Question

Find the mean for the following distribution table, using Deviation method.

Class Interval	$0-9$	$10-19$	$20-29$	$30-39$	$40-49$	$50-50$	$60-60$
Frequency	$8$	$10$	$22$	$26$	$18$	$9$	$7$

Answer 1

Let us find the class marks $x_i$ of each class by taking the average of upper class limit and lower class limit and put them in a table.

Let us assume $a=35$ and $h=10$

Class Interval	Frequency	Class marks $\left(x_i\right)$	$d_i=x_i-a$	$u_i=\frac{x_i-a}{h}$	$f_i{u}_i$
$0.5-9.5$	$8$	$5$	$-30$	$-3$	$-24$
$9.5-19.5$	$10$	$15$	$-20$	$-2$	$-20$
$19.5-29.5$	$22$	$25$	$-10$	$-1$	$-22$
$29.5-39.5$	$26$	$35$	$0$	$0$	$0$
$39.5-49.5$	$18$	$45$	$10$	$1$	$18$
$49.5-59.5$	$9$	$55$	$20$	$2$	$18$
$59.5-69.5$	$7$	$65$	$30$	$3$	$21$
Total	$\sum f_i=100$				$\sum f_i{u}_i=-9$

Using step deviation method,

$\overline{x}=a+\frac{\sum f_i{u}_i}{\sum f_i}\times h$

$=35+\frac{-9}{100}\times 9$

$=35-0.81$

$=34.19$