Correct Answer - Option 2 : 0
Given
y is the mean of x1, x2, ..., xn
Concept
Mean is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by the number of observations in the data set.
Calculation
y = (x1 + x2 + x3 +...+ xn)/n
⇒ ny = (x1 + x2 + x3 +...+ xn) _____(1)
(x1 - y) + (x2 - y) +...+ (xn - y) = (x1 + x2 + x3 +...+ xn) - (y + y + y... n times)
⇒ (x1 + x2 + x3 +...+ xn) - ny
⇒ ny - ny = 0 [using equation (1)]
∴ (x1 - y) + (x2 - y) +...+ (xn - y) = 0