# Variance

**DOI:**https://doi.org/10.1007/978-3-642-04898-2_634

The term “variance” was coined by Ronald Fisher in 1918 in his famous paper on population genetics, The Correlation Between Relatives on the Supposition of Mendelian Inheritance, published by Royal Society of Edinburgh: “It is … desirable in analyzing the causes of variability to deal with the square of the standard deviation as the measure of variability. We shall term this quantity the Variance …” (p. 399). Interestingly, according to O. Kempthorne, this paper was initially rejected by the Royal Society of London, “probably the reason was that it constituted such a great advance on the thought in the area that the reviewers were unable to make a reasonable assessment.”

The variance of a random variable (or a data set) is a measure of variable (data) dispersion or spread around the mean (expected value).

**Definition**Let

*X*be a random variable with second moment

*E*(

*X*

^{2}) and let μ =

*E*(

*X*) be its mean. The variance of

*X*is defined by (see, e.g., Feller 1968, p. 228)

## References and Further Reading

- Fisher R (1918) The correlation between relatives on the supposition of mendelian inheritance. Philos Trans Roy Soc Edinb 52:399–433CrossRefGoogle Scholar
- Dorsey EN (1944) The velocity of light. T Am Philos Soc 34(Part 1): 1–110, Table 22Google Scholar
- Feller W (1968) An introduction to the probability theory and its applications, 3rd edn. Wiley, New YorkGoogle Scholar
- Kempthorne O (1968) Book reviews. Am J Hum Genet 20(4):402–403Google Scholar
- Kendall M (1945) The advanced theory of statistics. Charles Griffin, LondonGoogle Scholar
- Loève M (1977) Probability theory I, 4th edn. Springer, New YorkzbMATHGoogle Scholar
- Mood AM, Graybill FA, Boes DC (1974) Introduction to the theory of statistics, 3rd edn. McGraw-Hill, LondonzbMATHGoogle Scholar
- Roussas G (1997) A course in mathematical statistics, 2nd edn. Academic, HardcoverzbMATHGoogle Scholar