4024/12 Oct/Nov 2023, Question 17: Drawing Cumulative Frequency Diagrams
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
From a cumulative frequency table for 80 plant heights, draw the cumulative frequency diagram, estimate the interquartile range, and find the height H above which 28 plants are sold.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Plot the given cumulative frequencies against the upper class boundaries on the grid and draw the cumulative frequency curve.
- 1Plot (2, 4), (4, 18), (6, 42), (8, 60), (10, 72), (12, 80), starting from (0, 0)
- 2Join the points with a smooth increasing curve (or straight lines)
AnswerCorrect cumulative frequency diagram
Part (b) · 2 marks
Use your cumulative frequency diagram to estimate the interquartile range of the plant heights.
- 1LQ at cumulative frequency 80 ÷ 4 = 20, UQ at 3 × 80 ÷ 4 = 60
- 2From a ruled polygon: LQ ≈ 4 + 2 × 2/24 ≈ 4.2, UQ = 8
- 3IQR = UQ − LQ ≈ 8 − 4.2 = 3.8 (your own UQ − LQ)
Answer3.8 (accept 3.6 to 4.0)
Part (c) · 2 marks
Given that 28 plants taller than H centimetres are sold, use the diagram to find H.
- 1Plants not sold = 80 − 28 = 52
- 2Read across from cumulative frequency 52 to the curve and down
- 3From a ruled polygon: H ≈ 6 + 2 × 10/18 ≈ 7.1 (your reading at CF 52)
Answer7.1 (accept 6.9 to 7.3)
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