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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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Richard W. Tarara