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A Gaussian distribution or Gauss distribution is a statistical model that describes a particular way that data can be distributed around the mean, the average. It is also sometimes called the normal distribution, and the Laplace–Gauss distribution, the bell curve (because its graph looks like a bell.)[note 1] It's incredibly useful for analyzing certain kinds of data in physics, medicine, anthropology, and many other types of science. At the same time, it is often misinterpreted and misused, especially by racialists.
A standard Gaussian distribution is such that the standard variance is one (unit variance) and such that the most likely something can occur is 1 (100%). As such, the standard Gaussian distribution may be written in the form: This makes the distribution technically in the exponential family of distributions. The Gaussian distribution is a specific kind of the more general Gaussian function.
Where it applies
Some examples of things that follow a Gaussian distribution:
- Standardized test scores - Test grades can be thought as measurements of person's knowledge, expertise, writing ability, etc., and so they can be modeled by the Gaussian distribution.
- IQ - IQ scores are also modeled using the normal distribution, based on a similar line of thinking to regular test scores. When high IQ societies talk about being "3 standard deviations above the norm" or allowing only the "top 1%", this is what they're going on about.
- Manufacturing and other process errors. This is where "six sigma" gets its name, the idea of the chance of an error occurring being more than six standard deviations from the mean
- Distance between stars and planets - In fact, Gauss encountered the normal distribution by studying the orbits of the planets.Pierre-Simon de Laplace used Gaussian distribution to show that the motion of planets remained invariant over time and so, contrary to Isaac Newton, there was no need for some sort of deity to come in and realign the Solar System.
- Accuracy of projectiles - In ballistics, the circular error probable describes the chances of a missile or other projectile landing within a certain distance of a target. It follows Gaussian probabilities and often appears in analyses regarding nuclear missiles and nuclear war.
Where it doesn't apply
- Though this isn't terribly useful since the graph for many other distributions look like bells, such as the Student's t-distribution and some versions of the logistic distribution and the Weibull distribution. While they're in a different class of distributions, the Poisson distribution and binomial distribution look like bells too. In fairness, however, as the parameters increase those other distributions become the Gaussian distribution.
- Wellenstein, A. (n.d.) MISSILEMAP Frequently Asked Questions (FAQ). Restricted Data.