# Exam-Style Question on Cumulative Frequency

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 701. This question is similar to one that appeared on a GCSE Higher paper in 2022. The use of a calculator is allowed.

The distance walked by each of 68 hikers was recorded. The results are shown in the cumulative frequency curve.

(a) Estimate the median.

(b) Estimate the interquartile range.

(c) Use the curve to complete the frequency table.

 Distance($$d$$ km) Frequency 0 < d ≤ 5 5 < d ≤10 10 < d ≤ 15 15 < d ≤ 20 20 < d ≤ 25 25 < d ≤ 30 30 < d ≤ 35 5 15

(d) Write down the modal class.

(e) Calculate an estimate for the mean.

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