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AQA GCSE · Question 07.1 · Statistics
120 people visit a maze.
80 are children, the rest are adults.
At the start of the maze you can turn left or right.
45 children turn left.
75 people in total turn left.
Complete the frequency tree.
120 people visit a maze.
80 are children, the rest are adults.
At the start of the maze you can turn left or right.
45 children turn left.
75 people in total turn left.
Complete the frequency tree.
How to approach this question
1. **Fill in the first branches (Children/Adults):**
- Total people = 120.
- Children = 80.
- Adults = Total - Children = 120 - 80 = 40. Write 80 in the Children circle and 40 in the Adults circle.
2. **Fill in the Children branches (Left/Right):**
- Total children = 80.
- Children who turn left = 45. Write 45 in the top-left final circle.
- Children who turn right = Total children - Children who turn left = 80 - 45 = 35. Write 35 in the top-right final circle.
3. **Fill in the Adults branches (Left/Right):**
- Total people turning left = 75.
- Children turning left = 45.
- Adults turning left = Total left - Children left = 75 - 45 = 30. Write 30 in the bottom-left final circle.
- Total adults = 40.
- Adults turning right = Total adults - Adults turning left = 40 - 30 = 10. Write 10 in the bottom-right final circle.
4. **Check your work:** The numbers in the final four circles should add up to the total number of people: 45 + 35 + 30 + 10 = 120. This is correct.
Full Answer
The completed frequency tree should have the following values:
- Adults: 40 (120 - 80)
- Children turning right: 35 (80 - 45)
- Adults turning left: 30 (75 - 45)
- Adults turning right: 10 (40 - 30)
A frequency tree is used to show how a group is broken down into smaller categories.
- **First split (Children/Adults):** We are told there are 120 people in total and 80 are children. The rest must be adults. Number of adults = 120 - 80 = 40.
- **Second split (Children):** We know there are 80 children. 45 of them turn left. The rest must turn right. Number of children turning right = 80 - 45 = 35.
- **Second split (Adults):** We know there are 40 adults. We are told 75 people in total turn left. Since 45 children turned left, the number of adults who turned left must be 75 - 45 = 30. The rest of the adults must have turned right. Number of adults turning right = 40 - 30 = 10.
The final numbers are: Children Left (45), Children Right (35), Adults Left (30), Adults Right (10).
Check: 45 + 35 + 30 + 10 = 120. Correct.
Common mistakes
✗ Putting numbers in the wrong places on the tree.\n✗ Calculation errors, especially with subtraction.\n✗ Confusing the total number turning left with the number of adults turning left.
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