Variance

Variance measures how spread out a random variable's values are around its mean: it is the average of the squared distances from the mean. A small variance means outcomes cluster tightly near the average; a large variance means they swing widely.

Variance is the standard mathematical measure of uncertainty or risk, and many formulas (like for the central limit theorem) are written in terms of it. Because it squares the distances, its units are squared (e.g. dollars-squared), which is awkward to interpret — that is exactly why the standard deviation exists.