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I have two data sets, one data set contains value in the range of 10,000- 1,000,000 and other data set contains the value between 1,000-10,000. I want to compare the variability means,which data has more variability.

Do I need to first standardized / normalized the data and then compare the variance, but standardization will give me mean 0 and variance 1.

Also, which is better Coefficient of variation or Interquartile Range

Thanks in advance

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    $\begingroup$ First you need to tell us what you mean by "variability". Any answer to your questions could be correct. $\endgroup$ – Peter Flom - Reinstate Monica Jan 13 '14 at 21:04
  • $\begingroup$ Thanks for your reply..By variability means volatility or scatteredness. $\endgroup$ – Arushi Jan 14 '14 at 9:13
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    $\begingroup$ You need to be more precise; in fact, you really need to almost answer your own question. Which measure of variability do you want? Which suits your purposes? $\endgroup$ – Peter Flom - Reinstate Monica Jan 14 '14 at 11:11
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    $\begingroup$ @Arushi If you standardize (variance = 1), then both samples would have the same variance. $\endgroup$ – AdamO Apr 25 '14 at 20:02
  • $\begingroup$ Since the data are drawn from ranges of such different sizes one might naturally expect the one from the wider range to have higher IQR or SD though this might not be the case. The coefficient of variation is perhaps sensible, as it measures variation relative to location, though it depends what you're trying to achieve. On seeing how the ranges differed by an order of magnitude my first thought was whether log transformation might make comparison easier. $\endgroup$ – Silverfish Nov 6 '14 at 11:15
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could you take the determinant of their covariance matrices? That would be the total variance of the dataset for each, I think there's an F test for such a comparison. I saw the test here: http://onlinelibrary.wiley.com/doi/10.1002/1096-8644(200009)113:1%3C79::AID-AJPA7%3E3.0.CO;2-3/abstract

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  • $\begingroup$ I don't think these are multivariate samples. $\endgroup$ – AdamO Apr 25 '14 at 20:03

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