[Aavso-photometry] average vs. median

[arne]

Tomas L. Gomez wrote:
> If I have N measurements, each one with error sigma,
> and I take the average, then the error will be reduced
> to sigma/sqrt(N).
> 
> If, instead of taking the average, I take the median,
> how is the error reduced?.
> 
> Knowing this could be very useful to decide whether
> to use the median of the average when stacking images,
> for instance.
> 
> Thank you in advance for any help anyone can give.
> 
Hi Tomas!
The usual rule of thumb is that the median gives 25% less signal/noise
than a straight average/sum. However, the benefit of a median is
for pixel rejection, to get rid of cosmic rays, satellite trails,
etc.  There are many more complex rejection schemes, but starting
with a median is a good choice if rejection is desired.

Remember, too, that all rejection schemes work best when you have
a reasonable number of images.  Trying median with 3 images will
often give poor results.  Most software packages, for photometry,
do a good job of removing discrepant pixels in the sky annulus,
so your only concern is if a bad pixel is contained in the measurement
aperture.  Statistically, you can have a lot of bad pixels before one
falls inside a small aperture.  I typically average frames if I'm
trying to go really deep, and median if I have signal/noise to give
away (such as a stack of flats) or if I'm trying to make a pretty
picture of an extended object.
Arne