Coefficient of Variation Guide
Coefficient of variation expresses standard deviation relative to the magnitude of the mean. It is useful for some ratio-scale comparisons but can be misleading near zero.
Method
- Calculate the mean of the observations.
- Calculate the relevant population or sample standard deviation.
- Divide standard deviation by the absolute mean.
- Multiply by 100 to express the result as a percentage.
Worked example
Mean 50 with population standard deviation 5 gives a population CV of 10%.
Notes
- CV is undefined when the mean is zero.
- CV is most meaningful on ratio scales with a meaningful zero.
- Comparing CV across fundamentally different measurement contexts can be misleading.
- Coefficient of variation becomes unstable when the mean is close to zero because a modest standard deviation is divided by a very small number. Avoid comparing CVs mechanically in that situation, and do not use CV on interval scales where zero is arbitrary.
Worked example: equal spread does not mean equal relative variation
Dataset A has mean 50 and standard deviation 10, so its coefficient of variation is 10 ÷ 50 × 100 = 20%. Dataset B has mean 100 and the same standard deviation 10, so its CV is 10%. The absolute spread is equal, but the variation relative to the mean is twice as large for A.
This comparison only makes sense when the measurement scale has a meaningful zero and the mean is sufficiently far from zero. If the mean approaches zero, CV becomes unstable or undefined, and a negative mean can make the signed ratio hard to interpret. The standard deviation and measurement units should remain visible beside CV.
Coefficient of variation measures spread relative to the mean
Lynara reports coefficient of variation as standard deviation divided by the absolute value of the mean, then expresses the result as a percentage. Using the mean magnitude keeps the displayed relative spread nonnegative, but CV is most interpretable for ratio-scale data with a meaningful zero and a positive mean.
A standard deviation of 5 is large relative to a mean of 10 and small relative to a mean of 100. CV makes that scale relationship explicit.
Avoid CV when the mean is near zero or the scale has an arbitrary zero
When the mean is close to zero, the ratio can become extremely large or unstable. Negative means also make interpretation awkward. Temperature in Celsius or Fahrenheit is a classic example where the zero point is arbitrary, so comparing variability with CV can be misleading.
Use the metric when the variable is on a ratio scale and the mean is meaningfully away from zero. Otherwise compare standard deviations or use another measure suited to the data.
Authoritative references
Primary or authoritative references for the external standard, scoring rule or identifier convention used on this page.
Editorial review and limitations
Continue with the related tools
Use the linked tools for your own inputs and scenarios.
- Standard Deviation Calculator — Calculate population and sample variance and standard deviation from a numeric data set.
- Mean Median Mode Calculator — Calculate mean, median, mode, minimum and maximum from a list of numeric values.
- Five Number Summary & Outlier Calculator — Calculate min, Q1, median, Q3, max, IQR, 1.5×IQR fences, box-plot whiskers and flagged outliers from numeric data.