Coefficient of variation

Coefficient of Variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. It is defined as the ratio of the standard deviation (Standard deviation) to the mean (Mean), and it is often expressed as a percentage. The coefficient of variation is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from each other.

Definition

The coefficient of variation (CV) is calculated using the formula:

CV = (σ / μ) × 100%

where σ is the standard deviation of the dataset, and μ is the mean of the dataset. This formula is applicable for sample data. For a population data set, the population standard deviation and the population mean are used.

Applications

The coefficient of variation is widely used in various fields such as finance, investing, engineering, and science to analyze the variability of different datasets. In finance, for example, it is used to measure the risk per unit of return of an investment. In the field of laboratory medicine, it is used to assess the precision of assay methods. It is particularly useful when comparing the degree of variation between datasets with different units or vastly different means.

Advantages and Limitations

One of the main advantages of the coefficient of variation is its ability to facilitate comparisons between datasets. However, it should be noted that the CV is only meaningful for ratio-level variables where a true zero point exists. It is not suitable for use with interval-level variables, which lack a true zero point, such as temperature scales.

Additionally, the CV can be misleading when dealing with datasets that include negative values or values close to zero, as the mean can be very small, leading to a disproportionately high CV.

Related Statistical Measures

Other statistical measures related to the coefficient of variation include the Standard deviation, which measures the absolute variability of a dataset, and the mean, which provides a measure of the central tendency of the data. The Variance is another related measure, representing the average of the squared differences from the Mean.

See Also

• Standard deviation
• Mean
• Variance
• Relative standard deviation