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0580/22 Oct/Nov 2022, Question 13: Drawing Cumulative Frequency Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

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The question, in short

From a cumulative frequency table for 50 children's masses, draw the cumulative frequency diagram and use it to estimate the 90th percentile.

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

Part (a) · 3 marks

Plot the cumulative frequency against mass k on the given grid, using the table values, to draw the cumulative frequency curve.

  1. 1Plot the points (20, 0), (22, 7), (24, 23), (28, 35), (32, 43), (36, 47), (42, 50)
  2. 2Join them with a smooth increasing curve (or straight line segments)

AnswerA correct cumulative frequency diagram

Part (b) · 1 mark

Read from your cumulative frequency graph the mass value corresponding to the 90th percentile.

  1. 190th percentile: 90% of 50 = 45th child
  2. 2Go across from 45 on the cumulative frequency axis to the curve, then down
  3. 345 is halfway between 43 (k = 32) and 47 (k = 36), so 90th percentile ≈ 34 kg

Answer33 to 34.5

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