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I'm doing an assignment on which I'm analyzing a data sample of roughly 1400 soccer players from Europe and I'm not sure how to interpret the coefficient of variation, to be honest.

For instance, when it comes to the variable "Age" the coefficient is 14.84%, on the variable "Weight" it's 8.24% and it's 3.39% for the "Height" variable.

When it comes to standard deviation I've read that values above 3 are considered to signify a large amount of spread in the data sample and I was wondering if there were similar cutoff values for the coefficient of variation as well?

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  • $\begingroup$ The coefficient of variation divided by the mean. It can be estimated from a sample by dividing the sample estimate of standard deviation by the sample mean. It is therefore a proportion that can be converted to a percentage by multiplying by 100. $\endgroup$ – Michael R. Chernick Mar 25 '18 at 2:59
  • $\begingroup$ @MichaelChernick naturally meant that the coefficient of variation is the SD divided by the mean. $\endgroup$ – Nick Cox Mar 25 '18 at 9:46
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    $\begingroup$ It's important to be consistent about 3 or 3%. True story: I once reported a coefficient of variation of about 2 in a paper and a reviewer complained that 2 was implausibly low for the kind of data being discussed. I had to underline that I had written and meant 2 (= 200%), not 2%. $\endgroup$ – Nick Cox Mar 25 '18 at 9:58
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There seems to be an idea lurking in some corners that the coefficient of variation in wrapping together SD and mean is somehow superior to either. That is more than can be reasonably expected.

The CV has some merit when one expects, or is checking for, roughly the same relative variability in different datasets. Thus mouse weights and elephant weights might be worth comparing, or the heights of raspberry bushes and redwood trees.

Here I would want to see both means and SDs because I really don't expect age, height and weight to have the same relative variability, even as a first approximation Thus using some plausible values I just made up (use your own if you prefer) I expect a mean age loosely like 25 years, a mean weight loosely like 60 kg, a mean height loosely like 180 cm and (even without knowing much about any sport) I expect relative variability to go in the sequence you mentioned. Thus ages might go from about 16 to over 30 in many set-ups, so relative variability of age is plausibly highest here.

My own rule of thumb is that coefficients of variation being useful goes hand in hand with logarithmic scales being natural for analysis, which seems unlikely here. For much more discussion see How to interpret the coefficient of variation?

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