Skewness
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Skewness in probability theory and statistics is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Similarly to kurtosis, it provides insights
Example of an asymmetric distribution with zero skewness. This figure serves as a counterexample that zero skewness does not imply symmetric distribution necessarily. (Skewness was calculated by Pearson's moment coefficient of skewness.)
Normal distribution
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In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probabi
Skewness
…Examples of distributions with finite skewness include the following. A normal distribution and any other symmetric distribution with finite third moment has a skewness of 0 A half-normal distribution has a skewness just below 1…
The bean machine, a device invented by Francis Galton, can be called the first generator of normal random variables. This machine consists of a vertical board with interleaved rows of pins. Small balls are dropped from the top and then bounce randomly left or right as they hit the pins. The balls are collected into bins at the bottom and settle down into a pattern resembling the Gaussian curve.
In 1809, Carl Friedrich Gauss showed that the normal distribution provides a way to rationalize the method of least squares.
Pierre-Simon Laplace proved the central limit theorem in 1810, consolidating the importance of the normal distribution in statistics.