Which formula defines the coefficient of variation?

Which formula defines the coefficient of variation?

• A. CV = mean / standard deviation × 100%
• B. CV = (median / mean) × 100%
• C. CV = (standard deviation / mean) × 100%
• D. CV = (variance) × 100%

Answer: (C)

The coefficient of variation measures how large the variability is relative to the average value, making it possible to compare spread across datasets with different scales. It’s computed as the standard deviation divided by the mean, then multiplied by 100 to express it as a percentage. This standardizes dispersion so the result is a unitless, comparable measure. If you used the mean divided by the standard deviation, you’d reverse the relationship and lose the correct sense of variability. Using the median instead of the standard deviation ignores how spread out the data are around the center. Using the variance would give a value in squared units and isn’t expressed as a simple percent of the mean. Therefore, the correct formula is CV = (standard deviation / mean) × 100%.

The coefficient of variation measures how large the variability is relative to the average value, making it possible to compare spread across datasets with different scales. It’s computed as the standard deviation divided by the mean, then multiplied by 100 to express it as a percentage. This standardizes dispersion so the result is a unitless, comparable measure.

If you used the mean divided by the standard deviation, you’d reverse the relationship and lose the correct sense of variability. Using the median instead of the standard deviation ignores how spread out the data are around the center. Using the variance would give a value in squared units and isn’t expressed as a simple percent of the mean. Therefore, the correct formula is CV = (standard deviation / mean) × 100%.