How to Calculate Standard Deviation if Variance Is Negative

Negative Variance Means You Have Made an Error

As a result of its calculation and mathematical meaning, variance can never be negative, because it is the average squared deviation from the mean and:

  • Anything squared is never negative.
  • Average of non-negative numbers can’t be negative either.

Therefore, if you have negative variance and you are wondering how to calculate standard deviation from it, first look at how you have got the negative variance in the first place. You (or the person who has calculated the variance) have made a mistake somewhere.

For example, a common mistake is that you forget to square the deviations from the mean (and that would result in a possibly negative variance).

There is simply no chance that variance can be negative if calculated correctly.

How to Calculate Standard Deviation

Here you can see how to calculate both variance and standard deviation in 4 easy steps.