The table below shows the marks obtained by forty pupils in a Mathematics test.
| Marks | 0 – 9 | 10 – 19 | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 |
| No of pupils | 4 | 5 | 6 | 12 | 8 | 5 |
(a) Draw a histogram for the mark distribution ;
(b) Use your histogram to estimate the mode ;
(c) Calculate the median of the distribution.
Explanation
(a)
| Marks | Class boundary | Freq | Cum freq |
| 0 – 9 | 0 – 9.5 | 4 | 4 |
| 10 – 19 | 9.5 – 19.5 | 5 | 9 |
| 20 – 29 | 19.5 – 29.5 | 6 | 15 |
| 30 – 39 | 29.5 – 39.5 | 12 | 27 |
| 40 – 49 | 39.5 – 49.5 | 8 | 35 |
| 50 – 59 | 49.5 – 59.5 | 5 | 40 |
(b) Mode = 35.5
(c) Median = (L_{1} + frac{(frac{N}{2} – sum f_{p}) times c}{f_{m}})
where (L_{1}) = lower class boundary of median class = 29.5
(N = sum f = 40) ; (sum f_{p}) = cumulative frequency before median class = 15.
(f_{m}) = frequency of median class = 12, c = class interval = 10.
Median = (29.5 + frac{(frac{40}{2} – 15) times 10}{12})
= (29.5 + frac{(20 – 15) times 10}{12})
= (29.5 + 4.17 = 33.67)