Question

How is the weighted arithmetic mean calculated by short cut method (S.C.M) or deviation method?

Answer 1

As with simple arithmetic mean, for Weighted arithmetic mean also we take an  arbitrary value in x i.e. Assumed value (A).

So,

di = xi - A

Proceeding further on , 

Thus, weighted arithmetic mean by short cut method (S.C.M) / Deviation method is:

x̅ = A + 1/N (∑fidi).

Weighted arithmetic mean by short cut method:

x̅ = A + 1/N (∑fidi).