What is important to know about Two-way tables?

The totals row and totals column must all match the grand total.

What is important to know about Two-way tables?

Each cell shows a frequency for a specific combination of the two variables.

What is important to know about Two-way tables?

To find a probability from a two-way table, divide the target frequency by the relevant total.

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Statistics & Probability · Foundation & Higher

Two-way tables

Two-way tables summarise data classified by two variables. Use row and column totals to find missing values, then answer probability or frequency questions.

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Key facts to remember

1The totals row and totals column must all match the grand total.
2Each cell shows a frequency for a specific combination of the two variables.
3To find a probability from a two-way table, divide the target frequency by the relevant total.

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Worked examples

Example 1

In a class of 30, 18 are girls. 12 students wear glasses, and 5 of these are boys. How many girls do NOT wear glasses?

Working

Total = 30. Girls = 18 → Boys = 12.
Boys wearing glasses = 5 → Boys without = 12 − 5 = 7.
Total wearing glasses = 12 → Girls with glasses = 12 − 5 = 7.
Girls without glasses = 18 − 7 = 11.

Answer11 girls do not wear glasses.

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Common mistakes

✗Confusing row totals with column totals.

✗Forgetting that all rows and columns must sum to the same grand total.

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Exam tips

✓Draw a neat grid and fill in the totals row and column first.

✓Work out any cell where only one value is missing before tackling harder cells.

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