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.
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