Coefficient of Variation Calculator
Spread as a percentage of the mean, so two things measured on different scales can be compared for variability.
Results
What this tool does
A standard deviation of ten means one thing for a set of numbers averaging twenty and something entirely different for one averaging ten thousand. The coefficient of variation strips the scale out by dividing the spread by the mean, leaving a bare percentage. It is how a laboratory compares the precision of two instruments, how a factory tracks consistency across product lines, and how anyone compares the reliability of two measurements taken in different units. Give it a mean and a standard deviation; give it a second pair and it compares them for you.
Formula
CV = standard deviation ÷ average × 100
Variables
| Symbol | Meaning | Unit |
|---|---|---|
mean_1 | Mean of the first | — |
sd_1 | Standard deviation of the first | — |
mean_2 | Mean of the second, if you are comparing | — |
sd_2 | Standard deviation of the second | — |
OUT | Coefficient of variation | % |
C2 | The second one | % |
DF | Difference between them | % |
MV | More variable | — |
RT | Ratio | x |
SM | As a plain ratio | — |
SP | How spread out | — |
Worked example
- Mean of the first50
- Standard deviation of the first7.5
- Mean of the second, if you are comparing120
- Standard deviation of the second24
- Coefficient of variation15.00 %
- The second one20.00 %
- Difference between them-5.00 %
- More variableThe second
- Ratio0.750 x
- As a plain ratio0.1500
- How spread outModerate
Frequently asked questions
Why not just compare the standard deviations?
Because a standard deviation carries the unit and the scale of what it measures. A spread of 24 on a mean of 120 and a spread of 7.5 on a mean of 50 cannot be ranked by the raw numbers: the first is three times larger and yet both are describing something that varies by roughly a sixth. Dividing by the mean strips the scale away and leaves a percentage you can put side by side — which is why laboratories use it to compare instruments and why it appears in quality control as the relative standard deviation.
When does it stop working?
When the mean is near zero, and when the scale has an arbitrary origin. A mean close to zero makes the ratio explode: a spread of 2 on a mean of 0.1 gives 2000 per cent, which is arithmetically right and practically meaningless. The second case is subtler — temperatures in Celsius have an arbitrary zero, so the same weather gives a completely different coefficient in Celsius and in Fahrenheit. The measure only means something on a scale where zero means none.