Question

Calculate standard deviation of the following data.

X	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
f	$10$	$8$	$15$	$8$	$4$

• A. $-12$
• B. $12$
• C. $12.36$
• D. $152.77$

Answer 1

The correct option is C $12.36$

Marks	Mid-values(X)	f	dxi$=X-25/10$	$fd{x}_{i}f$	$d{x}_i^2$
$0-10$	$5$	$10$	$-2$	$-20$	$40$
$10-20$	$15$	$8$	$-1$	$-8$	$8$
$20-30$	$25$	$15$	$0$	$0$	$0$
$30-40$	$35$	$8$	$1$	$8$	$8$
$40-50$	$45$	$4$	$2$	$8$	$16$
Total		$45$		$-12$	$72$

$\sqrt{\frac{72}{45}-\frac{144}{45\times 45}}\times 10$
$=12.36$