Coefficient of Variation
Relative variability as a percentage of the mean.
Formula
Variables
Example
Mean 50 with σ = 5 gives CV = 5/50 × 100% = 10%.
How it works
The coefficient of variation compares the spread of a dataset to its average size, so it tells you how large the standard deviation is relative to the mean. Dividing by the mean turns the spread into a scale-free quantity, which makes it useful for comparing variability across datasets with different units or very different averages. Multiplying by 100% expresses that relative spread as a percentage, making it easier to interpret and compare.
When to use it
Use this when you want to compare consistency across two or more datasets that may have different means or even different units, such as test scores from different classes, production measurements from different machines, or financial returns from different investments. It is especially helpful when the question is about relative variability rather than raw spread.
Worked example, step by step
Suppose a lab measures the concentration of a solution and finds a mean of 80 mg/L with a standard deviation of 12 mg/L. CV = (σ / x̄) × 100% CV = (12 / 80) × 100% CV = 0.15 × 100% CV = 15% So the standard deviation is 15% of the mean, which indicates moderate relative variability.
Common mistakes to avoid
- Using the variance instead of the standard deviation in the formula
- Forgetting to multiply by 100% when a percentage is required
- Applying CV when the mean is zero or very close to zero, which makes the result misleading or undefined
Did You Know?
The coefficient of variation lets you compare spread across data sets with completely different units.
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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.