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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
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> 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
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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.

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