Question

In an annual examination, marks(out of 90) obtained by students of Class X in mathematics are given below:
$\begin{array}{ccccccc}\text{Marks}& & & & & & \\ \text{obtained}& 0-15& 15-30& 30-45& 45-60& 60-75& 75-90\\ \text{Number of}& & & & & & \\ \text{students}& 2& 4& 5& 20& 9& 10\end{array}$ Find the mean marks.

Answer 1

Let us choose a = 52.5, h = 15,
then di = xi - 52.5
and ui = xi−52.5/15

Using Step-deviation method, the given data is shown as follows:

Marks obtained	Number of students (fi)	Class mark (xi)	di = xi- 52.5	ui = di/15	fiui
0 - 15	2	7.5	-45	-3	-6
15 - 30	4	22.5	-30	-2	-8
30 - 45	5	37.5	-15	-1	-5
45 - 60	20	52.5	0	0	0
60 - 75	9	67.5	15	1	9
75 - 90	10	82.5	30	2	20
Total	∑fi=50				∑(fi×ui)=10

The mean of given data is given by

$\overline{x}$=a+(∑fiui/∑fi)×h

= 52.5 + 10/50 x 15

= 52.5 + 3

= 55.5

Thus, the mean is 55.5.