A-LevelMathematicsProbability and statistics9709/53 · May/June 2025 · Q45 Marks

84 people attempt a particular puzzle. The times taken, in minutes, to complete the puzzle are recorded. These times are represented in the cumulative frequency graph below. [Figure X.X]

(a)Use the graph to estimate how many people took between 4 and 7.5 minutes to complete the puzzle.[1]
(b)On the grid below, draw a box-and-whisker plot to summarise the information in the cumulative frequency graph.[4]

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Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[B1] Accept 43 or 44.
[B1] Median = 4.8. Plotted on box.
[B1] LQ = 3.7 or 3.8, UQ = 6.5 or 6.6. Plotted on box.
[B1] Correct end points for whiskers (2 and 12). Whiskers not through box, not drawn at corners of box. Accept end points of whiskers as dots or without vertical line.
[B1] Linear scale and labelled Time in minutes. OE. Linear scale from 2 to 12, at least 3 equally spaces values marked using at least half of the grid. Label to include time and minutes.

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