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4024/11 May/Jun 2024, Question 17: Drawing Cumulative Frequency Diagrams

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 8 marks

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The question, in short

From a grouped frequency table of 60 children's play-area times, draw a cumulative frequency diagram and use it to estimate median, interquartile range and a count above 80 minutes.

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

Part (a) · 3 marks

Plot cumulative frequencies against upper class boundaries on the given grid and join to draw the cumulative frequency curve.

  1. 1Cumulative frequencies: 4, 11, 19, 43, 60
  2. 2Plot (0, 0), (10, 4), (40, 11), (60, 19), (90, 43), (120, 60) at the upper class boundaries
  3. 3Join with a smooth increasing curve

AnswerCorrect cumulative frequency curve

Part (bi) · 1 mark

Read from the curve the time corresponding to cumulative frequency 30 to estimate the median.

  1. 1Median at cumulative frequency 60/2 = 30
  2. 2Read across from 30 to the curve and down to the time axis (between 60 and 90 minutes)

Answer74 (accept 72 to 76)

Part (bii) · 2 marks

Use the curve to find lower and upper quartiles, then subtract to estimate the interquartile range.

  1. 1Lower quartile: read at CF 15 (between 40 and 60 minutes)
  2. 2Upper quartile: read at CF 45 (between 90 and 120 minutes)
  3. 3IQR = upper quartile − lower quartile

Answer43.5 (accept 40 to 47)

Part (biii) · 2 marks

Read cumulative frequency at 80 minutes and subtract from 60 to estimate children spending more than 80 minutes.

  1. 1Read up from t = 80 to the curve and across to the cumulative frequency axis
  2. 2Number = 60 − that reading

Answer25 (accept 23 to 27)

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Also searched as: 4024/11/M/J/24 · 4024_s24_qp_11 · 4024 s24 11 · question 17.
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