Coefficient of Variation Calculator

Coefficient of Variation Formula

The Coefficient of Variation (CV) is a standardized measure of the dispersion of a probability distribution or data set. It is defined as the ratio of the standard deviation to the mean:

CV = (σ / μ) × 100%

Where:

• CV is the coefficient of variation
• σ (sigma) is the standard deviation
• μ (mu) is the mean

The CV is often expressed as a percentage by multiplying the result by 100. It is also known as relative standard deviation (RSD).

When to Use the Coefficient of Variation

The coefficient of variation is particularly useful in these situations:

• Comparing dispersion across data sets with different units or scales - Since CV is unitless, it allows comparison of variability between different data sets regardless of their units or magnitudes.
• Comparing variability of data sets with different means - When means differ significantly, standard deviation alone can be misleading for comparing variability.
• Assessing measurement precision - In analytical chemistry, manufacturing, and laboratory testing, CV is used to assess the precision of measurements or processes.
• Financial analysis - CV is used to compare the volatility of different investments relative to their returns.

Interpreting the Coefficient of Variation

The interpretation of CV values depends on the context, but generally:

• CV < 5%: Data shows little variability relative to the mean (high precision)
• CV 5-10%: Data shows moderate variability
• CV 10-15%: Data shows moderately high variability
• CV 15-20%: Data shows high variability
• CV > 20%: Data shows very high variability relative to the mean (low precision)

Industry-specific norms may vary. For example, in clinical laboratory testing, analytical methods typically aim for a CV below 5%, while in manufacturing, acceptable CV values may be higher.

Limitations of the Coefficient of Variation

• Not suitable for data with a mean close to zero - As the mean approaches zero, CV approaches infinity, making it unstable.
• Not appropriate for data with both positive and negative values - The CV can be misleading when the data includes both positive and negative values.
• May not be valid for non-normal distributions - The interpretation of CV is most reliable for data that follows a normal distribution.