Re: the concept of average

[Dennis Roberts]

Seems to me, when we describe a feature of a group or set, we have to 
control for something(s). For example, we might administer a 30 item test 
to a class and then say ... on this test my class got 400 ... (which 
happens to be the sum of X) ... but surely, this is not very informative in 
and of itself. Another instructor might boast ... well MY class (on the 
same test) had 700! (Of course, this second instructor might have had about 
twice as many students ... actually, they might have done more poorly but, 
sum of X won't show that )

In this case, to make the comparison sort of fair ... we DIVIDE by the 
irritant, or n. Hence, the average.

We do this in any number of contexts ... for variability with the variance 
... for relationship in the correlation coefficient.

But, we do tend to OVER interpret such averages ... for example, in the 
class examples above, could be that about 1/2 of the students got 10 and 
the other half 30 ... and while the "average" is about 20 ... NO one was 
even close to that. So, to think that "average" means "typical" can be 
grossly off. So, while the average DOES reflect SOME feature of the group 
or set, it might not be THE feature we interpret it to be.



Dennis Roberts
[EMAIL PROTECTED]
http://www.personal.psu.edu/users/d/m/dmr/droberts.htm 

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