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    PracticeAQA GCSEAQA GCSE Maths Foundation Tier Paper 3 CalculatorQuestion 10
    Hard5 marksStructured
    StatisticsStatisticsFrequency TreesPercentages

    AQA GCSE · Question 10 · Statistics

    8400 Home Away 6850 Yes No Yes No Scarf Fans

    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).
    Question 09All questionsQuestion 11.1

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