Following are the total scores of three subjects of seventy four year 8 students from a high school.
10 1 4 6 7 8 9
11 0 2 3 3 3 6 8 8 8 9
12 0 0 0 0 1 1 2 2 3 4 6 7
13 3 3 4 5 6 7 7 9 9
14 0 1 2 5 7 7 9
15 0 2 3 4 8 9
16 1 4 6 6 8
17 0 7 7 9
18 1 4 8
19 4 5 7
20 3 4 6
21 2 4
22 3 6
23 8
24
25
26 2
(a)
(i) Find the five number summary for this data set.
(ii) Determine whether there are any outliers and sketch a box-plot showing clearly thresholds and outliers (if any).
(iii) Describe the shape of this distribution.
(b)
(i) Find the mean, variance and the coefficient of variation of this data set.
(ii) What proportion of total scores are within 1 standard deviation of the mean? Compare this proportion with the corresponding empirical rule and comment.