4MA1/2HR Jun 2024, Question 11: Drawing Cumulative Frequency Diagrams

Part (a) · 2 marks

Plot the cumulative frequency graph for the given table on the grid, cumulative frequency against time in hours.

1. 1plot points at (5, 6), (10, 17), (15, 27), (20, 42), (25, 53), (30, 60)
2. 2join points with a smooth curve or straight line segments

Answera fully correct cumulative frequency graph

Part (b) · 2 marks

Use your cumulative frequency graph to estimate the interquartile range of the times.

1. 1find lower quartile at cumulative frequency 15
2. 2find upper quartile at cumulative frequency 45
3. 3read off time values from the graph at these points
4. 4subtract lower quartile time from upper quartile time
5. 5estimate interquartile range as 11.5 to 13.5 hours

Answer11.5 to 13.5

Part (c) · 2 marks

Given 25 workers spent more than W hours, use your graph to estimate W.

1. 1total workers = 60
2. 225 workers spent more than W hours
3. 3so 60 − 25 = 35 workers spent W hours or less
4. 4use cumulative frequency 35
5. 5read off time value from graph at cf = 35
6. 6estimate W as 16.5 to 18.5 hours

Answer16.5 to 18.5

Part (d) · 1 mark

For a randomly chosen worker with time H, find the probability that 5 < H ≤ 10.

1. 1number of workers who spent between 5 and 10 hours = cumulative frequency at 10 minus cumulative frequency at 5
2. 217 − 6 = 11
3. 3probability = 11 / 60

Answer11/60

More past-paper questions on drawing cumulative frequency diagrams

• 4MA1/1HR Jun 2025 Q12 · 6 marks
• 4MA1/2H Jun 2025 Q13 · 6 marks
• 4MA1/2H Jun 2024 Q13 · 5 marks
• 4MA1/1HR Jan 2023 Q11 · 6 marks
• 4MA1/2H Jan 2023 Q12 · 5 marks
• 4MA1/1H Jun 2023 Q12 · 4 marks