ExpertHard5 marksStructured
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
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).
Practice the full AQA GCSE Maths Foundation Tier Paper 3 Calculator
43 questions · hints · full answers · grading
More questions from this exam
Q01.1A village has four bus stops. The bar chart shows information about the people at the bus stops a...EasyQ01.2Using the bar chart from the previous question, how many more people were at the School bus stop ...EasyQ02Here are four temperatures in degrees C:
-5, 3, -7, -1
Write the temperatures in order, starting ...EasyQ03.1Here are the first three terms of a linear sequence:
5, 11, 17
Write down the next term.EasyQ03.2The first three terms of a linear sequence are 5, 11, 17.
Describe the term-to-term rule.Easy