# normal distribution

In statistics, a normal distribution is an ideal distribution which is symmetrical about its mean. It can be written in the form:

where *f(x)* is the relative frequency, *σ* is the standard
deviation, *μ* is the mean, and *π* and *e* have their usual values. Note that
in a normal distribution the mean, median,
and mode coincide. The characteristic bell-shaped
curve shown when *f(x)* is plotted against *x* is called
the **normal curve**. The perfect bell curve or normal distribution only occurs
when variables are perfectly random.

The normal distribution is also known as the Gaussian distribution for Karl Gauss.