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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