What Is Mean, SD and CV?
The mean says where the data are centred, the standard deviation says how far values typically sit from it, and the coefficient of variation (CV) divides one by the other to give spread as a percentage of the mean.
Enter one set, or two to compare. The CV lets you compare variability for data on different scales, such as weights in grams against weights in kilograms, where raw standard deviations are not comparable.
The CV only makes sense for ratio-scale data with a mean well above zero. If the mean is near zero, the CV becomes unstable.
How to Use the Mean, SD and CV Calculator
- Enter data set A.
- Optionally enter set B.
- Read the mean, SD and CV.
- Compare the CVs.
Mean, SD and CV Formula
Coefficient of variation
Mean, SD and CV Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| x̄ | Mean | |
| s | Sample standard deviation | |
| CV | Coefficient of variation = s ÷ x̄ × 100% | |
| n | Number of values |
Mean, SD and CV Worked Example
Set A has mean 52.7 and SD about 3.15, so its CV is about 6 %. Set B has mean 227.6 and SD about 21.8, a CV of about 9.6 %. B has a much larger SD but also a larger mean, and it varies more relative to its mean.
With the example values loaded in the calculator above, the steps are:
- Set A: mean = 52.714286, sample SD = 3.1471832.
- CV = SD ÷ |mean| × 100 = 3.1471832 ÷ 52.714286 × 100 = 5.97027 %.
- Set B: mean = 227.57143, sample SD = 21.823971, CV = 9.58994 %.
- B varies more relative to its mean, even if its SD is also larger.
Result: Mean of A = 52.714286; Standard deviation of A (sample) = 3.1471832; CV of A = 5.97027 %; CV of B = 9.58994 %.
How to Read the Coefficient of Variation
The CV is the standard deviation as a percentage of the mean, so it measures spread relative to size. Set A has mean 52.7 and SD 3.15, a CV of about 6%. Set B has mean 227.6 and SD 21.8, a CV of about 9.6%.
Set B has a far larger SD, but only because its values are bigger. Relative to its mean, B varies about 1.6 times as much as A. That comparison is the reason to use the CV rather than the raw SD.
Where Mean, SD and CV Is Used
Comparing different scales
Compare the variability of two sets measured in different units or at very different sizes.
Lab precision
Report repeatability of an assay as a percentage.
Quality control
Check that two production lines are equally consistent relative to their output.
Finance
Compare the risk per unit of average return of two assets.
Common Mean, SD and CV Mistakes to Avoid
- The CV needs ratio-scale data, where zero means none. Do not use it for temperatures in °C.
- If the mean is close to zero, the CV becomes huge and unstable.
- Use the same SD version for both sets. The calculator shows the sample SD and a population-SD CV.
- A CV is unit-free, so it is easy to compare, but it hides the actual size of the spread.
Mean, SD and CV Terms and Definitions
- CV
- Standard deviation as a percentage of the mean.
Mean, SD and CV FAQs
What is the coefficient of variation?
It is the standard deviation divided by the mean, usually written as a percentage. It tells you how large the spread is relative to the average.
When should I use the CV?
Use it to compare the variability of data sets with different units or very different means. For one set on its own, the standard deviation is usually enough.
What is a good CV?
There is no universal threshold. A lower CV means more consistent data, and acceptable limits depend on the field and the method, so compare against a standard in your own area.
Is CV the same as RSD?
Yes. The relative standard deviation is the same ratio, often quoted in analytical chemistry. Some texts include the percentage sign and some do not.