Variability Problem

Question

Is it possible to obtain a negative value for the variance or standard deviation?

Answer 1

Dee Dee.

No. The standard deviation tells us about data spread - how far our data is from the mean, so it must be positive. The variance is the standard deviation squared, so clearly that must be positive.

Also the way the standard deviation is defined involves the square root of a positive or zero quantity.

A positive number can have two square roots, eg √4 = + / - 2 but conventionally in math we always take the positive square root only. So that's a second reason why the standard deviation cannot be negative.

MIKE