Question

Find the arithmetic mean of the following frequency distribution using the step deviation method.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	9	12	15	10	14

Answer 1

Class	Frequency $\left(f_i\right)$	$x_i$	$u_i=\frac{x_i-A}{h}$	$F_i{u}_i$
$0-10$	$9$	$5$	$-2$	$-18$
$10-20$	$12$	$15$	$-1$	$-12$
$20-30$	$15$	$25=A$	$0$	$0$
$30-40$	$10$	$35$	$1$	$10$
$40-50$	$14$	$45$	$2$	$28$
	$60$			$8$

Here,

$A=25,\sum f_i=60,\sum f_i{u}_i=8,h=10$

We know that, Arithmetic Mean $=A+\frac{\sum f_i{u}_i}{\sum f_i}\times h$

$=25+\frac{8}{60}\times 10$

$=25+1.33$

$=26.33$

Hence, the required arithmetic mean is $26.33$.