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?
Explanation
(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)