Question

Find the mean marks per student, using Step Deviation method method:
$\begin{array}{ccccccc}\text{Marks}& 5& 15& 25& 35& 45& 55\\ \text{Number of students}& 12& 18& 27& 20& 17& 6\end{array}$

Answer 1

Marks	Frequency (fi)		Deviation (di) di = (xi – 25)	(fidi)
5	12		-20	-240
15	18		-10	-180
25 = A	27		0	0
35	20		10	200
45	17		20	340
55	6		30	180
Total	∑fi=100			∑(fi×di)=300

Let A = 25 be the assumed mean.

Then we have

$Mean=A+\frac{\sum f_i{d}_i}{\sum f_i}=25+\frac{300}{100}=28$