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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
Calculation of Frequencies
Answer
To find the frequencies from the histogram, we estimate the area of each rectangle:
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For the interval [6.4, 6.8): Width = 0.4 m, Height = 20 (frequency density)
- Frequency = Width * Height = 0.4 * 20 = 8
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For the interval [6.8, 7.2): Width = 0.4 m, Height = 40
- Frequency = 0.4 * 40 = 16
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For the interval [7.2, 7.6): Width = 0.4 m, Height = 80
- Frequency = 0.4 * 80 = 32
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For the interval [7.6, 8.0): Width = 0.4 m, Height = 120
- Frequency = 0.4 * 120 = 48
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For the interval [8.0, 8.4): Width = 0.4 m, Height = 20
- Frequency = 0.4 * 20 = 8
Now, we can summarize the frequencies:
- [6.4, 6.8): 8
- [6.8, 7.2): 16
- [7.2, 7.6): 32
- [7.6, 8.0): 48
- [8.0, 8.4): 8
Step 2
Estimation of the Mean Distance
Answer
To calculate the mean distance:
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Compute the total number of jumps (sum of frequencies) = 80.
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Calculate the midpoint for each interval:
- Midpoint for [6.4, 6.8) = 6.6
- Midpoint for [6.8, 7.2) = 7.0
- Midpoint for [7.2, 7.6) = 7.4
- Midpoint for [7.6, 8.0) = 7.8
- Midpoint for [8.0, 8.4) = 8.2
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Calculate the weighted sum:
- Total = (8 * 6.6) + (16 * 7.0) + (32 * 7.4) + (48 * 7.8) + (8 * 8.2)
- = 52.8 + 112 + 236.8 + 374.4 + 65.6 = 841.6
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Finally, calculate the mean distance:
- Mean = Total / Total Frequencies = 841.6 / 80 = 10.52
Thus, the estimated mean distance is approximately 10.52 meters.