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4MA1/2H Jun 2021, Question 12: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

From a cumulative frequency table of distances travelled by 80 workers to Office A, draw the graph and use it to estimate median and interquartile range, then compare with Office B.

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

Part (a) · 2 marks

Draw a cumulative frequency graph on the grid using the six given cumulative frequencies plotted against the upper class boundaries 5, 10, 15, 20, 25, 30.

  1. 1Plot point at (5, 17)
  2. 2Plot point at (10, 32)
  3. 3Plot point at (15, 57)
  4. 4Plot point at (20, 70)
  5. 5Plot point at (25, 76)
  6. 6Plot point at (30, 80)
  7. 7Join points with smooth curve or line segments

AnswerA cumulative frequency graph through (5, 17), (10, 32), (15, 57), (20, 70), (25, 76) and (30, 80)

Part (b) · 1 mark

Use the cumulative frequency graph to estimate the median distance travelled by the workers.

  1. 1Find 40 on cumulative frequency axis (half of 80)
  2. 2Draw horizontal line to meet the curve
  3. 3Draw vertical line down to distance axis
  4. 4Read off value between 10.5 and 12

Answer10.5 to 12

Part (c) · 2 marks

Use the graph to estimate the lower and upper quartiles, then find the interquartile range of distances.

  1. 1Find 20 on cumulative frequency axis (lower quartile, 1/4 of 80)
  2. 2Draw horizontal line to meet the curve
  3. 3Draw vertical line down and read off LQ ≈ 5.5 to 7
  4. 4Find 60 on cumulative frequency axis (upper quartile, 3/4 of 80)
  5. 5Draw vertical line down and read off UQ ≈ 15.5 to 17
  6. 6Interquartile range = UQ − LQ ≈ (15.5 to 17) − (5.5 to 7)
  7. 7Answer is between 8.5 and 11.5

Answer8.5 to 11.5

Part (d) · 2 marks

Given Office B has median 15 km and interquartile range 5 km, write two comparisons of the distances travelled by workers at Office A and Office B.

  1. 1Compare medians: 15 km (B) > median from (b)
  2. 2So Office B workers travel further
  3. 3Compare interquartile ranges: IQR from (c) > 5 km
  4. 4So distances for Office A workers are more spread out

Answer1. Office B workers travel further 2. The distances for the office A workers are more spread out

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