Question

Find the standard deviation for the following data:

x :	3	8	13	18	23
f :	7	10	15	10	6

Answer 1

$x_i$	$f_i$	$f_i{x}_i$	$\left(x_i-\overline{X}\right)$	${\left(x_i-\overline{X}\right)}^2$	$f_i{\left(x_i-\overline{X}\right)}^2$
3	7	21	−9.79	95.84	670.88
8	10	80	−4.79	22.94	229.4
13	15	195	0.21	0.04	0.6
18	10	180	5.21	27.14	271.4
23	6	138	10.21	104.24	625.44
	$\sum f_i=48$	$\sum f_i{x}_i=614$			$\sum f_i{\left(x_i-\overline{X}\right)}^2=1797.32$

Variance, ${\sigma }^2=\frac{\sum f_i{\left(x_i-\overline{X}\right)}^2}{\sum f_i}=\frac{1797.32}{48}=37.44$

$SD,\sigma =\sqrt{37.44}=6.12$