Sheet № 237 · Foundation + Higher · AQA · Edexcel · OCR
Two-Way Tables –
Two-way tables are a staple of GCSE Maths papers at both Foundation and Higher tier across AQA, Edexcel and OCR. They organise data into rows and columns so you can read off values, fill in missing entries and calculate probabilities. Whether the question asks you to complete a table, find a total or work out the probability of a randomly
§Key definitions
Question:
120 students were asked whether they prefer football, tennis or swimming. The results are shown below.
Answer:
Boys swimming = 18, Girls football = 20, Swimming total = 36.
(a)
Girls who prefer tennis = 22. Grand total = 120.
(b)
Football total = 48.
Q1 (Foundation):
80 people were asked whether they prefer tea or coffee. 35 are male; 20 males prefer tea; 30 females prefer coffee. Complete the table and find the total who prefer tea.
§Formulas to memorise
Row total = sum of all values in that row
Column total = sum of all values in that column
P(event) = frequency of event ÷ grand total
Read the table carefully — identify which category is on the rows and which is on the columns.
Use row and column totals — to find any missing values: subtract the known cells from the total.
Check your work — every row must add to its row total, every column must add to its column total, and all row totals must add to the grand total.
Worked example
120 students were asked whether they prefer football, tennis or swimming. The results are shown below. | | Football | Tennis | Swimming | Total | |---|---|---|---|---| | Boys | 28 | 14 | ? | 60 | | Girls | ? | 22 | 18 | 60 | | Total | 48 |
Working:
⚠ Common mistakes
- ✗Adding across then down and getting different totals. Always cross-check: row totals summed must equal column totals summed and both must equal the grand total.
- ✗Confusing a joint frequency with a marginal total. The cell in the body of the table gives the count for a specific combination; the margin gives the overall category count.
- ✗Giving a probability as a ratio or "1 in 5". Always express probability as a fraction, decimal or percentage.
✦ Exam tips
- →Work systematically: fill in the easiest missing values first, then use totals to find the rest.
- →If the question says "a person is chosen at random", you must divide by the grand total, not a row or column total (unless told otherwise).
- →Two-way table questions often lead into probability — be ready to simplify your fraction.
- →For harder probability from tables, see probability from two-way tables.