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The histogram summarises a health score for a group of people - OCR - GCSE Maths - Question 10 - 2017 - Paper 1
Question 10
The histogram summarises a health score for a group of people. (a) Estimate the fraction of the group who had a score of 45 or more. (b) What assumption did you ma... show full transcript
Worked Solution & Example Answer:The histogram summarises a health score for a group of people - OCR - GCSE Maths - Question 10 - 2017 - Paper 1
Step 1
(a) Estimate the fraction of the group who had a score of 45 or more.
Answer
To estimate the fraction of the group who had a score of 45 or more, observe the histogram. We need to find the area of the bars corresponding to scores of 45 and above.
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Identify the relevant range: The scores of 45-100 correspond to the histogram bars that start at 40 and end at 100.
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Estimate the height of the bars: From the histogram, the height at 40-50 is approximately 0.5, and from 50-60, it is approximately 0.9, with decreasing values for the remaining intervals.
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Calculate the area under these bars:
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For the 40-50 interval (height 0.5 and width 10):
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For the 50-60 interval (height 0.9 and width 10):
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For the 60-70 interval (height 0.4 and width 10):
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For the 70-80 interval (height 0.2 and width 10):
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For the 80-90 interval (height 0.1 and width 10):
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Sum the areas:
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Estimate the total number of participants from the histogram, if treated as 100:
Therefore, the estimated fraction of the group who had a score of 45 or more is approximately 0.21.
Step 2
(b) What assumption did you make in answering part (a)?
Answer
In answering part (a), I assumed that the distribution of health scores represented in the histogram is uniform within each interval. This means I considered all values in a specific interval to contribute equally to the total area, without accounting for any variability that might exist within those intervals.