A-LevelMathematicsProbability and statistics9709/63 · May/June 2017 · Q711 Marks

The following histogram represents the lengths of worms in a garden. [Figure X.X]

(i)Calculate the frequencies represented by each of the four histogram columns.[2]
(ii)On the grid on the next page, draw a cumulative frequency graph to represent the lengths of worms in the garden.[4]
(iii)Use your graph to estimate the median and interquartile range of the lengths of worms in the garden.[3]
(iv)Calculate an estimate of the mean length of worms in the garden.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[M1] freq = fd × cw 10, 40, 120, 30 Attempt to multiply at least 3 fds by their 'class widths'
[A1]
[B1] length <5 <10 <20 <25, cf 10 50 170 200 3 or more correct cfs heights on graph 10, 50, 170, 200
[B1] Labels correct cf and length(cm), linear scales from zero (allow 0.5 on horizontal axis)
[M1] Attempt (at least three) at plotting at upper end points (either 5 or 5.5, 10 or 10.5 etc.)
[A1] Starting at (0, 0) polygon or smooth curve increasing with plotted points at lengths 5, 10, 20 and 25
[B1] median = 14.2 Median (accept 13.2 – 15.2)
[M1] '18.5'- '10' Subt their LQ from their UQ if reasonable from their graph
[A1FT] IQ range = 8.5 Correct FT using LQ = 10 and UQ between 17.5 and 19.5
[M1] mean = (2.5×10 +7.5×40 + 15×120 +22.5×30) / 200 Using mid points (± 0.5) and their frequencies from 7(i) in correct formula
[A1] = 14

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