The algebraic sum of the deviations of a set of n values from their mean is
Mean = =
x̅ =
x1 + x2 + x3 + …. + xn = n (i)
Algebraic sum of the deviation from the mean is:
Sum = (x1 - ) + (x2 - ) + (x3 - ) + …. + (xn - )
= x1 + x2 + x3 + …. + xn – ( + + + …. n times)
= x1 + x2 + x3 + …. + xn - n
Using (i), we get
Sum = n - n
= 0
Hence, algebraic sum of the deviations of a set of n values from mean is 0.