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

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

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The question, in short

Sandeep recorded walk times for 100 adults in a cumulative frequency table; draw the cumulative frequency graph and use it to estimate the median time and a probability.

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 from the given table of times and cumulative frequencies.

  1. 1Plot each cumulative frequency at the end of its interval
  2. 2Points: (40, 6), (50, 20), (60, 56), (70, 84), (80, 95), (90, 100)
  3. 3A cumulative frequency curve through (40, 6), (50, 20), (60, 56), (70, 84), (80, 95), (90, 100), plotted at the end of each interval

AnswerA cumulative frequency curve through (40, 6), (50, 20), (60, 56), (70, 84), (80, 95), (90, 100), plotted at the end of each interval

Part (b) · 2 marks

Use your cumulative frequency graph to estimate the median walking time for the 100 adults.

  1. 1Find cumulative frequency 50 on graph
  2. 2Read off time corresponding to 50 people
  3. 3Time = 58 − 59 minutes

Answer58.5 (accept 57.5 to 59.5)

Part (c) · 3 marks

Use your graph to estimate the probability that a randomly chosen adult walked for more than 72 minutes.

  1. 1Find time = 72 minutes on x-axis
  2. 2Read up to curve and across to find cumulative frequency at 72 minutes
  3. 3Cumulative frequency at 72 minutes ≈ 88
  4. 4Number of adults who walked more than 72 minutes = 100 − 88 = 12
  5. 5Probability = 12/100

Answer0.12 to 0.14

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