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Maths · Statistics & Probability

Two-way tables

Read data from two-way tables and answer questions.

Not startedCAMBRIDGE · 8CBSE · VIIIIB · MYP-2

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What is a two-way table?

A two-way table organises data by two different categories at once. Each row represents one category and each column represents another. The cells show how many items match both categories. Sometimes called a contingency table.

Reading totals

Two-way tables often include row totals and column totals. The row total is the sum across all columns in that row. The column total is the sum down all rows in that column. The grand total (bottom-right) sums everything.

Finding specific data

To find data in a two-way table, locate the correct row and column. Follow them until they meet. That cell holds the answer. Always check row and column labels carefully before reading any number.

Answering comparison questions

Two-way tables let you compare groups quickly. You can add cells together to find subtotals. You can subtract to find differences. Read the question carefully to know which cells to use.

Worked examples

  1. 1. A survey asked 100 students about their favourite sport. 28 boys chose football, 12 boys chose tennis. 22 girls chose football, 38 girls chose tennis. How many students chose football?

    1. Draw a two-way table with rows for boys and girls, columns for football and tennis.
    2. Fill in the known values: boys-football = 28, boys-tennis = 12, girls-football = 22, girls-tennis = 38.
    3. To find total students who chose football, add the football column: 28 + 22 = 50.
    4. So 50 students chose football.

  2. 2. In a class, 15 students walk to school and 10 cycle. There are 18 boys total and 7 girls walk. How many boys cycle?

    1. Set up a table: rows for boys and girls, columns for walk and cycle.
    2. Total students who walk = 15. Girls who walk = 7. So boys who walk = 15 - 7 = 8.
    3. Total boys = 18. Boys who walk = 8. So boys who cycle = 18 - 8 = 10.
    4. Therefore 10 boys cycle to school.

  3. 3. A shop sold 45 red items and 35 blue items. 30 were small and 50 were large. If 18 red items were small, how many blue items were large?

    1. Create a table: rows for red and blue, columns for small and large.
    2. Red items total = 45. Red small = 18. So red large = 45 - 18 = 27.
    3. Total large items = 50. Red large = 27. So blue large = 50 - 27 = 23.
    4. Answer: 23 blue items were large.

Try it yourself

A library recorded loans over one week. Fiction books: 42 adult, 58 children. Non-fiction books: 28 adult, 22 children. How many children's books were loaned in total?

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