A-LevelMathematicsProbability and statistics9709/51 · May/June 2020 · Q711 Marks

The numbers of chocolate bars sold per day in a cinema over a period of 100 days are summarised in the following table. Number of chocolate bars sold [1-10, 11-15, 16-30, 31-50, 51-60]; Number of days [18, 24, 30, 20, 8]

(a)Draw a histogram to represent this information.[5]
(b)What is the greatest possible value of the interquartile range for the data?[2]
(c)Calculate estimates of the mean and standard deviation of the number of chocolate bars sold.[4]

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Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[1] Class widths: 10, 5, 15, 20, 10
[1] Frequency density = frequency/their class width: 1.8, 4.8, 2, 1, 0.8
[1] All heights correct on diagram (using a linear scale)
[1] Correct bar ends
[1] Bar ends: 10.5, 15.5, 30.5, 50.5, 60.5
[1] 11–15 and 31–50 (referring to the classes containing Q1 and Q3, respectively)
[1] Greatest IQR = 50 – 11 = 39
[1] Mean = (18×5.5 + 24×13 + 30×23 + 20×40.5 + 8×55.5) / 100 = 2355 / 100 = 23.6
[1] Var = (18×5.5^2 + 24×13^2 + 30×23^2 + 20×40.5^2 + 8×55.5^2) / 100 - mean^2 = 77917.5 / 100 - 23.6^2
[1] Variance = 779.175 - 556.96 = 222.215
[1] Standard deviation = 15.0 (FT their variance)

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