A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2019 · Q59 Marks

Last Saturday, 200 drivers entering a car park were asked the time, in minutes, that it had taken them to travel from home to the car park. The results are summarised in the following cumulative frequency table. | Time (t minutes) | t≤10 | t≤20 | t≤30 | t≤50 | t≤70 | t≤90 | | :-------------------- | :--- | :--- | :--- | :--- | :--- | :--- | | Cumulative frequency | 16 | 50 | 106 | 146 | 176 | 200 |

(i)On the grid, draw a cumulative frequency graph to illustrate the data.[2]
(ii)Use your graph to estimate the median of the data.[1]
(iii)For 80 of the drivers, the time taken was at least T minutes. Use your graph to estimate the value of T.[2]
(iv)Calculate an estimate of the mean time taken by all 200 drivers to travel to the car park.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[B1] Axes labelled 'cumulative frequency' (or cf) and 'time (or t) [in] min(utes)', linear scales from 0 to 90 and 0 to 200 with at least 3 values marked on each axis.
[B1] (0, 0); (10, 16); (20, 50); (30, 106); (50, 146); (70,176); (90,200) 7 correctly plotted points above upper boundaries joined in a curve or line segments
[B1] 28 <= median < 30
[M1] For seeing 120 in a calculation or marked on the graph
[A1FT] 36 <= Ans < 39 or FT from their graph SC1 unsupported answer in range
[B1] Seen. Allow unsimplified
[M1] At least 4 correct midpoints (5, 15, 25, 40, 60, 80) used in a calculation
[M1] Summing products of their 6 mid-points (not lower or upper bound or class width) × their frequencies / 200 (or their Σf), unsimplified
[A1] Accept 36.6

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