Question

Calculate the standard deviation of the following data.
$10,20,15,8,3,4$

• A. $5.97$
• B. $59.7$
• C. $4.97$
• D. None of these

Answer 1

The correct option is A $5.97$

$\Rightarrow$ The given numbers are $3,4,8,10,15,20$.

$\Rightarrow$ $\overline{X}=\frac{3+4+8+10+15+20}{6}=10$

$X$	$X-\overline{X}$	$(X-\overline{X}{)}^2$
$3$	$-7$	$49$
$4$	$-6$	$36$
$8$	$-2$	$4$
$10$	$0$	$0$
$15$	$5$	$25$
$20$	$10$	$100$
		$\sum (X-\overline{X}{)}^2=214$

$\Rightarrow$ $S=\sqrt{\frac{(X-\overline{X}{)}^2}{N}}$

$=\sqrt{\frac{214}{6}}$

$=\sqrt{35.66}$

$=5.97$