The table shows the frequency distribution of marks scored by some candidates in an examination.
Marks
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99
Freq
2
5
8
18
20
15
5
4
2
1
(a) Draw the cumulative frequency curve of the distribution. (b) Use your graph to estimate the : (i) semi-interquartile range of the distribution; (ii) percentage of candidates who passed with distinction if the least mark for distinction was 72.
Explanation
Marks
Class boundaries
Freq
Cum Freq
0-9
0 - 9.5
2
2
10 - 19
9.5 - 19.5
5
7
20 - 29
19.5 - 29.5
8
15
30 - 39
29.5 - 39.5
18
33
40 - 49
39.5 - 49.5
20
53
50 - 59
49.5 - 59.5
15
68
60 - 69
59.5 - 69.5
5
73
70 - 79
69.5 - 79.5
4
77
80 - 89
79.5 - 89.5
2
79
90 - 99
89.5 - 99.5
1
80
(a) (b)(i) Lower quartile, Upper quartile, Semi-interquartile range = = = (ii) Number of students that passed with distinction = (80 - 74) = 6 students Percentage =
