Question

The mean of n numbers is x. if each observation is multiplied by 4, what will be the new mean? give reason for your answer.

Answer 1

By this -X1 + X2 + X3........Xn / Y = X bar [Y = total no. of observations] –1

 

==>(X1 - a) + (X2- a)+(X3 - a)........(Xn - a) = X bar Y - a [ '-a' subtracted from all the obs. (both the side)]

 

==> -a ( X1 + X2+ X3........Xn) = X bar Y - a

 

Now substituting X1 + X2 + X3........Xn with X bar Y,

 

We get ==> -a ( X bar Y ) = X bar Y - a

 

Hope This Helps :)