Standard deviation divided by the mean
The variance and standard deviation are absolute measures of dispersion that are directly influenced by size and the unit of measurement. The variance and standard deviation for sales revenue will almost always exceed those for net profit because net profit (defined as revenue minus cost) is almost always less than total revenues. In a true economic sense, however, profits tend to be more unpredictable than sales revenue because profit variation reflects the underlying variability in both sales (demand) and cost (supply) conditions. As a result, managers often rely on a measure of dispersion that does not depend on size or the unit of measurement. The coefficient of variation compares the standard deviation to the mean in an attractive relative measure of dispersion within a population or sample. For a population, the coefficient of variation equals
For a sample, the coefficient of variation equals
Because it is unaffected by size or the unit of measure, the coefficient of variation can be used to compare relative dispersion across a wide variety of data. In capital budgeting, for example, managers use the coefficient of variation to compare "risk/reward" ratios for projects of widely different investment requirements or profitability. Because managers are sometimes only able to withstand a fixed dollar amount of loss or foregone profit, the coefficient of variation is often used in conjunction with absolute risk measures such as the variance and standard deviation. Taken together, absolute and relative measures give managers an especially useful means for assessing the magnitude of dispersion within a population or sample of data.
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