A-LevelMathematicsProbability and statistics9709/51 · May/June 2021 · Q58 Marks

The times taken by 200 players to solve a computer puzzle are summarised in the following table. Time (t seconds) 0 ≤ t < 10 10 ≤ t < 20 20 ≤ t < 40 40 ≤ t < 60 60 ≤ t < 100 Number of players 16 54 78 32 20

(a)Draw a histogram to represent this information.[4]
(b)Calculate an estimate of the mean time taken by these 200 players.[2]
(c)Find the greatest possible value of the interquartile range of these times.[2]

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Mark scheme

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

[M1] At least 4 frequency densities calculated, accept unsimplified. May be read from graph using their scale, 3SF or correct
[A1] All heights correct on graph
[B1] Bar ends at 0, 10, 20 .., etc. with a horizontal linear scale with at least 3 values indicated, 0 < horizontal axis < 100
[B1] Axes labelled: Frequency density (fd), time (t) and seconds. Linear vertical scale, with at least 3 values indicated 0 < vertical axis < 5.4
[M1] Uses at least 4 midpoint attempts (e.g. 5 ± 0.5). Accept unsimplified expression, denominator either correct or their Σfrequencies
[A1] Accept 32.2
[M1] A value in correct UQ (40–60) – a value in correct LQ (10-20)
[A1] Condone 49.9

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