way table sorts them two ways at the same time, which is why it is so useful. This one crosses year group with how students get to school. To read a cell, find its row and its column: the highlighted 8 sits in the Year 3 row and the Walks column, so it means eight Year 3 students walk. Every single number in the middle answers two questions at once.

Two-way tables usually have totals around the edge, and they do a lot of work. Add across a row and you get everyone in that year: 8 plus 5 plus 7 is 20 Year 3 students. Add down a column and you get everyone using that transport: 8 plus 6 is 14 walkers. The corner at the bottom right is the grand total, 39 students altogether. The neat part is that you can reach 39 by adding the row totals or the column totals — both routes must agree, which is a built-in check that the table is right.

Because the totals have to work, a missing number is never really missing — you can always work it out. Here the number of girls with cats is blank. Use the row: the girls total 18, and 7 plus 3 is 10, so the missing number is 8. Or use the column: cats total 12, and boys have 4, so girls have 8. Both routes give 8, and the fact that they agree tells you the answer is right. Working it out both ways takes a few extra seconds and makes a mistake almost impossible.

Most marks on two-way tables are lost by answering a slightly different question from the one asked. How many Year 3 students walk is one cell, 8. How many walk altogether is a column total, 14. How many Year 4 students there are is a row total, 19. And how many do not walk needs a subtraction: 39 minus 14 is 25. Before you write anything, decide whether you need a single cell, a total, or a total minus something. That decision is the actual skill.

Sometimes you have to build the table yourself from a raw list. Go through the list once, adding a mark to the right cell each time, then count up. The check at the end matters: the numbers in the middle must add to the number of entries in the list. Eight entries here, and the cells add to eight, so nothing was missed or counted twice. And notice the zero — no Year 4 student came by car, so the cell gets a nought. A blank cell looks like you forgot; a zero says you checked.