Why are so many things Gaussian?

The central limit theorem is a fundamental concept in statistics that offers insight into why the Gaussian random variable is prevalent in various applications.

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The theorem essentially states that when a large number of independent, randomly distributed values are added together, their sum tends to follow a normal distribution, also known as the Gaussian distribution.

This principle can be observed in numerous natural phenomena where macroscopic outcomes are the result of the combined effects of many independent, microscopic processes.

For instance, in physics, the movement of individual particles may be random and unpredictable, but their collective behavior often results in well-defined statistical patterns.