Authors: Miodrag Lovric (Radford University, Virginia, USA) and Abdulbari Bener (Weill Cornell Medical College, Qatar)
This article provides a comprehensive exploration of the concept of variance, from its historical origin—coined by R. A. Fisher in 1918—to its central role in modern statistics and its widespread applications across numerous disciplines. Defined as the average squared deviation from the mean, variance serves as a fundamental measure of variability or dispersion.
The authors begin with formal definitions for discrete and continuous random variables, followed by derivations for standard distributions such as binomial, Poisson, uniform, and normal. Key properties of variance, including Bienaymé’s equality and Bessel’s correction, are outlined, and a worked example from Michelson’s 1879 speed-of-light experiments is presented.
Beyond theory, the article offers a sweeping overview of real-world applications of variance:
Variance is shown to be not only a technical statistic but a universal lens through which scientists interpret uncertainty, structure, and diversity in nature and society.
For full mathematical definitions, derivations, and interdisciplinary illustrations, see the complete article in the International Encyclopedia of Statistical Science.