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4MA1/1HR Jan 2020, Question 12: Finding the Median and Quartiles

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks

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The question, in short

From a cumulative frequency graph of waiting times at Hospital A, estimate the median and interquartile range, then compare these with Hospital B's median of 28 minutes and interquartile range of 19 minutes.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Read off the waiting time at the middle value of the cumulative frequency.

  1. 1Read cumulative frequency value at half of total frequency (60 ÷ 2 = 30)
  2. 2Find waiting time corresponding to cumulative frequency of 30 on the graph
  3. 3Estimated waiting time is 23 minutes

Answer23

Part (b) · 2 marks

Find the waiting times at the upper and lower quartiles, then subtract to get the spread.

  1. 1Find lower quartile: cumulative frequency = 60 × 0.25 = 15
  2. 2Read waiting time at cumulative frequency 15 → approximately 17 minutes
  3. 3Find upper quartile: cumulative frequency = 60 × 0.75 = 45
  4. 4Read waiting time at cumulative frequency 45 → approximately 29 minutes
  5. 5Interquartile range = 29 − 17 = 12 minutes

Answer12

Part (c) · 2 marks

State how Hospital A's median and spread differ from Hospital B's 28 minutes and 19 minutes.

  1. 1Compare medians: 23 < 28, so waiting times at Hospital A are shorter on average
  2. 2Compare IQRs: 12 < 19, so variation in waiting times is smaller at Hospital A
  3. 3State both comparisons with context

AnswerThe median waiting time at Hospital A (23 minutes) is less than at Hospital B (28 minutes). The interquartile range at Hospital A (12 minutes) is smaller than at Hospital B (19 minutes), meaning waiting times at Hospital A are less spread out.

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