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Difference between revisions of "Coefficient of variation"

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A dimensionless measure of the spread of the distribution of a random variable. This coefficient may be defined in several ways. In practice, its most frequent definition is by the formula
 
A dimensionless measure of the spread of the distribution of a random variable. This coefficient may be defined in several ways. In practice, its most frequent definition is by the formula
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022910/c0229101.png" /></td> </tr></table>
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$$V=\frac\sigma\mu,$$
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022910/c0229102.png" /> is the variance and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022910/c0229103.png" /> is the mathematical expectation (<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022910/c0229104.png" /> must be positive). This expression is often used in its percentage form, viz., <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022910/c0229105.png" /> %. This definition was proposed in 1895 by K. Pearson.
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where $\sigma^2$ is the variance and $\mu$ is the mathematical expectation ($\mu$ must be positive). This expression is often used in its percentage form, viz., $V=100\sigma/\mu$ %. This definition was proposed in 1895 by K. Pearson.

Revision as of 16:39, 11 April 2014

A dimensionless measure of the spread of the distribution of a random variable. This coefficient may be defined in several ways. In practice, its most frequent definition is by the formula

$$V=\frac\sigma\mu,$$

where $\sigma^2$ is the variance and $\mu$ is the mathematical expectation ($\mu$ must be positive). This expression is often used in its percentage form, viz., $V=100\sigma/\mu$ %. This definition was proposed in 1895 by K. Pearson.

How to Cite This Entry:
Coefficient of variation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Coefficient_of_variation&oldid=11580
This article was adapted from an original article by T.S. Lel'chuk (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article