Descriptive Statistics
Coefficient of Variation Calculator
The coefficient of variation divides the sample standard deviation by the mean, and a second list can be compared when you paste one.
Worksheet
Press Calculate to see the result.
The coefficient of variation divides the sample standard deviation by the mean, and a second list can be compared when you paste one.
What this calculator answers
Scores 72, 80, 85, 90, and 93 have a sample standard deviation of about 8.3 points and a mean of 84. Dividing those two numbers produces 0.0992, or 9.9246 percent of the mean. That ratio is the coefficient of variation. It lets a spread in points be compared with a spread in another unit, as long as each mean is a meaningful baseline and neither mean is zero. An optional second list is scored on its own and shown beside the first. The lists are not pooled into one standard deviation.
The headline is the first list's sample standard deviation divided by its mean. If the second box has numbers, that list gets its own coefficient. A mean of zero is an error. Supporting counts and intermediate terms sit under the headline so a reader can see what was divided by what. When a checkbox or a tail setting changes the divisor or the rejection region, that choice appears in the steps rather than vanishing into a silent default.
The formula, written out
Coefficient of variation uses this relationship.
CV = (sample standard deviation) / mean. Percent form = 100 * CV.
- s. Sample standard deviation, divisor n minus 1.
- mean. Arithmetic mean of the same list. It must not be zero.
- CV. s divided by the mean, the headline.
- percent. 100 times CV, the same ratio written as a percent of the mean.
Dividing the standard deviation by the mean cancels the unit when the mean and the spread share one. The sample divisor is used so the coefficient matches the sample standard deviation page. A second list repeats the same ratio. It is not a pooled estimate. The algebra is the named textbook identity for this worksheet. Intermediate products and quotients appear in order so a calculator and a pencil can agree to the displayed rounding. If a neighbouring page uses a different divisor or a continuity correction, that page says so on its own ticket.
A full worked example
Example loaded in the worksheet
The form is prefilled with a small example so every arithmetic step can be checked by hand. Change one field after you finish the walkthrough and confirm the ticket moves the way the formula predicts.
The first list is 72, 80, 85, 90, 93. The count is 5 and the mean is 84. The sample standard deviation, dividing by 4, is 8.3367.
The coefficient of variation is 8.3367 / 84 = 0.0992. As a percent of the mean, that is 9.9246 percent. The headline is the ratio 0.0992.
The second box is empty, so only one coefficient is reported. A mean of zero would have made the ratio undefined. This mean is 84.
| Coefficient of variation | 0.0992 |
|---|---|
| As a percent of the mean | 9.9246% |
| Sample standard deviation | 8.3367 |
| Mean | 84 |
A second situation
Temperatures 18 through 22 are compared with the original scores
The first list is 18, 19, 20, 21, 22. The count is 5 and the mean is 20. The sample standard deviation, dividing by 4, is 1.5811.
The coefficient of variation is 1.5811 / 20 = 0.0791. As a percent of the mean, that is 7.9057 percent. The headline is the ratio 0.0791.
The second list is 72, 80, 85, 90, 93, with mean 84 and sample standard deviation 8.3367. Its coefficient of variation is 0.0992. The two lists were not pooled.
| Coefficient of variation | 0.0791 |
|---|---|
| As a percent of the mean | 7.9057% |
| Sample standard deviation | 1.5811 |
| Mean | 20 |
| Second coefficient of variation | 0.0992 |
| Second list as a percent | 9.9246% |
The temperature list 18, 19, 20, 21, 22 has a coefficient of 0.0791. The score list 72, 80, 85, 90, 93 has a coefficient of 0.0992. The temperatures are tighter relative to their own mean, even though the comparison is across units. The second example changes the feature that this formula is sensitive to, and the ticket shows the new figure beside the same definition. That contrast is the fastest way to see which input owns the movement.
What moves when the input moves
The last score changed from 93 to 40, which moves both the mean and the standard deviation. The headline result went from 0.0992 to 0.27.
The nudged inputs
The first list is 72, 80, 85, 90, 40. The count is 5 and the mean is 73.4. The sample standard deviation, dividing by 4, is 19.8192.
The coefficient of variation is 19.8192 / 73.4 = 0.27. As a percent of the mean, that is 27.0016 percent. The headline is the ratio 0.27.
The second box is empty, so only one coefficient is reported. A mean of zero would have made the ratio undefined. This mean is 73.4.
| Coefficient of variation | 0.27 |
|---|---|
| As a percent of the mean | 27.0016% |
| Sample standard deviation | 19.8192 |
| Mean | 73.4 |
How to read the result
A coefficient of 0.0992 means the sample standard deviation is about one tenth of the mean. The percent form, 9.9246 percent, is the same fact. It is not a score of 9.9246 points. Say the unit, the sample size or contract terms, and the formula name in the same sentence as the figure. A number without those three pieces invites a later reader to invent a definition that this page never used.
