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4MA1/1H Jan 2019, Question 9: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

From a grouped frequency table of 60 cycle speeds, complete the cumulative frequency table, draw the cumulative frequency graph, and estimate the interquartile range.

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 each speed class up to 60 km/h.

  1. 1Add each frequency to the running total
  2. 23, then 3 + 16 = 19, then 19 + 24 = 43
  3. 343 + 10 = 53, 53 + 5 = 58, 58 + 2 = 60
  4. 43, 19, 43, 53, 58, 60

Answer3, 19, 43, 53, 58, 60

Part (b) · 2 marks

Plot the cumulative frequency graph on the given grid of speed against cumulative frequency.

  1. 1Plot each cumulative frequency at the upper end of its class
  2. 2Points: (10, 3), (20, 19), (30, 43), (40, 53), (50, 58), (60, 60)
  3. 3Join the points with a smooth curve or straight line segments

AnswerA cumulative frequency graph through (10, 3), (20, 19), (30, 43), (40, 53), (50, 58), (60, 60)

Part (c) · 2 marks

Use the cumulative frequency graph to estimate the interquartile range of the speeds.

  1. 1There are 60 speeds, so the lower quartile is at cumulative frequency 60 ÷ 4 = 15
  2. 2Reading across from 15 on the cumulative frequency axis to the curve gives a speed of about 18 km/h
  3. 3The upper quartile is at cumulative frequency 3 × 60 ÷ 4 = 45
  4. 4Reading across from 45 on the cumulative frequency axis to the curve gives a speed of about 32 km/h
  5. 5Interquartile range = 32 − 18 = 14 km/h

Answer14 (accept 13 to 15)

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