In a data, sum of the deviations about the mean is always:

Correct option is A

Concept Used:

The sum of the deviations of a given set of data about their mean is always zero i.e. sum of positive deviation from mean is equal to the sum of negative deviations. 

Example:

Consider the following data set: 3, 7, 9, 12, 14

Step 1: Calculate the Mean (x̅)

Mean (x̅) = (3 + 7 + 9 + 12 + 14) / 5 = 45 / 5 = 9

Step 2: Calculate the deviations of each value from the mean (xi - x̅)

xi| xi - x̅

3|-6

7|-2

9|0

12|+3

14|+5

Step 3: Sum of the deviations about the mean

∑(xi - x̅) = -6 - 2 + 0 + 3 + 5 = 0

Thus, the sum of the deviations about the mean is always zero.