The table below shows the weekly profit in naira from a mini-market.
Weekly profit (N)
1-10
11-20
21-30
31-40
41-50
51-60
Freq
6
6
12
11
10
5
(a) Draw the cumulative frequency curve of the data;
(b) From your graph, estimate the : (i) median ; (ii) 80th percentile
(c) What is the modal weekly profit?
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Class Interval
(x)
Frequency
(f)
Cum. Freq
1 - 10
6
6
11 - 20
6
12
21 - 30
12
24
31 - 40
11
35
41 - 50
10
45
51 - 60
5
50
(b)(i) Median = N30.50
(ii) 80th percentile = N45
(c) The modal weekly profit = Lower class boundary of modal class + \(\frac{(f - f_{1}) \times c}{(f - f_{1}) + (f - f_{2})}\)
where \(f_{1}\) = frequency above the modal class ; \(f_{2}\) = frequency below modal class; c = class width; f = frequency of modal class.
\(\therefore \text{Modal profit} = 20.5 + \frac{(12 - 6) \times 10}{(12 - 6) + (12 - 11)}\)
= \(20.5 + \frac{60}{7}\)
= \(N29.07\)
Source: Myschool Past Questions Archive (Record #54605)