Coefficient of Variation Calculator
Enter a data set for a sample or population to calculate the coefficient of variation for the data.
Results:
| Coefficient Of Variation (CV): | |
|---|---|
| Expressed as a Percentage: | |
| Standard Deviation (σ): | |
| Mean (μ): | |
| Sum of Squares (SS): | |
| Population Size (N): |
Steps to Solve the Coefficient Of Variation
Step One: Find the Mean
Mean (μ) = sum / population size (N)
Step Two: Find the Sum of Squares
Sum of Squares (SS) = ∑(xi - μ)²
Step Three: Calculate the Standard Deviation
Standard Deviation (σ) = √SS / N
Step Four: Calculate the Coefficient Of Variation
CV = σ / μ
| Coefficient Of Variation (CV): | |
|---|---|
| Coefficient Of Variation %: | |
| Standard Deviation (s): | |
| Mean (x̄): | |
| Sum of Squares (SS): | |
| Sample Size (n): |
Steps to Solve the Coefficient Of Variation
Step One: Find the Mean
Mean (x̄) = sum / sample size (n)
Step Two: Find the Sum of Squares
Sum of Squares (SS) = ∑(xi - x̄)²
Step Three: Calculate the Standard Deviation
Standard Deviation (s) = √SS / n - 1
Step Four: Calculate the Coefficient Of Variation
CV = s / x̄
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How to Calculate the Coefficient of Variation
Coefficient of variation, or just CV, is a measure of relative variability or dispersion of data around the mean in a sample or population. More simply, it is a ratio of the standard deviation to the mean, and it’s often used to compare the amount of variability between distributions or sets of data.
The coefficient of variation is primarily used in statistics, but it’s also used in finance to measure risk and volatility in investments and in quality assurance to audit the precision of a particular process.
Coefficient of Variation Formula
Because the coefficient of variation is a ratio, you can find it using a standard ratio formula.
Thus, the formula to calculate the coefficient of variation (CV) is:
CV = σ / μ
Where:
CV = coefficient of variation
σ = standard deviation
μ = mean
The formula states that the coefficient of variation CV is equal to the standard deviation σ (pronounced sigma) divided by the mean μ (pronounced mu).
The coefficient of variation is often expressed as a percentage. To express CV in percent form, multiply by 100, then add a percent symbol (%).
percent form = CV × 100%
For example, let’s calculate the coefficient of variation given a standard deviation of 0.783 and a mean of 23.41.
CV = 0.783 / 23.41
CV = 0.0334
In this example, the coefficient of variation is equal to 0.0334.
To express CV as a percentage, multiply it by 100.
0.0334 × 100 = 3.34%
In this example, the coefficient of variation is equal to 0.0334 or 3.34%.
The coefficient of variation is actually very similar to the relative standard deviation. The only difference between these two statistical measures is that the relative standard deviation is the absolute value of the CV, so it’s always positive.
Frequently Asked Questions
What is the coefficient of variation used for?
The CV can be used for several reasons in statistics and data analysis such as comparing variability, risk assessment, and quality control. Oftentimes, the CV is used to compare variability across data sets. One problem with the coefficient of variation is if the mean is 0 then the CV is not defined.
Another issue is that if the mean is close to 0, then the estimated CV may be very noisy in the sense that small changes in the estimated mean can produce big changes in the CV. If one’s data only contains positive or negative values, then both issues are less likely.
Can the coefficient of variation be greater than 1?
Yes, the coefficient of CV can be greater than 1. This often occurs when the standard deviation of a dataset is larger than the mean.
Is a higher or lower CV better?
In most cases, a lower CV is “better” due to lower variability, stability, and comparisons. Lower CV indicates that data is closer to the mean, making it more consistent and predictable.