A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2018 · Q610 Marks

The daily rainfall, x mm, in a certain village is recorded on 250 consecutive days. The results are summarised in the following cumulative frequency table. Rainfall, x mm x ≤ 20 x ≤ 30 x ≤ 40 x ≤ 50 x ≤ 70 x ≤ 100 Cumulative frequency 52 94 142 172 222 250

(i)On the grid, draw a cumulative frequency graph to illustrate the data.[2]
(ii)On 100 of the days, the rainfall was k mm or more. Use your graph to estimate the value of k.[2]
(iii)Calculate estimates of the mean and standard deviation of the daily rainfall in this village.[6]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] Appropriate linear scales starting at (0,0), axes labelled cf and Rainfall, mm
[B1] Correct graph, points plotted at ucb, allow straight lines or curve
[M1] Read off from increasing graph at cf = 150
[A1] 42; Correct answer (41 ≤ r ≤ 43)
[B1] Correct frequencies
[B1] Correct midpoints (allow one error)
[M1] Using Efx/250 with mid-points attempt, not cf, cw, lb, ub
[A1] =9980/250 = 39.9(2) oe; Correct answer
[M1] Attempt at variance using their midpoints and their mean
[A1] = 539.59; σ = 23.2; Correct answer for sd

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