Math CentralQuandaries & Queries


Question from JR, a student:

I have read your responses regarding the coefficient of variation (CV) and find them very useful. I still have a question about interpreting the CV. Let's that the CV of sample #1 is 3% and that of sample #2 is 12%. Can I report that Sample #2 is 4 times more variable than sample #1? Thanks in advance!


That would be ambiguous, because it is not always clear whether the coefficient of variation or the actual standard deviation is the appropriate figure to compare. Neither one is accurately represented by informal phrases such as "four times more variable"

For instance, a voltmeter that is accurate to ±1 volt in 10V is comparable to one accurate to ±10V in 100V. However, if a GPS or barometric altimeter measures altitude accurate to ±5m at 10 meters above sea level, it will also be accurate to about ±5m at 1000 meters.
This depends partly on whether there is a natural zero, and partly on how the measurement is made.

For this reason, it is better to be explicit about whether you are comparing standard deviations or coefficients of variation. (If you are unsure which is relevant report both.)



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