Covariance

Covariance measures whether two variables tend to move in the same direction. It is positive when above-average values of one variable line up with above-average values of the other, negative when one being high pairs with the other being low, and near zero when there is no consistent pattern.

Its weakness is that its size depends on the units, so a covariance of 500 between income (in dollars) and spending tells you the sign but not the strength — swap dollars for cents and the number explodes. That is exactly why we usually divide covariance by the two standard deviations to get the correlation coefficient, which strips out the units and lands neatly between -1 and +1.