Question:
If mean of a set of observations is x bar, then evaluate sigma(xi-x bar).
Answer:
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
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