Question

In an annual examination, marks (out of 90) obtained by students of class X in mathematics are given below:

Marks obtained	0−15	15−30	30−45	45−60	60−75	75−90
Number of students	2	4	5	20	9	10

Find the mean marks.

Answer 1

​Let us choose a = 52.5, h = 15, then d_i = x_i − 52.5 and u_{i =} $\frac{x_i-52.5}{15}$.

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

Marks obtained	Number of students (fi)	Class mark (xi)	di = xi − 37.5	ui = $\frac{{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{52}\mathbf{.}\mathbf{5}}{\mathbf{15}}$	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				∑ fiui = 10

The mean of given data is given by

$$\begin{gathered} \overline{x}=a+\left(\frac{{\displaystyle \sum _i}{f}_i{u}_i}{{\displaystyle \sum _i{f}_i}}\right)\times h \\ =52.5+\left(\frac{10}{50}\right)\times 15 \\ =52.5+3 \\ =55.5 \end{gathered}$$

​Thus, the mean is 55.5.