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AQA GCSE · Question 08.1 · Data Visualization and Representation
100 students go to London for a weekend on a school trip. On one afternoon, students can choose to go to a theatre (T) or visit a museum (M) or do neither.
- 16 chose to do neither.
- Three times as many chose the theatre as chose the museum.
Complete the Venn diagram.
100 students go to London for a weekend on a school trip. On one afternoon, students can choose to go to a theatre (T) or visit a museum (M) or do neither.
- 16 chose to do neither.
- Three times as many chose the theatre as chose the museum.
Complete the Venn diagram.
How to approach this question
1. Start with the total number of students: 100.
2. The number of students who did neither is 16. This number goes outside the two circles.
3. Calculate the number of students who went to either the theatre or the museum: 100 - 16 = 84.
4. Let the number of students who chose the museum be 'x'. The number who chose the theatre is '3x'.
5. The question implies no student chose both, so the intersection is 0. The total in the circles is the sum of those who chose only theatre and only museum.
6. Set up an equation: 3x + x = 84.
7. Solve for x: 4x = 84, so x = 21. This is the number for the Museum.
8. Calculate the number for the Theatre: 3x = 3 * 21 = 63.
9. Fill these numbers into the correct sections of the Venn diagram.
Full Answer
The completed Venn diagram should have 63 in the Theatre only circle, 21 in the Museum only circle, 0 in the intersection, and 16 outside the circles.
Total students = 100.
Students who did neither = 16. This number goes outside the circles.
Number of students who went to Theatre or Museum = 100 - 16 = 84.
Let M be the number of students who chose the museum.
Let T be the number of students who chose the theatre.
We are told T = 3M.
The problem implies that students chose one or the other, but not both, so the intersection is zero.
Therefore, T + M = 84.
Substitute T = 3M into the equation:
3M + M = 84
4M = 84
M = 84 / 4 = 21.
So, 21 students chose the museum.
T = 3 * 21 = 63.
So, 63 students chose the theatre.
We fill the Venn diagram with 63 in the T circle, 21 in the M circle, and 16 outside.
Common mistakes
✗ Forgetting to subtract the 16 students from the total before calculating the ratio.\n✗ Incorrectly setting up the ratio (e.g., x + 3 = 84).\n✗ Placing numbers in the intersection when it should be zero.
Practice the full AQA GCSE Statistics Foundation Tier Paper 2
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