S1 January 2012 Q4

EdexcelOld spec13 marksData Processing

4. The marks, \(x\), of 45 students randomly selected from those students who sat a mathematics examination are shown in the stem and leaf diagram below.

MarkTotals
36 9 9(3)
40 1 2 2 3 4(6)
45 6 6 6 8(5)
50 2 3 3 4 4(6)
55 5 6 7 7 9(6)
60 0 0 0 1 3 4 4 4(9)
65 5 6 7 8 9(6)
71 2 3 3(4)

Key (3|6 means 36)

(a) Write down the modal mark of these students. (1)
(b) Find the values of the lower quartile, the median and the upper quartile. (3)

For these students \(\sum x = 2497\) and \(\sum x^2 = 143\,369\)

(c) Find the mean and the standard deviation of the marks of these students. (3)
(d) Describe the skewness of the marks of these students, giving a reason for your answer. (2)

The mean and standard deviation of the marks of all the students who sat the examination were 55 and 10 respectively. The examiners decided that the total mark of each student should be scaled by subtracting 5 marks and then reducing the mark by a further 10%.

(e) Find the mean and standard deviation of the scaled marks of all the students. (4)
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