Which statement correctly defines the coefficient of variation (CV)?

• A. CV equals the standard deviation divided by the mean, expressed as a percentage.
• B. CV equals the mean divided by the standard deviation.
• C. CV is the range of measurements divided by the mean.
• D. CV is the variance divided by the mean.

Answer: (A)

The coefficient of variation measures how large the variability is relative to the size of the data. It is defined as the standard deviation divided by the mean, usually written as CV = (SD / mean) × 100%, so it’s expressed as a percentage. This makes the amount of dispersion a dimensionless quantity, allowing direct comparisons of variability across datasets with different units or different means. A small CV means measurements are tightly clustered around the mean; a larger CV means more relative variability for that mean value.

The correct approach uses the standard deviation in the numerator and the mean in the denominator, and then commonly converts to a percentage. Using the mean divided by the standard deviation would invert the ratio, the range divided by the mean isn’t the CV, and variance divided by the mean isn’t the CV either.