Question

Prove that sigma (fixi-x bar) =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

So ∑ (xi - X) = 0

Hope you understood the sequence of steps.  

All the best.

Answer 2

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