The table below shows the frequency distribution of the marks scored by fifty students 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
3
4
6
13
10
5
3
2
2
(a) Draw the cumulative frequency curve for the distribution. (b) Use your curve to estimate the : (i) upper quartile; (ii) pass mark if 60% of the students passed.
Explanation
Marks
Upper classboundary
Freq
Cum Freq
0-9
9.5
2
2
10-19
19.5
3
5
20-29
29.5
4
9
30-39
39.5
6
15
40-49
49.5
13
28
50-59
59.5
10
38
60-69
69.5
5
43
70-79
79.5
3
46
80-89
89.5
2
48
90-99
99.5
2
50
(a) (b)(i) Upper quartile \(Q_{3}\) = 57 marks (ii) Pass mark if 60% of the class passed = 42 marks
