Question

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

Marks obtained	number of students
Less than 10	14
Less than 20	22
Less than 30	37
Less than 40	55
Less than 50	67
Less than 60	75

Answer 1

Step deviation method

class interval	number of students (f)	mid point of class interval	Deviation $d_i^{\prime }=\frac{x_i-A}{h}$	$f_i{d}_i^{\prime }$
0-10 10-20 20-30 30-40 40-50 50-60	14 22 37 55 67 75	5 15 25 35 45 55	-2 -1 0 1 2 3	-28 -22 0 55 134 225
total	$\sum f=270$			$\sum f_i{d}_i^{\prime }=364$

By step deviation method

mean $=A+\frac{\sum f_i{d}_i^{\prime }}{\sum f}\times h$

$=25+\frac{364}{270}\times 10$

$=25+\frac{364}{27}$

$=25+13.48$

mean $=38.48$

where h is class width

$h=10$

A is assumed mean

$A=25$