Coefficient of variation

In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation   σ {displaystyle sigma } to the mean   μ {displaystyle mu } (or its absolute value, | μ | {displaystyle |mu |} ). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R. In addition, CV is utilized by economists and investors in economic models and in determining the volatility of a security. The coefficient of variation (CV) is defined as the ratio of the standard deviation   σ {displaystyle sigma } to the mean   μ {displaystyle mu } : c v = σ μ . {displaystyle c_{ m {v}}={frac {sigma }{mu }}.} It shows the extent of variability in relation to the mean of the population.The coefficient of variation should be computed only for data measured on a ratio scale, as these are the measurements that allow the division operation. The coefficient of variation may not have any meaning for data on an interval scale. For example, most temperature scales (e.g., Celsius, Fahrenheit etc.) are interval scales with arbitrary zeros, so the coefficient of variation would be different depending on which scale you used. On the other hand, Kelvin temperature has a meaningful zero, the complete absence of thermal energy, and thus is a ratio scale. While the standard deviation (SD) can be meaningfully derived using Kelvin, Celsius, or Fahrenheit, the CV is only valid as a measure of relative variability for the Kelvin scale because its computation involves division. Measurements that are log-normally distributed exhibit stationary CV; in contrast, SD varies depending upon the expected value of measurements. A more robust possibility is the quartile coefficient of dispersion, half the interquartile range ( Q 3 − Q 1 ) / 2 {displaystyle {(Q_{3}-Q_{1})/2}} divided by the average of the quartiles (the midhinge), ( Q 1 + Q 3 ) / 2 {displaystyle {(Q_{1}+Q_{3})/2}} . In most cases, a CV is computed for a single independent variable (e.g., a single factory product) with numerous, repeated measures of a dependent variable (e.g., error in the production process). However, data that are linear or even logarithmically non-linear and include a continuous range for the independent variable with sparse measurements across each value (e.g., scatter-plot) may be amenable to single CV calculation using a maximum-likelihood estimation approach.