A PROOF FOR RHIEL'S RANGE ESTIMATOR OF THE COEFFICIENT OF VARIATION FOR SKEWED DISTRIBUTIONS1

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Abstract

In this research study is proof that the coefficient of variation (CVhigh-low) calculated from the highest and lowest values in a set of data is applicable to specific skewed distributions with varying means and standard deviations. Earlier Rhiel provided values for dn, the standardized mean range, and an, an adjustment for bias in the range estimator of. μ These values are used in estimating the coefficient of variation from the range for skewed distributions. The dn and an values were specified for specific skewed distributions with a fixed mean and standard deviation. In this proof it is shown that the dn and an values are applicable for the specific skewed distributions when the mean and standard deviation can take on differing values. This will give the researcher confidence in using this statistic for skewed distributions regardless of the mean and standard deviation.

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