Using the range to calculate the coefficient of variation
Department of Information Systems/Decision Sciences, College of Business and Public Administration, Old Dominion University, Norfolk, VA 23529, USA.Psychological Reports (Impact Factor: 0.53). 01/2005; 95(3 Pt 1):1043-9. DOI: 10.2466/PR0.95.7.1043-1049
In this research a coefficient of variation (CVhigh-low) is calculated from the highest and lowest values in a set of data. Use of CVhigh-low when the population is normal, leptokurtic, and skewed is discussed. The statistic is the most effective when sampling from the normal distribution. With the leptokurtic distributions, CVhigh-low works well for comparing the relative variability between two or more distributions but does not provide a very "good" point estimate of the population coefficient of variation. With skewed distributions CVhigh-low works well in identifying which data set has the more relative variation but does not specify how much difference there is in the variation. It also does not provide a "good" point estimate.
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ABSTRACT: In this research a coefficient of variation (CVS(high.low)) is developed that is calculated from the highest and lowest values in a set of data for samples from skewed distributions. A correction factor is determined such that CVS(high-low) is a dose estimate of the population coefficient of variation when sampling from three skewed chi-squared distributions and three skewed empirical distributions. The empirical distributions are from "real-world" data sets in psychology and education.
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