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Facts and limits of this method
| Formula | CV = standard deviation ÷ |mean| × 100% |
|---|---|
| Standard deviation | Sample, divisor n−1 |
| Units | None — that is the entire point |
| Below 10% | Low variability; the mean describes the data well |
| 10–33% | Moderate variability |
| Above 33% | High variability; a single average is misleading on its own |
When it misleads you
- The coefficient breaks down when the mean approaches zero. The denominator shrinks towards nothing and the ratio explodes, producing enormous percentages that describe arithmetic rather than data.
- It is meaningless on data that can be negative, and on interval scales where zero is arbitrary. Temperatures in Celsius are the standard counterexample: the same physical spread gives completely different coefficients in Celsius and Fahrenheit because zero sits in a different place.
- The 10% and 33% thresholds are conventions borrowed from manufacturing quality control. They travel poorly: 40% variability is alarming in machining and unremarkable in daily sales.
- Because it inherits the standard deviation, it inherits its sensitivity to outliers. One extreme value inflates the numerator and can double the coefficient.
How it is calculated
The sample standard deviation is divided by the absolute value of the mean and multiplied by 100. Taking the absolute value of the mean keeps the coefficient positive when the average happens to be negative, though on such data the measure should be treated with suspicion anyway.
Removing the units is the entire purpose. A standard deviation of 0.15 kg and one of 3.2 minutes cannot be compared; coefficients of 3.4% and 14% can, and they say that the second process is roughly four times more variable relative to its own scale.
The verdict band is reported alongside the number because the raw percentage means little to most readers. The thresholds come from manufacturing quality control, where a coefficient under 10% is the usual target for a stable process.
The mean and the standard deviation are shown next to the coefficient so the ratio can be checked at a glance. A coefficient that looks surprising is almost always explained by a mean much closer to zero than expected.
Questions and answers
When is the coefficient of variation the right measure?
When you need to compare the variability of quantities measured in different units or at very different scales — machine A against machine B, one product line against another, this month against last.
Why is my coefficient enormous?
Almost certainly because your mean is close to zero. The coefficient divides by the mean, so a small denominator produces a huge ratio that says more about the arithmetic than about the data.
Can I use it on temperatures?
Not in Celsius or Fahrenheit. Both are interval scales where zero is an arbitrary point, so the ratio changes when you change units. It works on Kelvin, and on any scale with a true zero.
Is a CV of 25% good or bad?
It depends entirely on the field. For a machining process it would be a serious problem; for daily retail sales it is unremarkable. Compare against your own historical values rather than against a universal threshold.
Is my data uploaded?
No. The calculation runs in your browser.