Which formula defines the coefficient of variation for a sample?

• A. CV = x_bar / s
• B. CV = (range) / x_bar
• C. CV = s / x_bar
• D. CV = s / mu

Answer: (C)

The coefficient of variation is a unitless measure of how spread out the data are relative to the mean. It’s defined as the standard deviation divided by the mean, which lets you compare variability across datasets that have different units or scales. for a sample, you estimate this with the sample standard deviation divided by the sample mean: CV = s / x̄. This is why the correct form uses s in the numerator and x̄ in the denominator.

Using the range would not properly capture distribution because it only looks at the extremes and ignores how the data are spread in between. Inverting the ratio to x̄ / s would give a different interpretation, essentially how many standard deviations fit into the mean, not the variability relative to the mean. The form s / μ would be the population version, which you’d use only if you know the true population mean; with a sample, the standard approach is s / x̄.