Coefficient of Variation: Definition & Calculations

Instructor: David Karsner

David holds a Master of Arts in Education

In statistics, you will need to compare the standard deviation of one data set to the standard deviation of another data set. This lesson will explain that if the data sets do not have the same measurements, then you will need to use the coefficient of variation to compare them.

Three Brothers and Coefficients of Variation.

Thomas, Todd, and Tyler are three brothers. Thomas, Todd, and Tyler play three different sports: football, basketball, and soccer respectively. As brothers, they argue not only about who is the best player but who is the most consistent player. Thomas had a season average of 20 points per game. Todd had a season average of 12 points per game, and Tyler had a season average of 3 points per game.

Since the points in all three sports are recorded using different units, it is difficult to make a comparison about who the best player is. However, it is possible to find who the most consistent player is by using the coefficient of variation. This lesson will give the definition of the coefficient of variation. How to calculate the coefficient of variation and finally which brother is the most consistent player.

Coefficient of Variation Definition

The coefficient of variation is a measurement of variation. Variation is a measure of how far from the mean the data set varies. The coefficient of variation has no units. It is used with samples that don't have the same unit or scale of measurement. The coefficient of variation compares the standard deviation to the mean of each sample. The samples must be non-negative.

How to Calculate the CV

To calculate the coefficient of variation you will need to know the sample standard deviation (standard deviation is the average of how much each data value from the sample varies from its mean) and the sample mean (The mean is a measure of center that is obtained by adding all the values of x in the sample and then dividing by the number of data points).

The sample standard deviation is usually represented by a lower case s. The sample mean is usually represented by x bar (x with a bar above it). To calculate the CV, divide the standard deviation by the sample mean and then multiply by 100. If needed round your CV to one decimal place. Your answer should be a percentage.

Example 1

If Sample A has a mean of $100 and a standard deviation of $10 and Sample B has a mean of 300 pounds and a standard deviation of 20 pounds, which sample has greater variation? Notice how Sample A and Sample B have different units.

Sample A

10 / 100 = .1

.1 x 100 = 10%

Sample B

20 / 300 .067

.067 x 100 = 6.7%

Sample A has a higher CV and therefore more variation.

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