Hi and Alan,
Not sure that I can answer the specific question regarding waypoint averaging, but I've commenced some testing.
However, ... even with perfect reception, clear sky and flat ground, the best track accuracy you will achieve with any recreational GPS is +/- 5m.
So say you walked a perfectly straight line, with 1 sec track capture, the best accuracy of any point captured would fall in the range +/- 5m. The points will most likely line up pretty nicely; if captured in the space of 15 minutes or so.
Walk the same line, 24 hours later and you may get a different but similar straight'ish track.
Average this over several captures and draw the median of the points and you'll be getting pretty close.
It's the way OSM works. Many captures make for accurate tracks.
John k - Garmin Oregon 300, GPSmap76 & GPS16 plus various WinCe PNDs with OziCe & IGO8