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0580/22 Feb/Mar 2025, Question 16: Finding the Median and Quartiles

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 6 marks

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The question, in short

From a stem-and-leaf diagram of 13 packet masses in grams, find the interquartile range and a probability for two randomly chosen packets.

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

Part (a) · 3 marks

Work out the interquartile range of the 13 masses shown in the stem-and-leaf diagram.

  1. 1Ordered: 31, 32, 38, 40, 41, 42, 43, 43, 48, 51, 52, 53, 54 (n = 13)
  2. 2LQ = (38 + 40)/2 = 39
  3. 3UQ = (51 + 52)/2 = 51.5
  4. 4IQR = 51.5 − 39 = 12.5 g

Answer12.5

Part (b) · 3 marks

For two packets chosen at random, find the probability that one is over 50 g and the other under 50 g.

  1. 1More than 50 g: 4 packets; less than 50 g: 9 packets
  2. 2P(more, less) = 4/13 × 9/12 and P(less, more) = 9/13 × 4/12
  3. 3P = 2 × 4/13 × 9/12 = 72/156
  4. 4= 6/13

Answer6/13

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