Question

Calculate the standard deviation of the following data.

x	$3$	$8$	$13$	$18$	$23$
f	$7$	$10$	$15$	$10$	$8$

• A. $6.32$.
• B. $2.32$.
• C. $3.32$.
• D. None of these

Answer 1

The correct option is A $6.32$.

$x$	$f$	$xf$	$(x-\overline{x})$	$(x-\overline{x}{)}^2$	$(x-\overline{x}{)}^{2}f$
$3$	$7$	$21$	$-10.2$	$104.04$	$728.28$
$8$	$10$	$80$	$-5.2$	$27.04$	$270.4$
$13$	$15$	$195$	$-0.2$	$0.04$	$0.6$
$18$	$10$	$180$	$4.8$	$23.04$	$230.4$
$23$	$8$	$184$	$9.8$	$96.04$	$768.32$
	$\sum f=50$	$\sum xf=660$			$\sum (x-\overline{x}{)}^2=1998$

$\Rightarrow$ $\overline{x}=\frac{\sum xf}{\sum f}=\frac{660}{50}=13.2$

Now, calculate standard deviation :

$S=\sqrt{\frac{(x-\overline{x}{)}^2}{\sum f}}=\sqrt{\frac{1998}{50}}=\sqrt{39.96}=6.32$