The frequency distribution shows tha marks of 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
No. of
Students
2
4
9
13
18
32
13
5
3
1
(a) Draw cumulative frequency curve for the distribution .
(b) Use your curve to estimate : (i) the median ; (ii) the lower quartile ; (iii) the 60th percentile.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Marks
Frequency
Cum. freq
1 - 10
2
2
11 - 20
4
6
21 - 30
9
15
31 - 40
13
28
41 - 50
18
46
51 - 60
32
78
61 - 70
13
91
71 - 80
5
96
81 - 90
3
99
91 - 100
1
100
(b)(i) \(N = \sum f = 100\)
\(Median = \frac{1}{2}N = \frac{1}{2}(100)\)
= 50th percentile.
\(\therefore Median = 52\).
(ii) \(Q_{1} = \frac{1}{4} N = \frac{1}{4}(100)\)
= 25th percentile.
\(\therefore Q_{1} = 39\)
(iii) 60th percentile = 55.
Source: Myschool Past Questions Archive (Record #53193)