The sum of the deviations about the mean is always:

Correct option is B

Given:
We are asked about the sum of the deviations about the mean in a data set.
Concept Used:
Deviation about the mean refers to the difference between each data point and the mean of the data set.
The sum of all such deviations from the mean, when calculated for any set of data, always equals zero. This is because the positive deviations cancel out the negative deviations.
Formula Used:
Deviation of a data point xi from the mean μ is (xi – μ)
The sum of all deviations about the mean is:
∑ (xi – μ) = 0
Solution: By the properties of the mean, the sum of deviations from the mean will always balance out to zero.
Final Answer: (b) zero