A-LevelMathematicsProbability and statistics9709/51 · May/June 2022 · Q39 Marks

The times taken to travel to college by 2500 students are summarised in the table. Time taken (t minutes) | 0 ≤ t < 20 | 20 < t < 30 | 30 ≤ t < 40 | 40 < t < 60 | 60 < t < 90 Frequency | 440 | 720 | 920 | 300 | 120

(a)Draw a histogram to represent this information.[4]
(b)From the data, the estimate of the mean value of t is 31.44. Calculate an estimate of the standard deviation of the times taken to travel to college.[3]
(c)In which class interval does the upper quartile lie?[1]
(d)It was later discovered that the times taken to travel to college by two students were incorrectly recorded. One student's time was recorded as 15 instead of 5 and the other's time was recorded as 65 instead of 75. Without doing any further calculations, state with a reason whether the estimate of the standard deviation in part (b) would be increased, decreased or stay the same.[1]

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Mark scheme

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

[M1] At least 4 frequency densities calculated (Frequency / class width, e.g. 440/20, condone 440/19.5, 440/20.5) Accept unsimplified, may be read from graph using their scale
[A1] All heights correct on graph NOT FT
[B1] Bar ends at [0,] 20, 30, 40, 60, 90 at axis with a horizontal linear scale with at least 3 values indicated. 0 <= horizontal scale <= 90
[B1] Axes labelled frequency density (fd), time (t) and minutes (mins) or in a title. Linear vertical scale, with at least 3 values indicated 0 <= vertical axes <= 92 (condone 90 used).
[B1] At least 4 correct midpoints seen
[M1] Correct formula for variance or standard deviation (- mean² included with their midpoints (not upper bound, lower bound, class width, frequency density, frequency or cumulative frequency) and their ∑f if calculated. Condone 1 data error.
[A1] WWW, allow 15.16[3...]
[B1] 30-40
[B1] Stays the same, data still in same intervals

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