Why can't variance be negative?
The underlying mathematical principle involved makes variance non-negative.
Variance is a measure of the deviations of individual values from the mean.
The deviation can be negative or positive.
An important property of the mean is that the sum of all deviations from the mean is always equal to zero..
This is because, the negative and positive deviations cancel out each other.
hence, to get positive values, the deviations are squared.
This is the reason why, the variance can never be negative.