Coefficient of Variation 

Coefficient of Variation (CoV) is a measure of relative variability. It is calculated as the ratio of standard deviation (SD) to mean. CoV does not have any unit as it is a ratio of SD to mean.

 

Applications of CoV 

CoV is useful for comparison of variability between two variables or two tests. It can be used for comparison only for ratio-scale variables.

 

Investment Decision Example

Suppose you have an option to invest in Mutual Fund A or Mutual Fund B. The two mutual funds have different expected returns and standard deviations. The expected return of Mutual Fund A is 15% and Mutual Fund B is 10%. Standard Deviation of the returns of these Mutual funds is 10% and 5% respectively. Which is a better investment?

For a risk-averse investor, Mutual Fund B would be better investment because its CoV (5% / 10% = 0.5) is less than the CoV of Mutual Fund A (10% / 15% = 0.67)

 

Exploratory Data Analysis Example

Assume, you are working as a data scientist. You are analyzing the data of Retail Customers. Between the two variables Age and Spend, you have to decide which variable has more variability.

The mean age of customers is 30 years with a standard deviation of 6
The mean Spend of customers is Rs. 6000 with a standard deviation of 1000

From the absolute value of standard deviation, you cannot say whether Age has more variability or the Spend. This is because the two variables have different units. Age is in Years and Spend is in Rs. 

Assume the Age information is given to you in days. Then the standard deviation of age would be 6 * 365 = 2190 days instead of 6 years. So to be able to compare the two variables we will have to compute the Coefficient of Variation.

CoV Age = standard deviation / mean = 6 / 30 = 0.20

CoV Spend = 1000 / 6000 = 0.167

As CoV of Spend is less than Age, we conclude that the variance in Age is more than Spend.

 

Next Blog

In our upcoming blog, we will discuss the two measures of relationship – covariance and correlation.