A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2021 · Q36 Marks

The times taken, in minutes, by 360 employees at a large company to travel from home to work are summarised in the following table. Time, t minutes | 0 ≤ t < 5 | 5 ≤ t < 10 | 10 ≤ t < 20 | 20 ≤ t ≤ 30 | 30 ≤ t < 50 Frequency | 23 | 102 | 135 | 76 | 24

(a)Draw a histogram to represent this information.[4]
(b)Calculate an estimate of the mean time taken by an employee to travel to work.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[M1] At least 4 frequency densities calculated (f/cw), accept unsimplified and class widths ±1 of true values. May be implied by graph.
[A1] All heights correct on graph NOT FT
[B1] Bar ends at 0, 5, 10, 20, 30, 50 clear intention not to draw at 4.5 or 5.5 etc.
[B1] Axes labelled: Frequency density (fd), time (t) and mins (or appropriate title). Linear scales between 0 and 20.4 or above on vertical axis, and 0 and 50 or above on the horizontal axis. (Axes may be reversed.)
[M1] Uses at least 4 midpoint attempts (e.g. 2.5 ± 0.5) in correct formula, accept unsimplified expression, denominator either correct or their Σfrequencies.
[A1] Evaluated.

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