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 =( x_i−52.5 )/ 15`

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

Weight	Number of students `(f_i)`	Class mark `(x_i)`	`d_i = x_i – `37.5	`u_i = (x_i−52.5)/ 15`	`(f_i u_i)`
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	`Ʃ f_i` = 50				`Ʃ f_i u_i` = 10

The mean of the given data is given by,

x = a + `((Ʃ  _ i f_i u_i)/(Ʃ_i f_i)) xx h `

   =52.5`+(10/50) xx 15`

   = 52.5 + 3
   = 55.5
Thus, the mean is 55.5.