Question

Can we use assumed mean method to find the mean of grouped data when its class interval are irregular.If not why?

Answer 1

When the class intervals are continuous but each of the given classes of unequal width, then we can find the mean with the help of any of the 3 methods :

Direct method

Assumed mean method

Step deviation method

Consider the following example.

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

No. of days	0-6	6-10	10-14	14-20	20-28	28-38	38-40
No. of students	11	10	7	4	4	3	1

Here is the solution.

CLASS INTERVAL	FREQUENCY (fi)	CLASS MARKS(xi)	fixi
0-6	11	3	33
6-10	10	8	80
10-14	7	12	84
14-20	4	17	68
20-28	4	24	96
28-38	3	33	99
38-40	1	39	39
Total	∑ fi = 40		∑ fi xi = 499

Mean = ∑ fi xi / ∑ fi = 499/40 = 12.475 ≈ 12.48

Note: Direct method should be used when the given data is small. Assumed mean method for intermediate data and for huge data we can use step deviation method.