Frequency Trees

This lesson covers frequency trees — a method for organising and displaying data involving two characteristics or events. Frequency trees are part of the AQA GCSE Mathematics specification and are a common exam topic at both Foundation and Higher tier.

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What Is a Frequency Tree?

A frequency tree is a diagram that splits a group of items (usually people) into categories based on two characteristics. Unlike a probability tree (which shows probabilities on branches), a frequency tree shows actual counts (frequencies).

graph LR
    Total[Total: 80 students] -->|Male| M[Male: 45]
    Total -->|Female| F[Female: 35]
    M -->|Pass| MP[Pass: 30]
    M -->|Fail| MF[Fail: 15]
    F -->|Pass| FP[Pass: 25]
    F -->|Fail| FF[Fail: 10]

At each stage, the numbers on the branches must add up to the number at the node they came from.

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Drawing a Frequency Tree

Worked Example 1

A school surveys 120 Year 11 students about whether they walk to school.

• 70 are boys, 50 are girls.
• 28 boys walk to school.
• 35 girls walk to school.

Draw a frequency tree and find the number of students who do not walk to school.