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4024/13 May/Jun 2025, Question 16: Constructing a Cumulative Frequency Table

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

From a cumulative frequency curve for 80 students' exam marks, complete a grouped frequency table and estimate median, 30th percentile, and count scoring 76 or more.

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

Part (a) · 2 marks

Use the cumulative frequency graph to fill in the missing frequencies for the intervals 40 < m ≤ 55, 55 < m ≤ 70, 70 < m ≤ 90, and 90 < m ≤ 100.

  1. 1Frequency = difference between cumulative frequencies at the ends of each class
  2. 240 < m ≤ 55: 35 − 15 = 20
  3. 355 < m ≤ 70: 60 − 35 = 25
  4. 470 < m ≤ 90: 77 − 60 = 17
  5. 590 < m ≤ 100: 80 − 77 = 3

Answer| Mark (m) | 40 < m ≤ 55 | 55 < m ≤ 70 | 70 < m ≤ 90 | 90 < m ≤ 100 | | Frequency | 20 | 25 | 17 | 3 |

Part (bi) · 1 mark

Read from the cumulative frequency curve to estimate the median mark.

  1. 1Median: 1/2 × 80 = 40th student
  2. 2Read across from cumulative frequency 40: median ≈ 58 marks

Answer58

Part (bii) · 2 marks

Use the cumulative frequency diagram to estimate the 30th percentile mark.

  1. 130% of 80 = 0.3 × 80 = 24
  2. 2Read across from cumulative frequency 24: 30th percentile ≈ 48 marks

Answer48

Part (biii) · 2 marks

Use the graph to find how many students scored 76 marks or more.

  1. 1Read up from 76 marks: cumulative frequency ≈ 66
  2. 2Scored 76 or more: 80 − 66 = 14 students

Answer14

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