# Gaussian (Normal) Distribution

Interactive plot of the Gaussian (normal) distribution

The Gaussian distribution, (also known as the Normal distribution) is a probability distribution. Its bell-shaped curve is dependent on $$\mu$$, the mean, and $$\sigma$$, the standard deviation ($$\sigma^2$$ being the variance).

$f(x,\mu,\sigma) = \frac{1}{\sigma\sqrt{2\pi}}e^\frac{-(x-\mu)^2}{2\sigma^2}$

The peak of the graph is always located at the mean and the area under the curve is always exactly equal to 1. 68% of all the values lie within one standard deviation of the mean. At $$2\sigma$$, this increases to 95%, and 99.7% of the values lie within $$3\sigma$$ of the mean.