Mean Question

Question

The average of n numbers x^1, x^2, x^3, ........, x^n is M. If x^n is replaced by x', then new average
is______

Answer 1

If the average of n numbers is M then the sum of the n numbers is n*M, so 

 

x^1 + x^2 + x^3 + ... + x^(n-1) + x^n = n*M

 

If x^n is replaced by x' then x^n is subtracted from the sum and x' is added so 

 

x^1 + x^2 + x^3 + ... + x^(n-1) + x' = n*M - x^n + x' 

 

There are n numbers in the sum on the left so the new average is the sum divided by n which is 

 

(n*M - x^n + x')/n = M - x^n/n + x'/n = M + (x' - x^n)/n