A coefficient of variation, often abbreviated as CV, is a way to measure how spread out values are in a dataset relative to the mean. It is calculated as:
CV = σ / μ
- σ: The standard deviation of dataset
- μ: The mean of dataset
In plain English, the coefficient of variation is simply the ratio between the standard deviation and the mean.
When to Use the Coefficient of Variation
The coefficient of variation is often used to compare the variation between two different datasets.
In the real world, it’s often used in finance to compare the mean expected return of an investment relative to the expected standard deviation of the investment. This allows investors to compare the risk-return trade-off between investments.
For example, suppose an investor is considering investing in the following two mutual funds:
Mutual Fund A: mean = 7%, standard deviation = 12.4%
Mutual Fund B: mean = 5%, standard deviation = 8.2%
Upon calculating the coefficient of variation for each fund, the investor finds:
CV for Mutual Fund A = 12.4% / 7% = 1.77
CV for Mutual Fund B = 8.2% / 5% = 1.64
Since Mutual Fund B has a lower coefficient of variation, it offers a better mean return relative to the standard deviation.
Example: Calculating the Coefficient of Variation in Google Sheets
There is no built-in function in Google Sheets to calculate the coefficient of variation for a dataset, but it’s relatively easy to calculate using simple formulas.
Suppose we have the following dataset that contains 20 values:
To calculate the coefficient of variation for this dataset, we only need to know two numbers: the mean and the standard deviation. These can be calculated using the following formulas:
To calculate the coefficient of variation, we then divide the standard deviation by the mean:
The coefficient of variation turns out to be 0.0864.