Calcylator
Coefficient of Variation

Coefficient of variation:
standard deviation ÷ mean

Compare the spread of datasets measured in different units or on different scales, and learn the cases where this ratio misleads.

Calcylator Editorial Team

Updated · 6 min read

What is the coefficient of variation?

The coefficient of variation (CV) is the standard deviation divided by the mean, multiplied by 100 to give a percentage. A CV of 26.35% means the typical spread around the average is about a quarter of the average itself.

Plain standard deviation is stated in the units of the data, so a spread of 8 minutes and a spread of 474 rupees cannot be compared. Dividing by the mean removes the unit, which is why the CV is also called the relative standard deviation.

The calculator on this site uses the sample standard deviation (dividing by n minus 1), so the result matches what most spreadsheets give for the sample version.

Coefficient of variation formula

Coefficient of variation =CV = (s ÷ mean) × 100
s:
sample standard deviation of the values
mean:
arithmetic mean of the values
CV:
spread relative to the average, in percent
The calculator takes a list of values and returns stdevS(values) / mean(values) × 100.

  • Delivery times (minutes)

    20, 25, 30, 35, 40

  • Mean

    30

  • Sample standard deviation

    7.9057

Coefficient of variation

26.35%

7.9057 ÷ 30 × 100 = 26.35%.

  1. Enter the values as a list, at least two numbers for a sample standard deviation.
  2. The calculator finds the mean and the sample standard deviation.
  3. It divides the second by the first and multiplies by 100.
  4. Read the percentage: bigger means more relative spread.

Comparing spread across different units

The real strength of the CV is a fair comparison. Take a courier whose delivery times are 20, 25, 30, 35 and 40 minutes, and a shop whose order values are 1,200, 1,500, 1,800, 2,100 and 2,400 rupees. The standard deviations are 7.91 minutes and 474.34 rupees, which cannot be compared.

Same data shape, different units
DatasetMeanSample SDCV
Delivery times (min)307.905726.35%
Order values (rupees)1,800474.341626.35%
Steady machine part (mm)501.58113.16%

Both the delivery times and the order values have a CV of 26.35%, so they are equally variable in relative terms. The machine part readings of 50, 52, 48, 51 and 49 millimetres are far more consistent at 3.16%.

Where the coefficient of variation is used

  • Laboratories use it to report how repeatable an assay is across replicate samples.
  • Investors compare the volatility of two assets with different average prices.
  • Quality teams check whether a packing line fills bags consistently at different target weights.
  • Schools compare score spread between tests marked out of 20 and out of 100.

In each case the question is the same: relative to its own size, how much does this measurement wobble?

Common mistakes with the coefficient of variation

  • Using it when the mean is close to zero. Dividing by a tiny mean makes the CV explode, so it is not meaningful for data that can be negative, like temperatures in Celsius.
  • Using it on interval data. The ratio only makes sense when zero truly means none, as with minutes, rupees or millimetres.
  • Mixing up sample and population standard deviation. The two give slightly different CVs for small datasets.
  • Treating a high CV as bad. A high CV just means high relative spread, which may be natural for the thing measured.

Common questions

What is the coefficient of variation used for?

It compares the relative spread of datasets that have different units or very different averages. Because it divides the standard deviation by the mean, the result is a unit-free percentage, so a CV of 5% and one of 20% can be compared directly.

How do you calculate the coefficient of variation?

Divide the standard deviation by the mean and multiply by 100. For the values 20, 25, 30, 35 and 40, the sample standard deviation is 7.9057 and the mean is 30, so the CV is 26.35%.

What is a good coefficient of variation?

There is no universal good value; it depends on the field. A lower CV means more consistent data. A machine fitting readings might target a few percent, while delivery times or sales can naturally sit above 20%.

Can the coefficient of variation be negative or above 100%?

It can exceed 100% when the standard deviation is larger than the mean, which happens in skewed data. It is not meaningful when the mean is zero or near zero, and negative means make the percentage hard to interpret.

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