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The histogram gives information about the distances 80 competitors jumped in a long jump competition - Edexcel - GCSE Maths - Question 18 - 2020 - Paper 3
Question 18
The histogram gives information about the distances 80 competitors jumped in a long jump competition. Calculate an estimate for the mean distance.
Worked Solution & Example Answer:The histogram gives information about the distances 80 competitors jumped in a long jump competition - Edexcel - GCSE Maths - Question 18 - 2020 - Paper 3
Step 1
Calculate Frequencies for Each Interval
Answer
To estimate the mean distance, we first need to find the frequency for each interval represented in the histogram.
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For the interval 6.4 to 6.8 m:
Frequency = Area = Width × Height = (6.8 - 6.4) × 20 = 0.4 × 20 = 8
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For the interval 6.8 to 7.2 m:
Frequency = (7.2 - 6.8) × 40 = 0.4 × 40 = 16
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For the interval 7.2 to 7.6 m:
Frequency = (7.6 - 7.2) × 80 = 0.4 × 80 = 32
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For the interval 7.6 to 8.0 m:
Frequency = (8.0 - 7.6) × 60 = 0.4 × 60 = 24
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For the interval 8.0 to 8.4 m:
Frequency = (8.4 - 8.0) × 10 = 0.4 × 10 = 4
So the frequencies for the intervals are:
- 6.4 to 6.8 m: 8
- 6.8 to 7.2 m: 16
- 7.2 to 7.6 m: 32
- 7.6 to 8.0 m: 24
- 8.0 to 8.4 m: 4
Step 2
Calculate the Estimate for the Mean Distance
Answer
Now we will use the frequencies to estimate the mean distance. The mean distance can be calculated using the formula:
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Calculate the midpoints for each interval:
- Midpoint for 6.4 to 6.8 m: 7.6
- Midpoint for 6.8 to 7.2 m: 7.0
- Midpoint for 7.2 to 7.6 m: 7.4
- Midpoint for 7.6 to 8.0 m: 7.8
- Midpoint for 8.0 to 8.4 m: 8.2
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Multiply each midpoint by its corresponding frequency:
- 7.6 × 8 = 60.8
- 7.0 × 16 = 112.0
- 7.4 × 32 = 236.8
- 7.8 × 24 = 187.2
- 8.2 × 4 = 32.8
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Sum these products:
- Total = 60.8 + 112.0 + 236.8 + 187.2 + 32.8 = 629.6
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Sum the frequencies:
- Total Frequency = 8 + 16 + 32 + 24 + 4 = 84
Finally, calculate the mean: