How to Calculate Relative Dispersion

By Matthew Weeks

The relative dispersion of a data set, more commonly referred to as its coefficient of variation, is the ratio of its standard deviation to its arithmetic mean. In effect, it is a measurement of the degree by which an observed variable deviates from its average value. It is a useful measurement in applications such as comparing stocks and other investment vehicles because it is a way to determine the risk involved with the holdings in your portfolio.

Determine the arithmetic mean of your data set by adding all of the individual values of the set together and dividing by the total number of values.

Square the difference between each individual value in the data set and the arithmetic mean.

Add all of the squares calculated in Step 2 together.

Divide your result from Step 3 by the total number of values in your data set. You now have the variance of your data set.

Calculate the square root of the variance calculated in Step 4. You now have the standard deviation of your data set.

Divide the standard deviation calculated in Step 5 by the absolute value of the arithmetic mean calculated in Step 1. Multiply it by 100 to get the relative dispersion of your data set in percentage form.

About the Author

Matthew Weeks has been a public policy and technology writer since 2003. He has been published on Men's News Daily and Free Republic. Weeks holds a bachelor's degree in political science from the College of New Jersey and a master's degree in public policy from Rutgers.