Normal distribution
lastmod 2018-08-17created 2014-11-124 edits
The red curve is the standard normal distribution
In probability theory and statistics, the normal distribution or Gaussian distribution is a continuous probability distribution. The normal distribution is often used to approximate the distribution of collected data, because by the central limit theorem the mean of independent random variables tends toward a normal distribution.
Overview
A key concept that explains countless things that happen in the human and natural world.
It is the most important of the various probability distributions used in statistics. It was established by applying limits to the probability density curve derived through random sampling for physics experiments, and when its graph is written out as a function, it is
\[ \displaystyle N\left(\mu,\sigma^{2}\right)\left(x\right)=\frac{1}{\sigma\sqrt{2\pi}}\exp\left(-\frac{\left(x-\mu\right)^{2}}{2\sigma^{2}}\right) \] (\(\sigma\): standard deviation, \(\mu\): mean)