Write the result with its unit, the inputs that produced it, and the name of the formula. Write the result with its unit, the inputs that produced it, and the name of the formula. If the ticket shows a decision sentence, quote the alpha and the tail with it. If the ticket shows a money or dose figure, quote the rate and the schedule that produced it.
Assumptions that have to stay true
- The mean is not zero.
- Sample standard deviation, with divisor n minus 1, is the numerator you want.
- The mean is a sensible baseline, not an interval scale parked far from zero by an arbitrary origin.
- A second list, if present, is a separate batch.
If an assumption above is false, do not average the discomfort away. Change the worksheet or change the question. A correct arithmetic step on the wrong model is still the wrong answer for the decision you are trying to make.
Mistakes that change the answer
- Dividing a population standard deviation by the mean and calling it this sample coefficient.
- Comparing coefficients when one mean is an arbitrary zero point, such as Celsius temperatures near freezing.
- Pooling the two lists before dividing.
- Reading the percent form as if it were still in the original unit.
Where a different calculator is the honest choice
Use the standard deviation calculator when the unit should stay in the answer. Use the mean calculator when only the baseline is needed. Use the variance calculator when you need the square before any ratio. Related links under the essay open pages that keep their own formulas instead of hiding a mode switch inside this ticket.
When the job changes, move to a page built for that job: Standard Deviation Calculator, Mean Calculator, Variance Calculator.
Check yourself
Scores are 72, 80, 85, 90, and 93, and no second list is pasted. What is the coefficient of variation?
The coefficient of variation is 0.0992, or 9.9246 percent.
Using the result in a sentence
Lab assays with different units, pay spreads in two currencies, and machine tolerances relative to a target level are coefficient-of-variation comparisons. Keep the count, the unit, and the assumption list beside any copy of the number that leaves this browser tab.
A mean close to zero makes the ratio huge even when the standard deviation is modest. The coefficient is also a poor comparison for scales that do not have a true zero. Pair the headline with the steps before you staff a route, set a grade boundary, or compare two contracts from a single number.
Questions people ask next
01What definition does the Coefficient of Variation Calculator commit to?
This page uses Coefficient of variation: CV = (sample standard deviation) / mean. Percent form = 100 * CV.. Dividing the standard deviation by the mean cancels the unit when the mean and the spread share one. The sample divisor is used so the coefficient matches the sample standard deviation page. A second list repeats the same ratio. It is not a pooled estimate. If a textbook uses a different divisor, a different continuity correction, or a different rounding rule, the last digits can move, so the definition is printed above the result. The worksheet asks for Numbers, Second list, optional, and it refuses a blank that the formula cannot interpret. Keep that printed definition in the sentence you write next to the figure so a later reader can rebuild the arithmetic without guessing which convention you chose.
02How should the worked example be read out loud?
In the loaded example the coefficient of variation is 0.0992. A coefficient of 0.0992 means the sample standard deviation is about one tenth of the mean. The percent form, 9.9246 percent, is the same fact. It is not a score of 9.9246 points. Say the unit and the count before you say whether the number is large or small. Read the steps in order rather than jumping to the headline, because the intermediate terms are where a swapped percent and proportion usually hide. If the ticket shows both a primary figure and a comparison figure, name which one you are quoting.
03What is the fastest way to get a misleading result?
Dividing a population standard deviation by the mean and calling it this sample coefficient. A mean close to zero makes the ratio huge even when the standard deviation is modest. The coefficient is also a poor comparison for scales that do not have a true zero. A second common failure is leaving a checkbox or tail setting in the wrong state and then treating the number as if the default had matched your plan. Reset the example, change one input, and confirm the ticket moves in the direction the formula predicts before you trust a live run.
04When should I leave this page for a different calculator?
Use the standard deviation calculator when the unit should stay in the answer. Use the mean calculator when only the baseline is needed. Use the variance calculator when you need the square before any ratio. The related links under the essay go to those worksheets, which keep their own formulas instead of hiding them in a mode switch. If the question changed from a summary to a test, from a payment to a refinance, or from a raw score to a percentile, switch pages rather than forcing this ticket to answer a job it was not built for.
05What belongs in the sentence next to the number?
The coefficient of variation is 0.0992, or 9.9246 percent. Name the formula, the sample size or the inputs, and the unit before you compare the figure with someone else's. A bare number without those three pieces cannot be audited when a score, a rate, or a lab value is challenged later. Store the inputs beside the result whenever the figure will travel into a report.