The frequency distribution table shows the marks obtained by 100 students in a Mathematics test.
Marks (%)
1-10
11-20
21-30
31-40
41-50
51-60
61-70
71-80
81-90
91-100
Frequency
2
3
5
13
19
31
13
9
4
1
(a) Draw the cumulative curve for the distribution. (b) Use the graph to find the : (i) 60th percentile ; (ii) probability that a student passed the test if the pass mark was fixed at 35%.
Explanation
Marks
frequency
cum freq
lower bound
upper bound
1 - 10
2
2
0.5
10.5
11 - 20
3
5
10.5
20.5
21 - 30
5
10
20.5
30.5
31 - 40
13
23
30.5
40.5
41 - 50
19
42
40.5
50.5
51 - 60
31
73
50.5
60.5
61 - 70
13
86
60.5
70.5
71 - 80
9
95
70.5
80.5
81 - 90
4
99
80.5
90.5
91 - 100
1
100
90.5
100.5
(a) (b) (i) 60th percentile is where the line from the cumulative frequency of 60 touches the curve i.e. 60th percentile = 58.5 (ii) If the pass mark was fixed at 35%, then the frequency will be 13 with the class mark 31 - 40.
