Q. Find the variance of the following data: $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$
Statistics
Solution:
From the given data, we can form the following table. Let $A= 14$
$x_i$
$y_{i} = \frac{x_{i} -14}{2}$
$\left(x_{i} -\bar{x}\right)$
$\left(x_{i} -\bar{x}\right)^{2}$
6
-4
-9
81
8
-3
-7
49
10
-2
-5
25
12
-1
-3
9
14
0
-1
1
16
1
1
1
18
2
3
9
20
3
5
25
22
4
7
49
24
5
9
81
Total
5
330
Therefore, Mean $\bar{x} =$ assumed mean + $ \frac{\sum\limits_{i=1}^{n} y_{i}}{n} \times h$
$= 14 + \frac{5}{10} \times2 = 15 $
and varience $\left(\sigma^{2}\right) = \frac{1}{n}\sum\limits_{i=1}^{10} \left(x_{i} \bar{x}\right)^{2}$
$ = \frac{1}{10} \times 330$
$ = 33$
| $x_i$ | $y_{i} = \frac{x_{i} -14}{2}$ | $\left(x_{i} -\bar{x}\right)$ | $\left(x_{i} -\bar{x}\right)^{2}$ |
|---|---|---|---|
| 6 | -4 | -9 | 81 |
| 8 | -3 | -7 | 49 |
| 10 | -2 | -5 | 25 |
| 12 | -1 | -3 | 9 |
| 14 | 0 | -1 | 1 |
| 16 | 1 | 1 | 1 |
| 18 | 2 | 3 | 9 |
| 20 | 3 | 5 | 25 |
| 22 | 4 | 7 | 49 |
| 24 | 5 | 9 | 81 |
| Total | 5 | 330 |