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A running club records the distances run by each member during December - OCR - GCSE Maths - Question 13 - 2023 - Paper 6
Question 13
A running club records the distances run by each member during December. The results are shown in this histogram. (a) 18 members run less than 20 km. (i) Work out ... show full transcript
Worked Solution & Example Answer:A running club records the distances run by each member during December - OCR - GCSE Maths - Question 13 - 2023 - Paper 6
Step 1
(i) Work out the number of members who run more than 30 km.
Answer
To find the number of members who run more than 30 km, we first analyze the histogram provided:
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From the histogram, we observe that the total number of members is determined by the heights of the bars corresponding to the intervals of distance.
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The number of members running less than 20 km is given as 18.
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Let's denote the number of members running between 20 km and 30 km as 'x'. We can sum the frequencies from the histogram to establish the total:
- For the range 20-30 km, the height of the bar indicates 12 members.
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To find the total number of members:
Total members = Members < 20 km + Members 20-30 km + Members > 30 km
Assuming the height for members > 30 km is 'y', we have:
Total = 18 + 12 + y.
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The left endpoint of the last bar shows 40 km, indicating that all members running more than 30 km falls within this range.
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Upon checking the histogram, we see that the number of members in the interval greater than 30 km (40-80 km) is represented as 5.
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Therefore:
Number of members who run more than 30 km = 5 members.
Step 2
(ii) Explain why Finley’s method is likely to overestimate the true value of the range.
Answer
Finley’s method involves calculating the range using the formula:
In this instance, Finley subtracted the smallest possible value (0) from the largest possible value (80):
However, this method overestimates the true range for the following reason:
- The maximum value (80 km) is the upper limit of the histogram but does not necessarily reflect the actual distances run by members.
- In real scenarios, the distances can be distributed in any way within that range, leading to the potential for actual maximum distances to be lower than 80 km.
- Similarly, the minimum value (0 km) implies that there are members who might not have run at all, but it might not represent a typical lower distance from the data.
- Consequently, many values may exist between these extremes that weren't accounted for, leading to an inflated total range.