Re: [Phys-l] Curve fitting versus averaging [was question on averaging]

[Brian Whatcott <betwys1@sbcglobal.net>]

Edmiston, Mike wrote:
> ...
> Anyway, suppose you can find "n" plunger positions that give resonance.
>
> The typical student just wants to find the differences between these
> positions and average the differences to find the average
> half-wavelength.  However, doing this actually only utilizes the first
> and last position because all the intermediate positions drop out during
> the averaging process.  This means you are wasting your time to find all
> those intermediate resonance points.....
> Am I looking at this correctly?
>
>
> Michael D. Edmiston, Ph.D.
I attempted to justify this assertion that measuring adjacent nodal 
displacements to get step size
estimates then averaging them is to throw away all but the beginning and 
ending displacement data.

I could not, at least not by using a simple model which added a random 
variable of uniform
(not gaussian)  frequency, variable  between plus and minus one unit to 
a step displacement staircase
of five units of distance.
If I took the difference between adjacent displacement pairs:  in the 
case of a ten step array
that would be nine differences, or in the case of a hundred step array, 
that would be ninety nine
differences and averaged those to approximate the step size (5) that 
average was always closer
to the mean than doing what appears to be suggested here: Subtract the 
end step observation
from the beginnig step value and divide by the appropriate number of steps.


But perhaps I misunderstand the assertion?

Brian W