Wilburforce - 2:10 pm on Mar 14, 2013 (gmt 0)
I was assuming Google was using the widely accepted definition of "Average"
Average is actually quite a murky term.
Most people think it means "mean" (sum of values in a series divided by the number of values). However, it can also mean "median" (the value in a series which has an equal number of values above and below it), or "mode" (the most common value in a series).
Google's "Average Position" isn't clearly defined (we don't know much about the series from which it derives, or how it is calculated), but what they do say is that it is the average of your own pages: if you have one page at #1 and another at #16 the "average position" will take both into account, whichever average is used.
In a series that varies with time (like SERPS), a major factor that can interfere with accuracy is the sample rate. I am pretty certain that Average Position in WMT derives from a small number of samples over the month (possibly a single sample). It is a bit like stating the average number of people in a bus queue when the data might be a single sample that was taken at a rural bus stop at 3:00 a.m.
I don't personally place much weight on it.