Talk:Coefficient of variation

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Mathematics rating:	Start Class	Mid Priority	Field: Probability and statistics
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Quality not rated to avoid WP:COI as i've just been editing article a fair bit (relative to its size) so i'll leave that for someone else who knows the field but is more impartial. Qwfp (talk) 16:04, 22 February 2008 (UTC)

[edit] comment by pboyd

The Wikipedia article on "Coefficient of Variation" appears to imply that it may be used to determine the relative magnitude of the variation of a single set of data. I'm not sure that I see that.

It seems that the coefficient of variation would not be very useful in assessing the magnitude of variation in 2 situations:
1) for any variable measured on an interval scale (arbitrary zero point) and
2) ratio scales where the range of observations are all significantly greater than zero (for example, scores on an examination where the average grade was, say, 85).

Am I missing something? Or, is there an alternative measure that does allow for the assessment of the magnitude of dispersion for a single data set?

PBoyd 14:57, 14 September 2006 (UTC)

If the article implies that the CV can, based on a single set of data, determine "relative magnitude", then yes, that's incorrect. Relative comparisons should only be used on multiple sets of data. Where in the article is this implied?

Also, the CV can be useful in ratio scales when comparing two sets of data. Suppose two instructors give exams with equal means, but CV1 = 5 while CV2 = 0.5. Then we can prove the variance of the 2nd instructor's exams is less than the first instructor's. The same reasoning can be applied to interval scales. TrueBlueMichigan 05:14, 1 January 2007 (UTC)

I think PBoyd's first point was entirely correct and important so i've added it to the article with a reference to back it up. (Sorry but i don't quite follow point (2)). Qwfp (talk) 15:58, 22 February 2008 (UTC)

OK. Point 2 was intended to address a situation where, say one instructor's exam had a mean of 75 and a variance of 10 and the second instructors exam had a mean 85 a variance of 10. Both could have identical ranges, IQRs, MADs. That is, except for their positions on the 100 point grading scale, the two distributions are identical. Yet, the first would have a CV of (10/75 =) 0.133 and the second would have a CV of (10/85 =) 0.118.

I would think that measures of the magnitude of dispersion need to be independent of the mean, rather than dependent upon it. —Preceding unsigned comment added by 76.119.112.183 (talk) 12:59, 17 April 2008 (UTC)