Averages

Average of the set X = {x1, x2, x3, … , xn} is A = (x1 + x2 + x3 +…..+ xn)/n.

Min(X) < A < Max(X).

k * ( each element of X ) => k*A.  (Each element of X)/k -> A/k. 

Each element of X ± K = A ± K.

Let A be the average of x1, x2, x3, ……, xn, y1, y2, y3, ……, yn. And A lie between {x1, x2, x3, ……, xn} and {, y1, y2, y3, ……, yn}   

then,

(A-x1)*(A-x2)*(A-x3)* ……*(A-xn) = (A-y1)*(A-y2)*(A-y3)*……*(A-yn).