The sum of the deviations of each data value from this measure of central location will always be zero. A. Median B. Standard deviation C. Mean D. Mode

C. Mean

Explanation:

Mean = (∑)/N

Median = central values when data is sorted

Mode = most repeated value

Standard deviation =

In standard deviation, formula you may see that deviation is being calculated from the mean (central location). But here we take square of the value before adding all of them.

But if we just take , it would be equal to zero.

EXAMPLE

Take 4, 9, 5 as data

mean = (4+9+5)/3 = 18/3 = 6

sum of deviations from mean = (4-6)+(9-6)+(5-6) = (-2)+(3)+(-1) = 0