Coefficient of Variation

The coefficient of variation express the standard deviation as a percentage of the mean.

If the standard deviations in sales for large and small stores selling similar goods are compared, the standard deviation for large stores will almost always be greater. A simple explanation is that a large store could be modeled as a number of small stores. Comparing variation using the standard deviation would be misleading. The coefficient of variation overcomes this problem by adjusting for the scale of units in the population.

Example: The owners are considering purchasing shares of stock A or shares of stock B, both listed on the New York Stock Exchange. From the closing date prices of both stocks over the last several months the means and standard deviations were found to be considerably found to be different , with   Should stock A be purchased, since the standard deviation of stock B is larger?

Solution: We might think that stock B is more volatile than stock A. The mean closing prices for the two stocks are Next, the coefficients of variation are computed to measure and compare the risk of these competing investment opportunities:

Notice that the market value of stock A fluctuates more from period to period than does that of stock B.