Question

Construct a sample (with at least two different values in the set) of 3 measurements whose variance is negative. If this is not possible, indicate "Cannot create sample".

Answer 1

This is not possible. Why not? Because the smallest the variance can get is 0.

Recall that 's' represents the standard deviation, so s^2 is the variance. It basically measures how spread out the values are. The higher the variance, the more spread out the data. You can think of it as "average distance from the mean". If the variance is 0, then all of the values are at the same point. So you could have a list like {2,2,2,2,2} which has variance 0. We cannot get any smaller variance than that. If your teacher insists all the values in the list are different, then the variance will be greater than 0.