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[Phys-L] Re: Average earlier or average later?



I was looking over an article recently where this issue came up. Or at
least it should have come up but didn't.

The article was measuring a property of some nanoparticles. There was a
considerable variation in the radii of the particles, and the authors
wanted to know the average size of the particles so that they could
determine the value per cubic meter. Well, they got a histogram of the
radii, found the average, and calculated 4/3 pi r^3. If you take that
average times the number of particle, you do NOT get the total volume.
What they really needed (IMHO) was to get a histogram of the volumes and
find the average of the volumes directly.

I second the idea that you should look to the physical meaning and
tailor the analysis to your desired goals.

Tim

-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu] On
Behalf Of ludwik kowalski
Sent: Friday, September 09, 2005 12:27 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: Average earlier or average later?

But, as illustrated by Pamela, in some situations averaging at the
level of the quantity we are "interested in as final result" might
lead to wrong conclusions. Averaging at the level of what was simulated
("measured"), on the other hand, produced an excellent "prediction." I
see no advantage in averaging at the level of final results. Yes, this
is no longer tedious; but it can lead to wrong conclusions. Traditional
way of averaging seems to be better.
Ludwik
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