How is the coefficient of variation defined?

The coefficient of variation is defined as the ratio of the standard deviation to the mean, which expresses the extent of variability in relation to the mean of the data set. This ratio is particularly useful in comparing the degree of variation from one data series to another, even if the means are drastically different.

When the standard deviation is divided by the mean, it allows for a scale-free measure of relative variability, enabling analysts to assess the consistency of data points in relation to their average value. This makes the coefficient of variation a crucial tool in finance, risk assessment, and various fields involving statistical analysis, where comparing relative variability among different sets of data is important.

The other choices describe relationships between statistical measures but do not accurately define the coefficient of variation. For example, the variance divided by the mean would yield a different measure that doesn't provide the same interpretive value regarding relative variability. Understanding this distinction is key to applying the coefficient of variation correctly in various analyses.