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

Step 1. Form a table showing different data.

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

Step 2. Find the mean

$A$is the median of the class mark and $h$is the interval of each class.

Here, $A=25,h=10$

Mean $=A+\frac{\sum f_i{u}_i}{\underset{}{\sum f_i}}\times h$

$$\begin{gathered} =25+\frac{8}{60}\times 10 \\ =26.33 \end{gathered}$$

Hence, the arithmetic mean is $26.33$.