As always, visualizations are great—necessary even—but on most occasions, we are going to quantify these correlations and summarize them with numbers.

The simplest measure of correlation that is widely used is covariance. For each pair of values from the two variables, the differences from their respective means are taken. Then, those values are multiplied. If they are both positive (that is, both the values are above their respective means), then the product will be positive too. If both the values are below their respective means, the product is still positive, because the product of two negative numbers is positive. Only when one of the values is above its mean will the product be negative:

Remember, in sample statistics, we ...