Statistics Question 7
Question 7 - 2024 (30 Jan Shift 1)
Let $M$ denote the median of the following frequency distribution.
| Class | $0-4$ | $4-8$ | $8-12$ | $12-16$ | $16-20$ |
|---|---|---|---|---|---|
| Frequency | 3 | 9 | 10 | 8 | 6 |
Then $20 \mathrm{M}$ is equal to :
(1) 416
(2) 104
(3) 52
(4) 208
Show Answer
Answer (4)
Solution
| Class | Frequency | Cumulative frequency |
|---|---|---|
| $0-4$ | 3 | $\mathbf{3}$ |
| $4-8$ | 9 | $\mathbf{1 2}$ |
| $8-12$ | 10 | $\mathbf{2 2}$ |
| $12-16$ | 8 | $\mathbf{3 0}$ |
| $16-20$ | 6 | $\mathbf{3 6}$ |
$\mathrm{M}=1+\left(\frac{\frac{\mathrm{N}}{2}-\mathrm{C}}{\mathrm{f}}\right) \mathrm{h}$
$M=8+\frac{18-12}{10} \times 4$
$M=10.4$
$20 M=208$
