(A) 0
Explanation:
Mean (x) = Sum of all the observations/ Number of observations
x = (f1x1 + f2x2 + …..+ fnxn) / f1 + f2 +……+ fn
x = Σfixi / Σfi, Σfi = n
x = Σfixi / n
n x = Σfixi …………… (1)
Σ (fixi – x) = (f1x1 – x) + (f2x2 – x)+ …..+ (fnxn – x)
Σ (fixi – x) = (f1x1 + f2x2 + …..+ fnxn) – (x +x +….n times)
Σ (fixi – x) = Σfixi –nx
Σ(fixi – x) = nx – nx ( From eq1)
Σ(fixi – x) = 0
Hence, option (A) is correct