What is considered a good coefficient of variation?

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A coefficient of variation, often abbreviated 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

where:

• σ: The standard deviation of dataset
• μ: The mean of dataset

Simply put, the coefficient of variation is the ratio between the standard deviation and the mean.

For example:

• A CV of 0.5 means the standard deviation is half as large as the mean.
• A CV of 1 means the standard deviation is equal to the mean.
• A CV of 1.5 means the standard deviation is 1.5 times larger than the mean.

The higher the coefficient of variation, the higher the standard deviation relative to the mean.

What is a Good Coefficient of Variation?

One questions that students often have is: What is considered a good value for a coefficient of variation?

The answer: There is no specific value for a coefficient of variation that is considered to be a “good” value. It depends on the situation.

In most cases, the lower the coefficient of variation the better because it means the spread of data values is low relative to the mean. The following examples illustrate this phenomenon in different fields.

Finance:

In the finance industry, the coefficient of variation is used to compare the mean expected return of an investment relative to the expected standard deviation of the investment.

For example, suppose an investor is considering investing in the following two mutual funds:

Mutual Fund A: mean = 9%, standard deviation = 12.4%

Mutual Fund B: mean = 5%, standard deviation = 8.2%

• CV for Mutual Fund A = 12.4% / 9% = 1.38
• CV for Mutual Fund B = 8.2% / 5% = 1.64

Since Mutual Fund A has a lower coefficient of variation, it offers a better mean return relative to the standard deviation.

Retail:

In the retail industry, companies often calculate the coefficient of variation to understand the variation of their revenue from one week to the next.

For example, consider the following mean weekly sales and standard deviation of weekly sales for two different companies:

• Company A: Mean Weekly Sales = $4,000, Standard Deviation = $1,500
• Company B: Mean Weekly Sales = $8,000, Standard Deviation  = $2,000

We can calculate the coefficient of variation for each store:

• CV for Company A: $1,500 / $4,000 = 0.375
• CV for Company B: $2,000 / $8,000 = 0.25

Since Company B has a lower CV, it has lower volatility in weekly sales relative to the mean compared to company A. This means Company B can likely predict their weekly sales with more certainty than Company A.

Economics:

Economists often calculate the coefficient of variation for annual income in different cities to understand which cities have more inequality.

For example, consider the mean and standard deviation of annual incomes for residents in two different cities:

• City A: Mean Income: $50,000, Standard Deviation = $5,000
• City B: Mean Income: $77,000, Standard Deviation = $6,000

We can calculate the coefficient of variation for each city:

• CV for City A: $5,000 / $50,000 = 0.1
• CV for City B: $6,000 / $77,000 = 0.078

Since City B has a lower CV, it has a lower standard deviation of incomes relative to its mean income. This means there is less variation in incomes relative to the mean income of residents in City B compared to City A.

Conclusion

There is no specific value that is considered “low” for a coefficient of variation.

Instead, the coefficient of variation is often compared between two or more groups to understand which group has a lower standard deviation relative to its mean.

In most fields, lower values for the coefficient of variation are considered better because it means there is less variability around the mean.