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# Frequency trees
- URL: https://www.esheets.io/frequency-trees/
- Published: 2025-10-01T19:14:43.000Z
- Updated: 2026-06-21T18:31:40.000Z
- Author: Richard Linnington
- Tags: Maths, Probability, Statistics

Frequency trees help you sort and count information in a clear way. They’re great for working out how many people or things fit into different groups, like how many students prefer different snacks or how many passed a test. It’s like building a picture of the data, step by step! [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise frequency trees with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Completing branches in a frequency tree.
- Using totals to find missing frequencies.
- Following categories through the tree.
- Interpreting two-stage frequency information.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Complete the frequency trees below.

## Topic guide

### What this worksheet practises

This worksheet provides practice on completing and interpreting frequency trees. Frequency trees are visual diagrams used to sort and break down a total population into smaller and smaller sub-categories. They are highly effective for solving multi-step logic problems without getting lost.

### Key method

The fundamental rule of a frequency tree is that the numbers in the branches must add up to the number in the circle they originated from.

- Identify the grand total (usually at the far left).
- When a circle splits into two or more branches, the numbers in the new circles must sum to the number in the previous circle.
- Use subtraction to find missing numbers. If a total of 50 splits into "Boys" and "Girls", and you know there are 20 Boys, the Girls must be 50 − 20 = 30.
- Fill in the tree systematically, working from left to right (using division/percentages) or right to left (using addition) depending on what information the question gives you.

### Worked example

**80 students take an exam. 45 are boys. 30 of the boys pass. 15 of the girls fail. Complete a frequency tree to find out how many girls pass.**

Step 1: Start on the left. The total is 80\. It splits into Boys and Girls.

Boys = 45\. We find the Girls by subtraction: 80 − 45 = 35.

Step 2: Look at the Boys branch. It splits into Pass and Fail.

We know 30 Boys pass. The Boys total was 45\. So, 45 − 30 = 15 Boys fail.

Step 3: Look at the Girls branch. It splits into Pass and Fail.

We know 15 Girls fail. The Girls total was 35\. So, 35 − 15 = 20 Girls pass.

The final answer is 20.

### Common mistakes to avoid

A frequent mistake is putting probabilities or fractions inside the circles. Frequency trees are for *whole numbers of items* (frequencies) only. The circles contain the actual headcounts, not the chance of an event happening.

### How to check your answer

The numbers in the final column of circles on the far right-hand side must all add up to the grand total in the first circle on the far left. In our example, the final circles are Boys Pass (30) + Boys Fail (15) + Girls Pass (20) + Girls Fail (15) = 80\. The arithmetic is correct.