Two-way tables
Objective. Organise and interpret paired categorical information.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A two-way table organises data across two categorical variables simultaneously, with rows representing one variable and columns representing the other, plus row and column totals. Each cell shows the frequency of pupils or items satisfying both the row and column condition at once. To find a missing value, use the fact that each row and column must sum to its stated total. Example: if a row totals 30 and one cell is 18, the other cell in that row must be 30 − 18 = 12.
Worked example
A two-way table shows that 50 pupils were surveyed about owning a pet. Of these, 28 own a dog. If 22 pupils do not own a dog, check this matches the total, then find how many pupils own a dog as a two-way table entry out of the total.
- 1The two-way table rows must add to the total: dog owners plus non-dog owners.
- 2Add the two given groups: 28 + 22.
- 3This gives 28 + 22 = 50, matching the stated total of pupils surveyed.
- 4Therefore 28 pupils own a dog out of the total 50 surveyed.
Answer: 28 pupils
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Practice
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Start practisingCommon mistake. Pupils sometimes confuse which total a missing cell belongs to, adding across the wrong row or column; always check both the row total and column total agree before confirming a missing value.
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