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4MA1/2H Jun 2019, Question 13: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

Using a grouped frequency table of 80 taxi journey times, complete a cumulative frequency table, draw its graph, then estimate the median and interquartile range from the graph.

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

Part (a) · 1 mark

Fill in the cumulative frequency column for the six time intervals ending at 5, 10, 15, 20, 25 and 30 minutes.

  1. 17
  2. 27 + 10 = 17
  3. 317 + 12 = 29
  4. 429 + 19 = 48
  5. 548 + 18 = 66
  6. 666 + 14 = 80

Answer7, 17, 29, 48, 66, 80

Part (b) · 2 marks

Plot the cumulative frequency against time on the grid and join the points with a smooth cumulative frequency curve.

  1. 1Plot each cumulative frequency at the top of its class
  2. 2Points: (5, 7), (10, 17), (15, 29)
  3. 3Then (20, 48), (25, 66), (30, 80)
  4. 4Join the points with a smooth curve or straight lines

AnswerA cumulative frequency graph through (5, 7), (10, 17), (15, 29), (20, 48), (25, 66) and (30, 80)

Part (c) · 1 mark

Read off the median journey time from your cumulative frequency graph.

  1. 1Find 40 on cumulative frequency axis
  2. 2Draw horizontal line to meet graph
  3. 3Draw vertical line down to time axis
  4. 4Read value between 17 and 19

Answer17 to 19

Part (d) · 2 marks

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

  1. 1Find 20 on cumulative frequency axis
  2. 2Draw horizontal line to meet graph
  3. 3Draw vertical line down to time axis to get lower quartile ≈ 11−13
  4. 4Find 60 on cumulative frequency axis
  5. 5Draw vertical line down to time axis to get upper quartile ≈ 22−24
  6. 6Interquartile range = upper quartile − lower quartile
  7. 722 − 13 = 9, 24 − 11 = 13
  8. 8Answer is between 9 and 13

Answer9 to 13

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