Lemmara logoLemmaraWorked solution

4MA1/1HR Jan 2023, Question 11: Drawing Cumulative Frequency Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

From a grouped frequency table of 80 patients' waiting times, complete a cumulative frequency table, draw its graph, and use it to estimate the median and 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 time interval up to 50 minutes.

  1. 1Cumulative frequency adds each frequency to the total so far.
  2. 20 < W ≤ 10: 7
  3. 30 < W ≤ 20: 7 + 10 = 17
  4. 40 < W ≤ 30: 17 + 15 = 32
  5. 50 < W ≤ 40: 32 + 32 = 64
  6. 60 < W ≤ 50: 64 + 16 = 80

Answer7, 17, 32, 64, 80

Part (b) · 2 marks

Plot the cumulative frequency graph on the given grid with axes for cumulative frequency and time.

  1. 1Plot points at (10, 7), (20, 17), (30, 32), (40, 64), (50, 80).
  2. 2Join the points with smooth curve or line segments.

AnswerA cumulative frequency curve through (10, 7), (20, 17), (30, 32), (40, 64), (50, 80)

Part (c) · 1 mark

Read the median waiting time from your cumulative frequency graph.

  1. 1Find median: half of 80 is 40.
  2. 2Go across from cumulative frequency 40 to the curve, then down to time axis.
  3. 3Read value: approximately 33 minutes.

Answer33 (accept 32 to 34)

Part (d) · 2 marks

Use the graph to estimate the lower and upper quartiles, then find the interquartile range.

  1. 1Lower quartile: 80 ÷ 4 = 20
  2. 2Go across from 20 to curve, then down: approximately 21.5
  3. 3Upper quartile: 3 × 80 ÷ 4 = 60
  4. 4Go across from 60 to curve, then down: approximately 37.5
  5. 5Interquartile range = 37.5 − 21.5 = 16

Answer16 (accept 15 to 17)

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 1HR January 2023 · 4MA1/1HR · 4ma1 jan23 1hr · question 11.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.