CV puts standard deviation on a relative scale
For replicate values, calculate the mean and a declared standard deviation convention. Analytical replicate summaries commonly use sample standard deviation, dividing squared deviations by n − 1. This calculator divides sample SD by the absolute mean and multiplies by 100.
Using the absolute mean prevents a negative sign, but it does not make CV scientifically meaningful for negative or near-zero responses. State the convention and review whether the measurement has a meaningful ratio scale.
%CV = sample standard deviation ÷ |mean| × 100Calculate replicate CV
Enter responses separated by commas, spaces, or line breaks. The calculator uses sample standard deviation (n − 1) and divides it by the absolute mean.
- n
- 4
- Mean
- 99.8500
- Sample SD
- 1.1561
- CV
- 1.16%
CV describes spread relative to the mean. Whether that variability is acceptable depends on the assay, response level, replicate design, and approved criterion.
Worked calculation: 98, 102, 101, and 99
The mean is 100. The sum of squared deviations is 10, so the sample variance is 10 ÷ 3 = 3.333. The sample standard deviation is 1.826, and the CV is 1.826 ÷ 100 × 100 = 1.83%.
Retain more precision during calculation and round only the displayed result. A report should show n, mean, SD, CV, units, and individual observations or a path to them.
| Statistic | Value |
|---|---|
| n | 4 |
| Mean | 100.000 |
| Sample SD | 1.826 |
| CV | 1.83% |
A near-zero mean makes CV unstable
When the mean approaches zero, small changes in the denominator produce very large CV values. CV is generally meaningful for ratio-scale data with a meaningful zero and positive values. Background-subtracted or normalized responses that cross zero often need an absolute variability measure instead.
CV also does not tell you whether variability comes from within a plate, between plates, days, analysts, instruments, or reagent lots. Variance-component designs are needed to separate those sources.
Avoid a universal CV threshold
A criterion should reflect assay level, endpoint, replicate design, intended use, historical performance, and the consequences of variability. Low-signal controls may need an SD rule while higher signals use CV.
Display both observed CV and configured criterion, and retain the method version that supplied the limit. A PASS/FAIL color is helpful only when the numeric evidence and rule remain readable.
Frequently asked questions
Should CV use sample or population standard deviation?
Declare the method. For a sample of replicate observations, sample SD is common; a fully enumerated population is different. Mixing conventions can change borderline outcomes.
Can I calculate CV when the mean is negative?
The interpretation is usually problematic because CV assumes a meaningful ratio scale. Review the response transformation and consider SD or another assay-appropriate measure.
Does a low CV prove an assay is accurate?
No. CV describes precision relative to the mean. Replicates can agree closely and still be biased or affected by systematic error.