A-LevelMathematicsProbability and statistics9709/52 · Feb/Mar 2022 · Q36 Marks

At a summer camp an arithmetic test is taken by 250 children. The times taken, to the nearest minute, to complete the test were recorded. The results are summarised in the table. Time taken, in minutes | 1–30 | 31–45 | 46–65 | 66–75 | 76–100 Frequency | 21 | 30 | 68 | 86 | 45

(a)Draw a histogram to represent this information.[4]
(b)State which class interval contains the median.[1]
(c)Given that an estimate of the mean time is 61.05 minutes, state what feature of the distribution accounts for the median and the mean being different.[1]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

M1 At least 4 frequency densities calculated
A1 All heights correct on graph
B1 Bar ends at 0.5, 30.5, 45.5, 65.5, 75.5, 100.5 (at axis), 5 bars drawn, condone 0 in first bar 0.5 < time axis < 100.5, linear scale with at least 3 values indicated.
B1 Axes labelled: Frequency density (fd), time (t) and mins (or appropriate title). Linear fd scale, with at least 3 values indicated 0 < fd axis < 8.6
Class Widths and Frequency Densities:
1-30: Width = 30, Frequency = 21, FD = 0.7
31-45: Width = 15, Frequency = 30, FD = 2
46-65: Width = 20, Frequency = 68, FD = 3.4
66-75: Width = 10, Frequency = 86, FD = 8.6
76-100: Width = 25, Frequency = 45, FD = 1.8
B1 Condone 65.5 – 75.5
66-75
B1 Or skewed, ignore nature of skew
Distribution is not symmetrical

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