How is the coefficient of variation calculated?

The coefficient of variation (CV) is a statistical measure that expresses the extent of variability in relation to the mean of the data set. It is calculated by taking the standard deviation and dividing it by the mean. This provides a standardized measure of dispersion, allowing for comparison between datasets with different units or vastly different means.

This method of calculation is particularly useful in fields such as finance and quality control, where understanding relative variability is essential. For example, a lower CV indicates more consistent data points around the mean, while a higher CV suggests greater dispersion.

The other options presented do not accurately reflect the definition of the coefficient of variation. Simply dividing the mean by the standard deviation doesn't provide a measurement of variability. Multiplying the standard deviation by the mean or dividing the sum of values by the sample size gives different statistical metrics, neither of which represent the standard deviation's relationship to the mean effectively for the purpose of identifying relative variability. Therefore, the method of dividing the standard deviation by the mean captures the essence of the coefficient of variation.