[Q]Question about Coeff of Variation

Question

If we’ve assumed a normal distribution (as often is the case) wouldn’t a major limitation of the Coeff of Variation (SD/Xbar) be that it only accounts for the data within 1 SD of the mean??

So for a normally distributed data set, that’s ~30% of the data not being represented in that calculation

Answer 1

> If we’ve assumed a normal distribution (as often is the case)

In general the sort of data you'd use it with will be necessarily positive and right skew.

> wouldn’t a major limitation of the Coeff of Variation (SD/Xbar) be that it only accounts for the data within 1 SD of the mean??

No. It doesn't "only account for the data within 1 SD of the mean". It's not even clear how you would come to that conclusion.

> So for a normally distributed data set, that’s ~30% of the data not being represented in that calculation

No

Answer 2

SD accounts for all data, not just the middle 30%, so the same is true for CV.

The problem with CV is that if the mean is close to zero, CV will approach infinity.