A-LevelMathematicsProbability and statistics9709/52 · Feb/Mar 2024 · Q38 Marks

The times taken, in minutes, by 150 students to complete a puzzle are summarised in the table. Time taken (t minutes) 0 < t < 20 20 ≤ t < 30 30 < t < 35 35 < t < 40 40 < t < 50 50 < t < 70 Frequency 8 23 35 52 20 12

(a)Draw a histogram to represent this information.[4]
(b)Calculate an estimate for the mean time for these students to complete the puzzle.[3]
(c)In which class interval does the lower quartile of the times lie?[1]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

[M1] At least five frequency densities (f/cw), e.g. 8/20, 23/10... Accept unsimplified.
[A1] All heights correct on graph (no FT).
[B1] Bar ends at [0,] 20, 30, 35, 40, 50, 70 with a linear scale and at least three values indicated ‘linearly'.
[B1] Axes labelled frequency density (fd) and time (mins). Frequency density scale vertical starts at 0 with a linear scale and at least three values indicated ‘linearly'. Axes can be reversed.
[B1] At least five correct mid-points seen or used in formula.
[M1] Correct mean formula using their 6 midpoints (must be within class, not upper bound, lower bound). Condone one error. If correct midpoints seen, accept 5362.5/150 or (80+575+1137.5+1950+900+720)/150.
[A1] Accept 35.8, not 143/4. If A0 scored, SC B1 for 35.75, 35 3/4 only.
[B1] Condone '3rd' interval, 30 – 35.

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