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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.