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0580/32 Feb/Mar 2025, Question 10: Stem-and-Leaf Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 6 marks

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The question, in short

Using a stem-and-leaf table with three unknown digits, plus given range, median and mean for ten values, determine A, B and C, then explain why no mode exists.

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

Part (a) · 5 marks

Find the three missing digits A, B and C using the stated range of 27, median of 16 and mean of 16.5 for the ten numbers.

  1. 1Range: largest − smallest = 27, so 20 + C = 2 + 27 = 29, C = 9
  2. 2Median = (5th + 6th)/2 = ((10 + B) + 17)/2 = 16, so 10 + B = 15, B = 5
  3. 3Total = 16.5 × 10 = 165
  4. 42 + A + 11 + 13 + 15 + 17 + 20 + 24 + 26 + 29 = 157 + A = 165
  5. 5A = 8, B = 5, C = 9

AnswerA = 8, B = 5, C = 9

Part (b) · 1 mark

Give a reason why the data set has no mode.

  1. 1There is no mode because all the numbers are different (each appears once)

AnswerAll the numbers are different

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