Question

Can standard deviation ever be negative ?

Answer 1

Hint:The standard deviation is a measure of amount of variation or dispersion of a set of values. In the given question, we have to find if the standard deviation of some observations can ever be negative.

Complete answer:
So, we have to check whether the standard deviation for a set of data or observations can be negative or not. The standard deviation of any set of observations can be minimum zero. Whenever, there are two unequal terms in the observations, the standard deviation is positive, that means greater than zero.

If all the observations are exactly equal, then the standard deviation is exactly zero.So, under no circumstances, the standard deviation can be negative or less than zero. We know that the standard deviation is the square root of variance of the observations. We also know that the square root of any quantity is always positive or zero.

Hence, the standard deviation is always non-negative.

Note:The given question revolves around the concepts of statistics. So, we should know the formulae for calculating the standard deviation and the properties that help to compute standard deviation of a given data set easily.