Find the variance and standard devaiation of the following frequency distribution.

${ x }_{ i }$	6	10	14	18	24	28	30
${ f }_{ i }$	2	4	7	12	8	4	3

Now we can prepare a table for calculating various & standard deviation

$x_i$	$f_i$	$x_i^2$	$f_ix_i$	$f_i x_i^2$
6 10 14 18 24 28 30	2 4 7 12 8 4 3	36 100 196 324 576 784 900	12 40 98 216 192 112 90	72 400 1372 3888 4608 3136 2700
Total	$40$		$760$	$16,176$

Here $\sum f = N = 40$

We know mean $\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i} = \dfrac{760}{40} = 19$

variance $(\sigma^2) = \dfrac{1}{N} \sum f_i x_i^2 - (\bar{x})^2$

$= \dfrac{1}{40} (16176) - (19)^2$

$= 404.4 - 361$

$= 43.4$

Standard deviation

$(\sigma) = \sqrt{variance}$

$= \sqrt{43.4}$

$= 6.59$ (Rounded two decimals)