Two Way Tables
A two-way table organises data by two categories at once, such as year group and travel method, with row and column totals used to check that all the numbers add up correctly. Completing and interpreting two-way tables is a key GCSE statistics and probability skill, often combined with simple probability questions.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the table carefully, noting which totals, such as row totals, column totals or the grand total, are already given.
- Use the rule that each row and each column must add up to its stated total to find missing values, working from the values you already know.
- Fill in missing cells one at a time, starting with any row or column that has only one missing value.
- Check your completed table: every row should sum to its row total, and every column should sum to its column total, and both should agree with the grand total.
- For probability questions, write the relevant frequency from the table over the appropriate total: the grand total for 'a person chosen from everyone', or a row/column total for 'given that'.
Worked example
A school surveyed 100 pupils about whether they prefer football or netball. Of the 55 boys, 38 prefer football. Of the 45 girls, 20 prefer football. Complete a two-way table, then find the probability that a pupil chosen at random prefers netball.
- Boys who prefer netball = 55 - 38 = 17.
- Girls who prefer netball = 45 - 20 = 25.
- Total who prefer football = 38 + 20 = 58.
- Total who prefer netball = 17 + 25 = 42 (check: 58 + 42 = 100).
- Probability of netball = 42/100 = 21/50.
- Final answer: 21/50.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
Mr Hughes asked 60 students whether they prefer Maths or Science. 34 of the students are boys. Of the boys, 21 prefer Maths. Of the girls, 15 prefer Science. (a) Draw and complete a two-way table to show this information. (3) (b) One student is chosen at random from the 60 students. Find the probability that this student prefers Science. (2)
A two-way table shows the results of a survey of 120 adults about how they travel to work, split by Car and Public transport, and by Full-time and Part-time. The Full-time row total is 80, and 55 full-time workers travel by car. The Part-time row total is 40, and 18 part-time workers travel by car. Work out the total number of adults who travel by public transport.
A two-way table shows the exam results of 90 students who each sat one exam, either History or Geography. 50 students sat History, of whom 36 passed. 40 students sat Geography, of whom 26 passed. A student claims that a greater proportion of Geography students passed than History students. Determine, showing your working, whether the student is correct.
See real past-paper questions on two way tables, organised by topic with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the two way tables worksheet pack - 20 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
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