Question

A test in General Knowledge was conducted for a class. The marks out of $40$, obtained by $6$ students were $20,14,16,30,21$ and $25$. Find the standard deviation of the data.

Answer 1

Now, A.M. $=\frac{\sum x}{n}=\frac{20+14+16+30+21+25}{6}$
$\Rightarrow \overline{x}=\frac{126}{6}=21$.
Let us form the following table.

x	$d=x-\overline{x}$	$d^2$
$14$	$-7$	$49$
$16$	$-5$	$25$
$20$	$-1$	$1$
$21$	$0$	$0$
$25$	$4$	$16$
$30$	$9$	$81$
$\sum x=126$	$\sum d=0$	$\sum d^2=172$

$\sigma =\sqrt{\frac{\sum d^2}{n}}=\sqrt{\frac{172}{6}}$
$=\sqrt{28.67}$
Thus, $\sigma \simeq 5.36$