Question

the mean of n observations is x . if constant "a" is substracted from each observation , then show that new mean"x - a

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