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4MA1/2HR Jan 2023, Question 15: Finding the Median and Quartiles

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks

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The question, in short

From Rutger's 11 listed ace counts, find the interquartile range with working, then compare with Kim's median 11 and IQR 5 for average and consistency.

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

Part (a) · 2 marks

Find the interquartile range of Rutger's 11 ace values, showing the working clearly.

  1. 1List the numbers: 1, 1, 2, 4, 6, 8, 8, 9, 11, 12, 15
  2. 2There are 11 values, so median is the 6th value: 8
  3. 3Lower quartile (Q1) is the median of the first 5 values: 2
  4. 4Upper quartile (Q3) is the median of the last 5 values: 11
  5. 5Interquartile range = Q3 − Q1 = 11 − 2 = 9

Answer9

Part (bi) · 1 mark

State whether Rutger or Kim served more aces on average, giving a reason.

  1. 1Rutger's median is 8
  2. 2Kim's median is 11
  3. 311 > 8, so Kim served more aces on average

AnswerKim as she has a higher median

Part (bii) · 1 mark

State whether Rutger or Kim was more consistent in aces served, giving a reason.

  1. 1Rutger's IQR is 9
  2. 2Kim's IQR is 5
  3. 35 < 9, so Kim was more consistent with the number of aces served

AnswerKim as she has a smaller IQR

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