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4MA1/2H Jun 2022, Question 13: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks

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The question, in short

Using a grouped frequency table for ages of 80 people, complete a cumulative frequency table, draw its graph, then estimate the median age and the number aged 18 to 65 going to work.

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 age band up to 70 years.

  1. 17 = 7
  2. 27 + 25 = 32
  3. 332 + 20 = 52
  4. 452 + 14 = 66
  5. 566 + 8 = 74
  6. 674 + 6 = 80

Answer7, 32, 52, 66, 74, 80

Part (c) · 1 mark

Read the median age from your cumulative frequency graph for the 80 people.

  1. 1Find cumulative frequency at half of 80: 80 / 2 = 40
  2. 2Read across from cumulative frequency 40 to the curve
  3. 3Read down to find the age
  4. 4Median age is approximately 33

Answer33 (accept 32 to 35)

Part (d) · 3 marks

Use the graph to estimate how many people aged 18 to 65 are going to work, given 60% of them do.

  1. 1Use graph to find cumulative frequency at age 18: approximately 6
  2. 2Use graph to find cumulative frequency at age 65: approximately 77
  3. 3Subtract: 77 − 6 = 71
  4. 4Find 60% of 71: 0.6 × 71 = 42.6
  5. 5Estimate number going to work: 43

Answer43 (accept 42 to 44)

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