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

[Scott Goelzer <s.goelzer@COMCAST.NET>]

Funny you should use this example,
I just wrote up and am testing a lab where the students are to try to
make a stopwatch (digital) stop on 1.00 s (at least 25 trys). This
gives some nice data for taking basic stats and makes evaluating
those stats a bit more tactile for the students. Stopping on 1.00s is
surprisingly frustrating, which makes for some good discussion about
how much a given measurement on a watch can be trusted.

The example below makes me rethink my understanding of the standard
deviation formula. I thought the point of the squares in the formula
was to eliminate signs and produce an absolute value for the
differences between the average and a given value. Now, I am not so
sure.

  Any deeper insight out there?

Scott



**********************************
Scott Goelzer
Physics Teacher
Coe-Brown Northwood Academy
Northwood NH 03261
603-942-5531e218
sgoelzer@coebrownacademy.com
**********************************


On Sep 9, 2005, at 8:56 AM, Rick Tarara wrote:

> ----- 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
>
> *********************************************************
> Richard W. Tarara
> Professor of Physics
> Saint Mary's College
> Notre Dame, Indiana
> rtarara@saintmarys.edu
> ********************************************************
> Free Physics Educational Software (Win & Mac)
>      Animations for Lectures
>      Photo-realistic Lab simulations
>      Energy management simulations
> www.saintmarys.edu/~rtarara/software.html
> Energy 2100--class project
> www.saintmarys.edu/~rtarara/ENERGY_PROJECT/ENERGY2100.htm
> ********************************************************
_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu
https://www.physics.buffalo.edu/mailman/listinfo/phys-l