Re: [Phys-l] projectile motion lab

["Krishna Chowdary" <professor.head@gmail.com>]

On 10/9/06, Folkerts, Timothy J <FolkertsT@bartonccc.edu> wrote:
> >I'm interested.  What is the mean time and the standard deviation
> >using this data set?  Also, I suspect that you should use the
> >standard deviation of the mean as your uncertainty.
>
> I don't think the standard deviation of the mean (aka "standard error")
> is what is needed here.  The st. dev. of the mean tells you how well you
> know the mean value, but that isn't what is important.  You want the
> effect of the variation of the individual trials, which is related to
> the plain old standard deviation.



Now that you point this out, I'm not sure what to do.

Let's consider Justin's original experiment, where he has 50 measurments of
the time it takes for the marble to roll between two photogates.  (Other
posters have pointed out the need to be careful with photogate measurements,
but I don't have much to say about that.)  From those 50 measurements of
time T, we can calculate the meant <T> in the standard way.  We can
calculate the standard deviation s in the standard way.  From this, I can
further calculate the standard deviation of the mean as s/Sqrt(N) where N is
the number of measurements.

If I were going to report the "time it takes for the marble to roll between
the two photogates", I would report <T> +/- s/Sqrt(N).  I hope that is
correct.

In propogating uncertainty through the calculation, should I use s as Tim
suggests, or should I use s/Sqrt(N) as I originally thought?  Another way to
think of this:  If I were going to do a Monte Carlo error analysis assuming
a Gaussian distribution, would the spread in my Gaussian be the standard
deviation or the standard deviation of the mean?


The standard deviation is related to
> how close the center of the trials would be to the "true" value.

Here I think it should say "standard deviation _of the mean_ is related to
how close the center (which I understand as the mean) of the trials would be
to the "true" value." ?  (seems like just a typo)

--
regards
-Krishna

Krishna Chowdary
Department of Physics & Astronomy
Bucknell University