Normal distribution

Normal Distribution

Normal Distribution (pronunciation: /ˈnɔːrməl ˌdɪstrɪˈbjuːʃən/), also known as the Gaussian distribution (pronunciation: /ɡaʊˈsiːən ˌdɪstrɪˈbjuːʃən/), is a type of probability distribution that has a bell-shaped density function. It is known as the most common type of distribution that occurs in nature. The term "normal distribution" was first introduced by Karl Pearson in 1895.

Etymology

The term "normal" is used in the sense of "conforming to a standard or common type". The term "Gaussian" is derived from the name of the mathematician Carl Friedrich Gauss, who first described this distribution.

Definition

In probability theory and statistics, the normal distribution is defined by the probability density function:

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

where:

$\mu$ is the mean or expectation of the distribution,
$\sigma$ is the standard deviation, and
$\sigma ^{2}$ is the variance.

Properties

The normal distribution has several important properties:

It is symmetric about its mean.
The mean, median, and mode of a normal distribution are equal.
The curve of the distribution is bell-shaped and reaches its maximum at the mean.
The total area under the curve of the distribution is 1.

Related Terms

External links

Medical encyclopedia article on Normal distribution
Wikipedia's article - Normal distribution

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Normal distribution