How this calculator works
The signed coefficient divides standard deviation by the arithmetic mean. It is dimensionless and changes sign if the mean is negative. In data mode choose the sample or population divisor. Ratio-scale quantities with a meaningful zero are the usual application. Values near a zero mean can produce enormous coefficients; a small change in the mean may then dominate the comparison.
Formula
CV = SD / mean; SD = CV × mean; mean = SD / CV. Percentage = 100 × CV.
Worked example
A mean of 20 and standard deviation of 5 give CV = 0.25, or 25%. The same standard deviation with mean -20 gives -0.25.
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Frequently asked questions
Can the coefficient be negative?
This signed convention retains the sign of the mean. Relative standard deviation uses its absolute value instead.
Can I compare Celsius temperatures?
Celsius has an arbitrary zero, so a coefficient can change simply by converting to Fahrenheit. Use a meaningful ratio scale where appropriate.
What does zero standard deviation mean?
All observations are equal. With a nonzero mean the coefficient is zero; two zeros cannot determine a unique mean.