Find the variance of the following data $6, 8, 10, 12, 14, 16 , 18, 20, 22, 24$.

Given Data

$6,8,10,12, 14, 16,18,20,22,24$

$x_1$	$\bar{x}$	$x_i - \bar{x}$	$(x_i - \bar{x})^2$
$6$ $8$ $10$ $12$ $14$ $16$ $18$ $20$ $22$ $24$	$15$ $15$ $15$ $15$ $15$ $15$ $15$ $15$ $15$ $15$	$-9$ $-7$ $-5$ $-3$ $-1$ $1$ $3$ $5$ $7$ $9$	$81$ $49$ $25$ $9$ $1$ $1$ $9$ $25$ $49$ $81$

We know

Mean $= \dfrac{\displaystyle \sum x}{n}$

where n is no" of observations

$\displaystyle \sum (x_i - \bar{x})^2$

$= 330$

$\therefore$ mean $(\bar{x}) = \dfrac{\displaystyle\sum x}{n} = \dfrac{6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{10}$

$= \dfrac{150}{10}$

$\bar{x} = 15$

$\therefore$ variance $= \dfrac{\displaystyle\sum (x_i - \bar{x})^2}{n - 1}$

$= \dfrac{330}{10-1}$

$= \dfrac{330}{9}$

variance $= 36.67$