Coefficient of Variation Calculator

The coefficient of variation is defined as the ratio of the standard deviation to the absolute value of the mean:

$$CV = \frac{\sigma}{|\mu|}$$

$$CV\% = \frac{\sigma}{|\mu|} \times 100$$

Where:

• σ is the standard deviation
• μ is the mean (absolute value is used to handle negative means)

The CV is particularly useful when you need to compare the variability of datasets measured in different units. For example, comparing the variability of heights (in cm) with weights (in kg) would be meaningless using standard deviations alone, but the CV normalizes both to a common dimensionless scale.

Interpretation guidelines:

• CV < 15%: Low variability, data points are tightly clustered around the mean
• 15% ≤ CV ≤ 30%: Moderate variability
• CV > 30%: High variability, data is widely spread

The CV has important applications across many fields. In analytical chemistry, the CV (often called the relative standard deviation or RSD) is a standard measure of assay precision. Regulatory agencies like the FDA often require that analytical methods demonstrate a CV below a certain threshold (e.g., 15%) for method validation. In finance, the CV is used to compare the risk-adjusted return of different investments; a lower CV indicates a more favorable risk-return trade-off.

One limitation of the CV is that it is undefined when the mean is zero and becomes unstable when the mean is close to zero. It is also most meaningful for ratio-scale data (where zero has a true meaning). For interval-scale data like temperature in Celsius, the CV is not appropriate because the zero point is arbitrary.

Karl Pearson first defined the CV in 1896, and it remains one of the most widely used measures of relative variability in both applied and theoretical statistics.

A CV of 0.20 (20%) means the standard deviation is 20% of the mean. Lower CV indicates more consistent data. Compare CV values across datasets to determine which has greater relative variability, regardless of measurement units.