Lemmara logoLemmaraWorked solution

4MA1/2H Jan 2023, Question 12: Drawing Cumulative Frequency Diagrams

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

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

From a cumulative frequency graph of shopping times for 60 people, estimate the median, count those over 55 minutes, and complete a grouped frequency table.

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

Part (a) · 1 mark

Use the cumulative frequency graph to estimate the median shopping time in minutes.

  1. 1Find 30 on the cumulative frequency axis (half of 60)
  2. 2Draw horizontal line to the curve
  3. 3Draw vertical line down to the time axis
  4. 4Read value: approximately 44

Answer43.5 − 44.5

Part (b) · 2 marks

Use the graph to estimate how many people took longer than 55 minutes to shop.

  1. 1Find 55 on the time axis
  2. 2Draw vertical line up to the curve
  3. 3Draw horizontal line left to the cumulative frequency axis
  4. 4Read cumulative frequency: approximately 48 to 49
  5. 5Subtract from total: 60 − 48 = 12
  6. 660 − 49 = 11
  7. 7Answer is 11 or 12

Answer11 or 12

Part (c) · 2 marks

Use the graph to fill in the missing frequencies for each 10-minute interval from 20 to 70 minutes.

  1. 1For 20 < m ≤ 30: read cumulative frequency at 30 min ≈ 15, subtract previous 8 → 15 − 8 = 7
  2. 2For 30 < m ≤ 40: read cumulative at 40 min ≈ 25, subtract previous 15 → 25 − 15 = 10
  3. 3For 40 < m ≤ 50: read cumulative at 50 min ≈ 40, subtract previous 25 → 40 − 25 = 15
  4. 4For 50 < m ≤ 60: read cumulative at 60 min ≈ 55, subtract previous 40 → 55 − 40 = 15
  5. 5For 60 < m ≤ 70: total 60, subtract 55 → 60 − 55 = 5
  6. 6Complete table with 7, 10, 15, 15, 5

Answer7, 10, 15, 15, 5

Stuck on a step? Read the free lesson: Drawing Cumulative Frequency Diagrams

Practise more drawing cumulative frequency diagrams questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on drawing cumulative frequency diagrams

Also searched as: 4MA1 2H January 2023 · 4MA1/2H · 4ma1 jan23 2h · question 12.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.