Question

Apply step-deviation method to find the AM of the following frequency distribution

Variate $\left(x\right)$:	$5$	$10$	$15$	$20$	$25$	$30$	$35$	$40$	$45$	$50$
Frequency $\left(f\right)$:	$20$	$43$	$75$	$67$	$72$	$45$	$39$	$9$	$8$	$6$

Answer 1

Let the assumed mean be $A=25$ and $h=5$

Calculation of Mean

Variable $x_i$	Frequency $f_i$	Deviations $d_i=x_i-A$	$u_i=\frac{x_i-25}{25}$	$f_i{u}_i$
$5$	$20$	$-20$	$-4$	$-80$
$10$	$43$	$-15$	$-3$	$-129$
$15$	$75$	$-10$	$-2$	$-150$
$20$	$67$	$-5$	$-1$	$-150$
$25\left(A\right)$	$72$	$0$	$0$	$0$
$30$	$45$	$5$	$1$	$45$
$35$	$39$	$10$	$2$	$78$
$40$	$9$	$15$	$3$	$27$
$45$	$8$	$20$	$4$	$32$
$50$	$6$	$25$	$5$	$30$
	$N=\sum f_i=384$			$\sum f_i{u}_i=-214$

We have,
$N=384,A=25,h=5$ and $\sum f_i{u}_i=-214$

$\therefore$ Mean $=\overline{X}=A+h[\frac{1}{N}\sum f_i{u}_i]$

$\Rightarrow$ Mean $=25+5\times \left(\frac{-214}{384}\right)=25-2.786=22.214$