The table shows the marks obtained by a group of students in a class test.
| Marks | 40 – 44 | 45 – 49 | 50 – 54 | 55 – 59 | 60 – 64 | 65 – 69 |
|
No of students |
4 | 9 | 18 | 23 | 10 | 6 |
(a) Draw a histogram for the distribution ;
(b) Use your histogram to estimate the median of the distribution.
Explanation
| Marks | No of students | Class boundaries |
| 40 – 44 | 4 | 39.5 – 44.5 |
| 45 – 49 | 9 | 44.5 – 49.5 |
| 50 – 54 | 18 | 49.5 – 54.5 |
| 55 – 59 | 23 | 54.5 – 59.5 |
| 60 – 64 | 10 | 59.5 – 64.5 |
| 65 – 69 | 6 | 64.5 – 69.5 |
| 70 |
(b) Median = (L_{1} + frac{(frac{N}{2} – sum f_{1}) times c}{f_{med}})
= (54.5 + frac{(frac{70}{2} – 31) times 5}{23})
= (54.5 + 0.9 = 55.4)