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4MA1/2HR Jun 2018, Question 11: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 8 marks

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The question, in short

From a grouped frequency table of money spent by 120 families, find the modal class, build cumulative frequencies, plot a cumulative frequency graph, and use it to estimate the interquartile range and a count above £450.

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

Part (a) · 1 mark

State which money-spent class has the highest frequency.

  1. 1The modal class is the one with the highest frequency.
  2. 2The frequency for 100 < m ≤ 200 is 36, which is the largest.
  3. 3So the modal class is 100 < m ≤ 200.

Answer100 < m ≤ 200

Part (b) · 1 mark

Fill in the cumulative frequency for each upper class boundary from 100 up to 600.

  1. 1Cumulative frequency is found by adding frequencies step by step.
  2. 20 < m ≤ 100: 10
  3. 30 < m ≤ 200: 10 + 36 = 46
  4. 40 < m ≤ 300: 46 + 34 = 80
  5. 50 < m ≤ 400: 80 + 20 = 100
  6. 60 < m ≤ 500: 100 + 15 = 115
  7. 70 < m ≤ 600: 115 + 5 = 120
  8. 8So the cumulative frequencies are 10, 46, 80, 100, 115, 120.

Answer10, 46, 80, 100, 115, 120

Part (c) · 2 marks

Plot the cumulative frequency graph on the given grid using money spent and cumulative frequency.

  1. 1Plot points at (100,10), (200,46), (300,80), (400,100), (500,115), (600,120).
  2. 2Join the points with a smooth curve or straight line segments.
  3. 3The graph starts at (0,0) and passes through all the plotted points at the upper ends of the intervals.

AnswerA cumulative frequency curve through (100, 10), (200, 46), (300, 80), (400, 100), (500, 115), (600, 120), plotted at the end of each interval

Part (d) · 2 marks

Read quartile values from the graph and find the interquartile range.

  1. 1Interquartile range = upper quartile − lower quartile.
  2. 2Lower quartile is at 1/4 × 120 = 30th value.
  3. 3Upper quartile is at 3/4 × 120 = 90th value.
  4. 4Read off the graph: when cumulative frequency is 30, money spent ≈ 155.
  5. 5When cumulative frequency is 90, money spent ≈ 350.
  6. 6Interquartile range ≈ 350 − 155 = 195.
  7. 7This is within the range 175 to 205, so estimate is 175 − 205.

Answer175 to 205

Part (e) · 2 marks

Use the graph to estimate how many families spent more than £450.

  1. 1Find cumulative frequency at £450 on the graph.
  2. 2Draw vertical line from £450 to the curve, then horizontal to cumulative frequency axis.
  3. 3Read off cumulative frequency ≈ 107 or 108.
  4. 4This is the number of families that spent £450 or less.
  5. 5Total families = 120.
  6. 6So number that spent more than £450 = 120 − 108 = 12.
  7. 7Or 120 − 107 = 13.
  8. 8So estimate is 12 or 13.

Answer12 (accept 11 to 14)

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