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AQA GCSE · Question 10 · Statistics
8400 fans go to a rugby match.
6850 of the fans support the Home team.
The remaining fans support the Away team.
20% of the Home fans wear a scarf.
2319 of all the fans wear a scarf.
Complete the frequency tree.
8400 fans go to a rugby match.
6850 of the fans support the Home team.
The remaining fans support the Away team.
20% of the Home fans wear a scarf.
2319 of all the fans wear a scarf.
Complete the frequency tree.
How to approach this question
1. **Find Away fans:** Subtract Home fans from Total fans. (8400 - 6850)
2. **Find Home fans with scarf:** Calculate 20% of Home fans. (0.20 × 6850)
3. **Find Home fans with no scarf:** Subtract Home fans with scarf from total Home fans. (6850 - result from step 2)
4. **Find Away fans with scarf:** You know the total number of fans with a scarf (2319) and the number of Home fans with a scarf (from step 2). Subtract one from the other. (2319 - result from step 2)
5. **Find Away fans with no scarf:** Subtract Away fans with a scarf from total Away fans. (result from step 1 - result from step 4)
Full Answer
The completed frequency tree should have the following values:
- Away fans: 1550
- Home fans wearing a scarf (Yes): 1370
- Home fans not wearing a scarf (No): 5480
- Total fans wearing a scarf (Yes): 2319
- Away fans wearing a scarf (Yes): 949
- Away fans not wearing a scarf (No): 601
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<text x="150" y="265" class="label">Away</text>
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<text x="310" y="195" class="label">No</text>
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<text x="390" y="120" class="text" fill="blue" font-weight="bold">1370</text>
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<text x="390" y="280" class="text" fill="blue" font-weight="bold">601</text>
<text x="490" y="50" class="label">Scarf</text>
<ellipse cx="490" cy="170" rx="50" ry="30" class="oval" stroke-dasharray="4"/>
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Let's fill in the frequency tree step-by-step.
1. **Number of Away fans:**
Total fans = 8400
Home fans = 6850
Away fans = Total fans - Home fans = 8400 - 6850 = **1550**
2. **Home fans wearing a scarf (Yes):**
20% of Home fans wear a scarf.
Number = 20% of 6850 = 0.20 × 6850 = **1370**
3. **Home fans not wearing a scarf (No):**
Total Home fans = 6850
Home fans with scarf = 1370
Home fans with no scarf = 6850 - 1370 = **5480**
4. **Away fans wearing a scarf (Yes):**
Total fans with scarf = 2319
Home fans with scarf = 1370
Away fans with scarf = Total fans with scarf - Home fans with scarf = 2319 - 1370 = **949**
5. **Away fans not wearing a scarf (No):**
Total Away fans = 1550
Away fans with scarf = 949
Away fans with no scarf = 1550 - 949 = **601**
**Summary of values to fill in:**
- Away fans: **1550**
- Home fans, Scarf Yes: **1370**
- Home fans, Scarf No: **5480**
- Away fans, Scarf Yes: **949**
- Away fans, Scarf No: **601**
Common mistakes
✗ Calculating 20% of the total fans instead of just the home fans.
✗ Mixing up the branches of the tree.
✗ Simple arithmetic errors.
✗ Not checking that the numbers in the final branches add up to the total (e.g., 1370 + 5480 + 949 + 601 should equal 8400).
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