Glossary
Coefficient of Variation (CV)
The coefficient of variation is the ratio of the standard deviation to the arithmetic mean of a dataset, often expressed as a percentage. It provides a dimensionless measure of relative variability, making it useful for comparing dispersion across variables measured on differe...
Definition
The coefficient of variation is the ratio of the standard deviation to the arithmetic mean of a dataset, often expressed as a percentage. It provides a dimensionless measure of relative variability, making it useful for comparing dispersion across variables measured on different scales.
Why It Matters
The CV allows researchers to compare the relative spread of datasets that have different units or vastly different means. A standard deviation of 5 is trivial for a mean of 1,000 but substantial for a mean of 10. By expressing variability relative to the mean, the CV reveals which dataset is more inherently variable, regardless of scale. It is widely used in finance (risk per unit of return), quality control (process consistency), and biomedical research (comparing assay precision).
Example
Two production lines fill bottles. Line A fills bottles with a mean volume of 500 mL and a standard deviation of 10 mL (CV = 2%). Line B fills bottles with a mean volume of 1,000 mL and a standard deviation of 15 mL (CV = 1.5%). Despite Line B having a larger absolute standard deviation, Line A is more variable relative to its mean, indicating less consistent filling.
Related Terms
Software Notes
- SPSS: Compute via Transform > Compute Variable:
SD / Mean * 100 - R:
cv <- sd(x) / mean(x) * 100; or use thecvfunction from therasterpackage - Stata:
summarize varname, thendisplay r(sd) / r(mean) * 100