If the standard deviation is high relative to the mean, what does this imply about the coefficient of variation?

If the standard deviation is high relative to the mean, what does this imply about the coefficient of variation?

• A. Low relative variability
• B. High relative variability
• C. No variability
• D. Negative variability

Answer: (B)

The coefficient of variation measures dispersion relative to the mean. It’s SD divided by the mean (often using the absolute value of the mean). When the standard deviation is large compared with the mean, that ratio becomes large, signaling high relative variability. In other words, the data are spread out a lot relative to the average. Note that if the mean is near zero, the CV can be unstable or undefined.

The coefficient of variation measures dispersion relative to the mean. It’s SD divided by the mean (often using the absolute value of the mean). When the standard deviation is large compared with the mean, that ratio becomes large, signaling high relative variability. In other words, the data are spread out a lot relative to the average. Note that if the mean is near zero, the CV can be unstable or undefined.