Q.
Find variance of the following data.
Class interval
Frequency
4-8
3
8-12
6
12-16
4
16-20
7
| Class interval | Frequency |
|---|---|
| 4-8 | 3 |
| 8-12 | 6 |
| 12-16 | 4 |
| 16-20 | 7 |
Statistics
Solution:
We have
Class Interval
Frequency
$f_i$
Mid point $x_i$
$f_i x_i$
$x_i - \bar x$
$(x_i - \bar x)^2$
$f_i (x_i -\bar x)^2$
4-8
3
6
18
-7
49
147
8-12
6
10
60
-3
9
54
12-16
4
14
56
1
1
4
16-20
7
18
126
5
25
175
Total
20
260
380
$\therefore $ Mean $\left(\bar{x}\right) =\frac{ \Sigma \,f_{i}x_{i}}{\Sigma \,f_{i}}$
$ = \frac{260}{20} = 13$
$ \therefore $ Varience $\left(\sigma^{2}\right) = \frac{\Sigma\, f_{i}\left(x_{i} -\bar{x}\right)^{2}}{\Sigma\, f_{i}}$
$ = \frac{380}{20}= 19$
| Class Interval | Frequency $f_i$ | Mid point $x_i$ | $f_i x_i$ | $x_i - \bar x$ | $(x_i - \bar x)^2$ | $f_i (x_i -\bar x)^2$ |
|---|---|---|---|---|---|---|
| 4-8 | 3 | 6 | 18 | -7 | 49 | 147 |
| 8-12 | 6 | 10 | 60 | -3 | 9 | 54 |
| 12-16 | 4 | 14 | 56 | 1 | 1 | 4 |
| 16-20 | 7 | 18 | 126 | 5 | 25 | 175 |
| Total | 20 | 260 | 380 |