Coefficient of Variation Calculator

Divide the standard deviation by the mean. For 12, 15, 11, 14, 13, 17, 16, 12 the mean is 13.75 and the sample standard deviation is 2.1213, so the CV is 2.1213 / 13.75 = 0.1543. Multiply by 100 to express it as a percentage.

CV% = (standard deviation / mean) × 100. Using the sample standard deviation 2.1213 and mean 13.75, CV% = 2.1213 / 13.75 × 100 = 15.43%. Type your data into the calculator and it shows the CV in percent along with the mean, SD and variance.

There is no single good value, because the acceptable limit depends on the field and the measurement. A lower CV means the values are tightly grouped around the mean. Replicate readings in the example have a CV of 1.7%, while test scores have 8.62%. Check the standard or specification that applies to your work for a real limit.

Relative standard deviation is the same as the coefficient of variation: RSD% = (SD / |mean|) × 100. For the six replicate readings 98.2, 101.5, 99.8, 100.4, 97.9, 102.1, the mean is 99.983, the sample SD is 1.7034 and the RSD is 1.704%. Choose the data mode and paste replicate results.

None in practice. Both are the standard deviation divided by the mean. Analytical chemistry usually says relative standard deviation or %RSD, while statistics and many other fields say coefficient of variation. Some sources write RSD as a percentage and CV as a ratio, so check which form is being reported.

It is the size of the typical spread expressed as a fraction of the mean. A CV of 8% means the standard deviation is 8 percent of the mean, as with a mean of 50 and SD of 4. Because it has no units, you can compare variability between data sets measured in different units.

It is a ratio, SD / mean, and it is very often written as a percentage by multiplying by 100. A ratio of 0.1543 and a percentage of 15.43% are the same thing. This calculator reports the percentage, which is the form most readers expect.

Compare it to what is normal for your measurement and use it to compare groups. A group with a CV of 8.6% is relatively more consistent than one with 15.4%. It does not say whether the values are good or bad, only how large the spread is next to the mean. The reading table gives an informal guide.

Yes, there are six on this page. For 12, 15, 11, 14, 13, 17, 16, 12 the mean is 13.75, the sum of squared deviations is 31.5, the sample variance is 4.5, the SD is 2.1213 and the CV is 15.43%. The solution view shows each step for your own data.

For a sample use =STDEV.S(range)/AVERAGE(range), and for a whole population use =STDEV.P(range)/AVERAGE(range). Format the cell as a percentage or multiply by 100. For 12, 15, 11, 14, 13, 17, 16, 12 the sample formula gives 0.1543, which is 15.43%, matching this calculator in sample mode.

This page works as a CV calculator on any phone browser, with no download. Type or paste the numbers, choose sample or population and press Calculate. It also accepts a mean and standard deviation directly, which is handy when your data come from a report that gives only those two figures.

People sometimes use coefficient of deviation to mean the coefficient of variation, which is SD / mean. A related measure, the coefficient of mean deviation, divides the mean absolute deviation by the mean instead. This calculator uses the standard deviation, so for 12, 15, 11, 14, 13, 17, 16, 12 it reports 15.43%.

Use the sample version when your numbers are a sample from a larger group, which is the usual case, and the population version only when you have every member of the group. The difference is the divisor, n − 1 or n. For eight values it is 15.43% against 14.43%.

Not here. If the mean is negative the calculator divides by its absolute value so the CV stays positive, which is a common convention. A negative mean often signals data where the CV is not meaningful. If the mean is zero, the CV is undefined and the calculator says so instead of returning a number.

Yes. When the standard deviation is larger than the mean, the CV is above 100%. A mean of 2.5 with an SD of 3.1 gives 124%. This typically happens with strongly skewed data, such as a few very large values among many small ones.

Because the formula divides by the mean, and division by zero has no value. Near zero the CV also becomes huge and unstable, since a tiny mean makes any spread look enormous. If your mean is zero or very close to it, the standard deviation alone describes the spread better.

Avoid it for data without a true zero, such as temperatures in Celsius or Fahrenheit, where adding a constant changes the mean but not the spread. It also behaves badly when the mean is near zero or the data can be negative. It suits ratio-scale data like weights, times, concentrations and prices.

The standard deviation is in the data's units, so 2.12 for the eight values. The CV divides by the mean and has no units, so it is 15.43%. A data set with a mean of 500 and SD of 5 has a smaller CV, 1%, than one with a mean of 10 and SD of 5, 50%.

Compute the CV of each and compare the percentages. The one with the smaller CV is more consistent relative to its own average, even if the units or sizes differ. The eight values have a CV of 15.4% and the ten test scores 8.6%, so the scores are relatively tighter.

Yes. The solution view lists the data, the mean, each deviation and its square, the sum of squares, the variance and standard deviation with the divisor you chose, and finally the CV and CV%. In mean and SD mode it shows the division and the conversion to percent. A button hides the steps if you only want the answer.

For normally distributed data, Wikipedia gives an approximately unbiased estimator that multiplies the sample CV by (1 + 1/(4n)). With n = 8 the factor is 1.0312, so 15.43% becomes 15.91%. This calculator reports the plain sample CV and does not apply that factor.

A sample standard deviation needs at least two values, a population one needs at least one, and the mean must not be zero. For a trustworthy CV you want many more. With only a handful of values the standard deviation is itself uncertain, so the CV can swing a lot with one new reading.