Question

Calculate standard deviation of the following data.

X	$10$	$11$	$12$	$13$	$14$	$15$	$16$	$17$	$18$
f	$2$	$7$	$10$	$12$	$15$	$11$	$10$	$6$	$3$

• A. $3.95$
• B. $1.99$
• C. $14$
• D. None of the above

Answer 1

The correct option is B $1.99$

X	f	fx	X-Mean	$f(X-x{)}^2$
$10$	$2$	$20$	$-4$	$32$
$11$	$7$	$77$	$-3$	$63$
$12$	$10$	$120$	$-2$	$40$
$13$	$12$	$156$	$-11$	$2$
$14$	$15$	$210$	$0$	$0$
$15$	$11$	$165$	$1$	$11$
$16$	$10$	$160$	$2$	$40$
$17$	$6$	$102$	$3$	$54$
$18$	$3$	$54$	$4$	$48$
Total	$76$	$fX=1064$		$f(X-X{)}^2=300$

${}^{-}X=\frac{1064}{76}=14$
$\sigma x=\sqrt{\frac{300}{76}}$
$=\sqrt{3.95}$
$=1.99$.