> some on various lists have claimed that the coefficient of variation ...
> which is usually expressed as a % of the following ratio: SD / mean ... is
> a useful tool
I can think of one use - in numerical analysis, it is useful in
analyzing the behavior of the misleadingly so-called "computational"
algorithms (like the one that simple-minded calculators use for the
standard deviation)
Of course, if you think that these formulae should never be used for
computation (without prejudice to their enormous utility in theoretical
matters) this isn't important except as an exercise.
In the case of the SAT scores, one *might* argue that a larger COV
means more bang for the (writing/grading) buck in terms of ability to
discriminate between high and low scores.
>let's say we have SAT scores where the mean is about 500 and the SD about
>100 ... here ... the COV is 100/500 = 20%
IF this were true, I can conclude: the vast majority of scores will be
above 300, with the result that a large proportion of the students'
test-writing time is spent on questions that pretty nearly everybody
gets and which thus have little predictive power. This might justify a
major revision of the testing protocol (or at least the admission that
the goal of making sure that nobody feels squashed is more important!)
It is a
>compared to another case where the data are temperatures ... where the SD =
>5 (and it's not even this in honolulu!) and the mean is 80 ... so the COV =
>5/80 = 6%
Now, that's naughty. "Obviously" the COV is meaningless on non-ratio
data. (If you _accept_ that it has a use, you can make fair use of this
cautionary tale in warning beginners.)
Even here, one *might* argue that the COV explains the reason that
Kelvin has never caught on in popular meteorology. We prefer measurement
scales in which the COV of commonly measured things is large, so we
aren't prefacing every temperature by "two-hunner'n-" except in
midsummer. It may also explain (and I'm really guessing here!) why
barometric pressure (COV < 5%) never really catches the public's
attention?
-Robert
.
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