A-LevelMathematicsProbability and statistics9709/51 · May/June 2023 · Q57 Marks

The populations of 150 villages in the UK, to the nearest hundred, are summarised in the table. Population | 100 – 800 | 900 – 1200 | 1300 – 2000 | 2100 – 3200 | 3300 – 4800 Number of villages | 8 | 12 | 50 | 48 | 32

(a)Draw a histogram to represent this information.[4]
(b)Write down the class interval which contains the median for this information.[1]
(c)Find the greatest possible value of the interquartile range for the populations of the 150 villages.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[M1] At least 4 frequency densities calculated (F/cw, e.g. 8/800, condone (799 ≤ n ≤ 801)). Accept unsimplified, may be read from graph using their scale.
[A1] All heights correct on graph.
[B1] Bar ends at 50, 850, 1250, 2050, 3250, 4850 read at the axis with a horizontal linear scale with at least 3 values indicated. 50 ≤ horizontal scale < 4850.
[B1] Axes labelled frequency density (fd) and population (pop) OE, or in a title. Linear vertical scale, with at least 3 values indicated. Vertical axis must cover at least the range 0 < vertical axis < 0.0625 . Axes may be reversed.
[B1] Accept 2050 – 3250 OE. Condone ‘4th interval'.
[M1] 2050 < UQ < 3250 - 1250 < LQ < 2050.
[A1] Condone 3250 – 1250 = 2000.

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