Coefficient of Variation
Relative variability as a percentage of the mean.
Formula
Variables
Example
Compares spread across scales
How it works
The coefficient of variation tells you how large the standard deviation is compared with the mean, then converts that ratio into a percentage. Because it divides by the mean, it measures spread in a relative way, making it useful when you want to know how variable data are compared with their typical size. A smaller CV means the data are more tightly clustered around the mean, while a larger CV means more relative scatter.
When to use it
Use it when comparing consistency across datasets that have different units or very different averages, such as test scores from two classes, production quality from two machines, or investment returns from different funds. It is especially helpful when the question is about variability relative to the size of the average, not just the raw spread.
Worked example, step by step
A lab measures the mass of identical tablets. Mean mass, μ = 250 mg Standard deviation, σ = 5 mg CV = (σ / μ) × 100 CV = (5 / 250) × 100 CV = 0.02 × 100 CV = 2% So the tablet masses vary by 2% of the mean mass.
Common mistakes to avoid
- Using the variance instead of the standard deviation in the formula
- Forgetting to multiply by 100 if the answer is required as a percentage
- Using the coefficient of variation with a mean that is zero or very close to zero
Did You Know?
The coefficient of variation is dimensionless, letting you compare the spread of prices and heights on equal footing.
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More in Statistics & Probability
View allArithmetic Mean
BasicThe average of a data set.
Median
BasicThe middle value separating the higher and lower halves.
Variance
IntermediateAverage squared deviation from the mean.
Standard Deviation
IntermediateSquare root of the variance; typical spread.
Z-Score
IntermediateNumber of standard deviations a value is from the mean.
Bayes' Theorem
IntermediateUpdates a probability given new evidence.