Coefficient of Variation Calculator
The coefficient of variation (CV) is the standard deviation divided by the mean, usually written as a percentage. Because it carries no unit, it lets you compare series measured on different scales or in different units: a standard deviation in kilograms cannot be set against one in centimeters, but their coefficients of variation can.
This calculator evaluates one or two data sets together. For each series it reports the mean, the standard deviation, the coefficient of variation, an approximate standard error for that coefficient, and a homogeneity reading; when a second series is entered, it states plainly which one is more homogeneous and reports the CV ratio and the difference in points. A comparison table, a bar chart, and a box plot back the results up.
Coefficient of Variation Formulas
For a sample: CV = s / |x̄| s = √[ Σ(xᵢ − x̄)² / (n − 1) ] For a population: CV = σ / |μ| σ = √[ Σ(xᵢ − μ)² / n ] As a percentage: CV(%) = (s / |x̄|) · 100 Standard error: SE(CV) ≈ CV / √(2n) Comparison: CV₁ < CV₂ ⇒ series 1 is relatively more homogeneous Inverse measure: signal-to-noise ratio = x̄ / s = 1 / CV
The coefficient of variation is also known as the relative standard deviation (RSD). In Excel, =STDEV.S(range)/AVERAGE(range) gives the same value, as does the Std. Deviation / Mean ratio from the SPSS Descriptives output.
How to Calculate
- Paste your first data set into the box and, if you like, give the series a name.
- If you want a comparison, enter the second data set as well; the two do not have to share a unit.
- Choose whether the data is a sample or a population — this sets the denominator of the standard deviation and therefore the CV.
- Read the coefficient of variation as a percentage: it says what percentage of the mean the standard deviation amounts to.
- If you entered two series, look at the 'more homogeneous series' card and the CV ratio; a lower CV means a more consistent measurement.
- Make sure the mean is not close to zero and that the data is on a ratio scale; otherwise the CV is misleading.
Worked Examples
Comparing the variability of height and weight
The height series has a mean of 172.10 cm and a standard deviation of 4.48 cm, giving CV = 2.61%; the weight series has a mean of 70.80 kg and a standard deviation of 11.10 kg, giving CV = 15.68%. The standard deviations are in different units and cannot be compared directly, but the coefficients of variation show that weight is roughly 6.02 times as variable as height.
Boy (cm) — Coefficient of variation (CV): 2.61% · Boy (cm) — Homogeneity: Very homogeneous · Boy (cm) — Number of values (n): 10
Homogeneity of a single series
Eight fill-weight measurements have a mean of 50 g and a sample standard deviation of 2 g, so CV = 4.00%. Being below 10%, this value shows that the production line runs very homogeneously. The approximate standard error of the CV is 1.00%, which puts the rough 95% confidence interval at 2.04% – 5.96% — so the true value is expected to stay below the 10% mark as well.
Coefficient of variation (CV): 4.00% · Homogeneity: Very homogeneous · Number of values (n): 8
Stability of two production lines
Line A has a mean of 120.75 and a standard deviation of 2.82, giving CV = 2.33%; line B has a mean of 312.88 and a standard deviation of 24.47, giving CV = 7.82%. Line B's standard deviation is numerically far larger (24.47 against 2.82), but its production level is higher too; even so, its relative variability is 3.35 times that of line A, so line A is the more stable of the two.
A hattı — Coefficient of variation (CV): 2.33% · A hattı — Homogeneity: Very homogeneous · A hattı — Number of values (n): 8