Question

Find the standard deviation of the numbers $62,58,53,50,63,52,55$.

Answer 1

Let us take $A=55$ as the assumed mean and form the following table.

$x$	$d=x-A=x-55$	$d^2$
$50$	$-5$	$25$
$52$	$-3$	$9$
$53$	$-2$	$4$
$55$	$0$	$0$
$58$	$3$	$9$
$62$	$7$	$49$
$63$	$8$	$64$
	$\sum d=8$	$\sum d^2=160$

$\sigma =\sqrt{\frac{\sum d^2}{n}-{\left(\frac{\sum d}{n}\right)}^2}$
$=\sqrt{\frac{160}{7}-{\left(\frac{8}{7}\right)}^2}$
$=\sqrt{\frac{160}{7}-\frac{64}{49}}$
$=\sqrt{\frac{1056}{49}}$
$=\frac{32.49}{7}$
$\therefore$ Standard deviation $\sigma \simeq 4.64$.