Two-way tables
Maths · Key Stage 3 · The School
What a two-way table shows
A TWO-WAY TABLE organises data by two categories at once — for example, year group down the side and favourite subject along the top. Each cell shows how many fit BOTH the row and the column it sits in. The final row and column usually hold TOTALS, and the very last cell holds the grand total of everyone.
Using the totals to fill gaps
Every row must add up to its row total, and every column must add up to its column total. If a table has some cells missing, the row and column totals let you work them out by subtraction — a row totalling 40 with cells of 15 and 12 filled in must have a missing cell of 40 − 15 − 12 = 13.
Calculating probability from a table
Once a two-way table is complete, a probability is just a fraction: the count in the cell (or cells) you want, divided by the grand total, or divided by a row or column total for a more specific question such as "given that a person is in Year 8, what fraction like Art?"
A survey of 50 students asks whether they walk or are driven to school, split by Year 7 and Year 8. Year 7 walk: 12. Year 7 driven: 8. Year 8 walk: 18. Year 8 driven: not given, but the grand total is 50, so Year 8 driven = 50 − 12 − 8 − 18 = 12. Now answer: what fraction of ALL students walk? (12 + 18)/50 = 30/50 = 3/5. What fraction of Year 8 students walk? 18/(18 + 12) = 18/30 = 3/5. Both use the same table; the second question restricts the denominator to Year 8 only, rather than everyone.