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Tree diagrams

Tree diagrams for GCSE Statistics AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Statistics
  • Higher
  • Spec P8 · P9 · P13
  • 9 min read
  • 7 revision boxes

Introduction

2 boxes
4 min read

What is tree diagrams?

Listen to this box

Transcript

A short spoken summary of tree diagrams and where it is used.

A spoken walk-through of tree diagrams before you read the notes.
The specification wording is precise here, and the mark scheme follows that wording exactly.
4 rows

The tree diagrams reference table

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing tree diagrams laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left
Row 3 column 4
Row 3 column 5

Learning

3 boxes
4 steps

How to work with tree diagrams

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: ×10\times 10 moves every digit one column left.
  1. Read the question and write down what is being asked for.
  2. Set out the working for tree diagrams in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
2 rules

Key facts: Tree diagrams

Work through the method one line at a time and write down what changes at each step.

  • Rule 1

    How tree diagrams behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How tree diagrams behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How tree diagrams behaves in the 3rd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
3 steps

How to work with tree diagrams

The specification wording is precise here, and the mark scheme follows that wording exactly.
The layout below is the one the mark scheme expects.

Diagram showing tree diagrams laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ×10\times 10 moves every digit one column left.
  1. Read the question and write down what is being asked for.
  2. Set out the working for tree diagrams in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: ×10\times 10 moves every digit one column left

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Examples

2 boxes
2 marks · worked

Worked example: tree diagrams

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing tree diagrams laid out step by step

The same idea drawn out, so the method is visible.
1 marks · worked

Practice question 7: ×10\times 10 moves every digit one column left

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: ×10\times 10 moves every digit one column left.

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Common questions

How many marks is tree diagrams usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Statistics AQA Higher paper?
Yes — it sits in the Markets and demand strand.