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# Confidence Interval of theCoefficient of Variation

The confidence interval can be estimated for a coefficient of variation in much the same way as for a mean.

Hence the 95% confidence interval of the coefficient of variation (CV) is given by t multiplied by the standard error of CV. The standard error of the CV is given by the CV divided the square root of double the number of observations:

#### Algebraically speaking -

95%CI (CV) = CV ± t α=0.05; df=(n-1) SE (CV)

where the standard error (SE) of the coefficient of variation (CV) is approximately:

 SE (CV) ≈ CV √2n

and the standard error (SE) of the coefficient of variation corrected for bias (CV*) is:

 SE (CV*) ≈ CV  (1+1/4n) √ 2n

These confidence limits to the coefficient of variation are only valid if sampling is from an approximately normally distributed population. Except where otherwise specified, all text and images on this page are copyright InfluentialPoints, all rights reserved. Images not copyright InfluentialPoints credit their source on web-pages attached via hypertext links from those images.