0580/41 May/Jun 2021, Question 8: Box-and-whisker plot

Part (ai) · 2 marks

Complete the cumulative frequency table for the five mass intervals using the given frequencies.

1. 1Keep adding: 3, 3 + 19 = 22, 22 + 21 = 43, 43 + 5 = 48, 48 + 2 = 50

Answer| Mass (k kg) | k ≤ 10 | k ≤ 25 | k ≤ 35 | k ≤ 40 | k ≤ 50 | | Cumulative frequency | 3 | 22 | 43 | 48 | 50 |

Part (aii) · 3 marks

Plot the cumulative frequency diagram on the grid with mass on the horizontal axis and cumulative frequency on the vertical axis.

1. 1Plot (0, 0), (10, 3), (25, 22), (35, 43), (40, 48), (50, 50) at the upper ends of the intervals
2. 2Join with a smooth increasing curve

Answercorrect diagram

Part (aiii) · 1 mark

Read from your cumulative frequency diagram an estimate for the number of children with mass 32 kg or less.

1. 1Read up from 32 kg to the curve and across
2. 2About 37 children

Answer35 to 38

Part (b) · 4 marks

Using the cumulative frequency curve and the tallest height 1.83 m and shortest height 1.45 m, draw a box-and-whisker plot on the grid.

1. 1Read from the curve at cumulative frequencies 25, 50, 75: LQ = 1.57, median = 1.64, UQ = 1.71
2. 2Draw a box from 1.57 to 1.71 with a line at 1.64
3. 3Draw whiskers out to 1.45 and 1.83

AnswerCorrect box-and-whisker plot: minimum 1.45, lower quartile 1.57, median 1.64, upper quartile 1.71, maximum 1.83

More past-paper questions on box-and-whisker plot

• 0580/42 Feb/Mar 2023 Q2 · 15 marks
• 0580/41 Oct/Nov 2021 Q3 · 16 marks