Question

Calculate the standard deviation of the following data (by Assumed mean method).
Assumed Mean $=25$

$C.I$	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
$f$	$7$	$10$	$15$	$8$	$10$

Answer 1

$C.I$	Class mark $\left(x_i\right)$	$f_i$	$d_i=x_i-M$	$f_i{d}_i$	$f_i{d}_i^2$
$0-10$	$5$	$7$	$-20$	$-140$	$12800$
$10-20$	$15$	$10$	$-10$	$-100$	$1000$
$20-30$	$25$	$15$	$0$	$0$	$0$
$30-40$	$35$	$8$	$10$	$80$	$800$
$40-50$	$45$	$10$	$20$	$200$	$4000$
				Total $=40$	Total $=8600$

Given, assumed mean$\left(A\right)=25$

Standard deviation$\left(\sigma \right)=\sqrt{\frac{\sum f_{i}d{i}^2}{n}-{\left\{\frac{\sum f_i{d}_i}{n}\right\}}^2}$

$\therefore$ $\sigma =\sqrt{\frac{8600}{5}-{\left\{\frac{40}{5}\right\}}^2}$

$=\sqrt{1720-64}$

$=\sqrt{1656}=40.69$

$\therefore$ $\sigma =40.69$.