Weighted Variance

I had to review some basic statistics, so I figured I'd post a quick summary.  I tend to forget how to treat error when averaging, so this is a good reminder.

If we have a series of measurements  with variances , we might like to average them.  But, how should we weight them?

The standard way to weight such points is by inverse variance, which is the part I tend to forget:


We recall that a weighted average is:



The weighted variance of these points is much as you'd expect, but with a correction for the effective number of points.  That's the tricky part.



where the effective number of points is



Source: Lyons' Statistics for Nuclear and Particle Physicists