Completing two-way tables, step by step
A two-way table sorts the same group two ways at once, and its margins are the totals that hold it together.
The question
| Sold | Left | Total | |
|---|---|---|---|
| Small | 14 | 20 | |
| Large | 8 | 23 | 31 |
| Total | 22 | 29 | 51 |
The Small and Left number is missing
SoldLeftTotalSmall14?20Large82331Total222951
20−14=6
29−23=6
SoldLeftTotalSmall14620Large82331Total222951
- Every number in a two-way table belongs to a row AND to a column. The gap is in the Small row and the Left column, so either one of them can find it — and if both give the same answer, it is right.
- Along the row first. The Small row adds up to 20, and the other number in it is 14. So the gap is 20 − 14 = 6.
- Down the column as a check. The Left column adds up to 29, and the other number in it is 23: 29 − 23 = 6. The same 6, which is what says the table hangs together.
- So the missing number is 6 — the Small row totals 20, and 20 − 14 = 6.
How it works.
- 01
Every number in a two-way table belongs to a row AND to a column. The gap is in the Small row and the Left column, so either one of them can find it — and if both give the same answer, it is right.
- 02
Along the row first. The Small row adds up to 20, and the other number in it is 14. So the gap is 20 − 14 = 6.
- 03
Down the column as a check. The Left column adds up to 29, and the other number in it is 23: 29 − 23 = 6. The same 6, which is what says the table hangs together.
- 04
So the missing number is 6 — the Small row totals 20, and 20 − 14 = 6.