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

----- Original Message -----
From: "Brian Whatcott" <betwys1@SBCGLOBAL.NET>


I think this is misleading direction.
One can demonstrate that for ANY amount of data
disposed equally about one value, a calculation can show a difference
between two processing methods for a result depending on multiplying
one well defined variable against another scattered variable.
The case in point involves multiplying the well defined length
by the inverse of (scattered) time.

Maybe the following simple example would be worth discussing--

Say you measure a series of times but your calculation will use the square
of the time.

T(s) T-squared
5 25
4.75 22.5265
4.75 22.5265
4.75 22.5265
4.75 22.5265
6 36
average
5 25.208
stdev
.5 5.38
% dev
10 21.3

Is there a clear cut choice here for choosing the square of the average or
the average of the squares? My gut is the square of the average, but being
without formal training in stats, I'm not sure. If I recall what little
stats I've had correctly, squaring the value of 5+/-10% yields 25+/-20%.

Rick

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