Q. The variance of the observations $2,3,5,7, 11, 13,17,22$ is
AP EAMCETAP EAMCET 2019
Solution:
According to the given information,
$x _{i}$
$x_{i}-\bar{x}$
$\left(x_{i}-\bar{x}\right)^{2}$
2
-8
64
3
-7
49
5
-5
25
7
-3
9
11
1
1
13
3
9
17
7
49
22
12
144
$\sum x_{i}=80$
$\Sigma\left(x_{i}-\bar{x}\right)^{2}=350$
$\bar{x}=\frac{\Sigma x_{i}}{8}=\frac{80}{8}=10$
$\because \Sigma\left(x_{i}-\bar{x}\right)^{2}=350$
$\therefore $ Variance of the given observations $=\frac{\Sigma\left(x_{i}-\bar{x}\right)^{2}}{8}$
$=\frac{350}{8}=43.75$
| $x _{i}$ | $x_{i}-\bar{x}$ | $\left(x_{i}-\bar{x}\right)^{2}$ |
|---|---|---|
| 2 | -8 | 64 |
| 3 | -7 | 49 |
| 5 | -5 | 25 |
| 7 | -3 | 9 |
| 11 | 1 | 1 |
| 13 | 3 | 9 |
| 17 | 7 | 49 |
| 22 | 12 | 144 |
| $\sum x_{i}=80$ | $\Sigma\left(x_{i}-\bar{x}\right)^{2}=350$ |