# The bell curve: “Normal” or “Gaussian”?

Most discussions of statistical quality refer to the “Normal distribution,” but “Normal” is a loaded word. If we talk about the “Normal distribution,” it implies that all other distributions are, in some way, abnormal. The “Normal distribution” is also called “Gaussian,” after the discoverer of many of its properties, and I prefer it as a more neutral term. Before Germany adopted the Euro, its last 10-Mark note featured the bell curve next to Gauss’s face.

The Gaussian distribution is widely used, and abused, because its math is simple, well known, and wonderful. Here are a few of its remarkable properties:

1. It applies to a broad class of measurement errors. John Herschel arrived at the Gaussian distribution for measurement errors in the position of bodies in the sky simply from the fact that the errors in x and y should be independent and that the probability of a given error should depend only on the distance from the true point.
2. It is stable. If you add Gaussian variables, or take any linear combination of them, the result is also Gaussian.
3. Many sums of variables converge to it.  The Central Limit Theorem (CLT) says that, if you add variables that are independent, identically distributed, with a distribution that has a mean and a standard deviation, they sum converges towards a Gaussian. It makes it an attractive model, for example, for order quantities for a product coming independently from a large number of customers.