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Frequency Trees

FoundationHigherAQAEdexcelOCR

Frequency Trees is a key statistics topic at GCSE Maths. This Foundation and Higher worksheet gives you exam-style questions on completing frequency trees, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. Each branch splits the total into groups that must add back up.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Higher

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Topic overview

A frequency tree splits data by two characteristics in turn, branching at each stage and showing the number of items following each path.

It looks like a probability tree but carries frequencies rather than probabilities. The numbers on each set of branches add to the number at the point they came from.

That additive property makes the diagram self-checking. If a branch splits \(60\) into \(25\) and \(34\), something has been miscounted, because the two parts must total the original figure.

Revision notes

Building the tree

Start with the total, then split it by the first characteristic, and split each of those by the second.

Each set of branches must add back to the number it came from, which is the key check at every stage.

Filling in missing values

Subtract the known branch from the total at that point.

If \(80\) splits into \(35\) and an unknown, the unknown is \(45\). Work outwards from whatever you know.

Using it for probability

The probability of a path is the number at its end divided by the overall total.

If \(18\) of \(80\) follow a particular path, the probability is \(\frac{18}{80}\).

Key points

  • A frequency tree shows counts, not probabilities.
  • Each set of branches adds to the number it came from.
  • Split by the first characteristic, then the second.
  • Subtract to find missing values.
  • The end numbers add to the overall total.
  • Probability is the end number over the total.

Worked examples

Example 1

A total of \(90\) splits into \(38\) and an unknown. Find the unknown.

Working

\[90 - 38\]subtract the known branch
\[= 52\]state the missing value

Example 2

A branch of \(52\) splits into \(30\) and an unknown. Find the unknown.

Working

\[52 - 30\]subtract from the branch total
\[= 22\]state the missing value

Example 3

\(24\) of \(90\) follow one path. Find the probability of that path.

Working

\[\frac{24}{90}\]end number over the overall total
\[= \frac{4}{15}\]simplify the fraction

Common mistakes

  • Confusing it with a probability tree.

    A frequency tree carries counts; the numbers add rather than multiply.

  • Branches not adding to their source.

    Each split must total the number it came from, which is a useful check.

  • Using a branch total as the probability denominator.

    Unless the question restricts to that branch, use the overall total.

  • Multiplying along branches.

    That applies to probability trees, not frequency trees.

Exam tips

  • Check every split adds back to its source number.
  • Work outwards from whatever values you are given.
  • Use the overall total as the denominator for probabilities.
  • Label each branch with what it represents.

Key terms

Frequency tree
A branching diagram showing counts.
Branch
One path in the tree.
Total
The starting number at the root.
Path
A complete route through the tree.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.