Question

The number of books read by $8$ students during a month are $2,5,8,11,14,6,12,10$. Calculate the standard deviation of the data.

Answer 1

x	$x^2$
$2$	$4$
$5$	$25$
$6$	$36$
$8$	$64$
$10$	$100$
$11$	$121$
$12$	$144$
$14$	$196$
$\sum x=68$	$\sum x^2=690$

Here, the number of items, $n=8$
Standard deviation, $\sigma =\sqrt{\frac{\sum x^2}{n}-{\left(\frac{\sum x}{n}\right)}^2}$
$=\sqrt{\frac{690}{8}-{\left(\frac{68}{8}\right)}^2}$
$=\sqrt{86.25-(8.5{)}^2}$
$=\sqrt{86.25-72.25}$
$=\sqrt{14}\simeq 3.74$.