Which statement best describes the coefficient of variation?

Which statement best describes the coefficient of variation?

• A. CV = s / x̄, expressed as a percentage, and measures relative dispersion.
• B. CV is the absolute range of the data.
• C. CV equals the population variance.
• D. CV is always equal to 1.

Answer: (A)

The main idea being tested is that the coefficient of variation is a standardized measure of dispersion that puts variability in context relative to the mean. It is calculated as the standard deviation divided by the mean (for a sample, s/x̄) and then expressed as a percentage. This makes it unitless, so you can compare variability across data sets that have different units or different scales. The reason this is the best description is that it specifically captures how large the variability is relative to the typical size of the values, rather than just the absolute spread. This contrasts with the other ideas: the absolute range describes how wide the data span, not a ratio to the mean; the population variance is the squared deviation from the mean, not a relative measure; and the coefficient of variation is not a constant 1—it's a value that changes depending on the data.

The main idea being tested is that the coefficient of variation is a standardized measure of dispersion that puts variability in context relative to the mean. It is calculated as the standard deviation divided by the mean (for a sample, s/x̄) and then expressed as a percentage. This makes it unitless, so you can compare variability across data sets that have different units or different scales. The reason this is the best description is that it specifically captures how large the variability is relative to the typical size of the values, rather than just the absolute spread.

This contrasts with the other ideas: the absolute range describes how wide the data span, not a ratio to the mean; the population variance is the squared deviation from the mean, not a relative measure; and the coefficient of variation is not a constant 1—it's a value that changes depending on the data.