Question

If x bar is the mean of 10 natural numbers x1, x2, x3................ x10.
Show that (x1-xbar) + (x2-xbar) + (x3-xbar) +...............+ (x10-xbar) =0.

Answer 1

Let total number of observation = n

Given mean of n observations = X

then (x1 +x2 +x3 +......+xn )/n = X

=> x1 +x2 +x3 +......+xn = n*X

Now ∑ (xi - X) = {(x1 -X) + (x2 -X) + (x3 -X)+......+(xn -X)} - n*X

= (x1 +x2 +x3 +......+xn ) - n*X

= n*X - n*X

= 0