The output of a GPS receiver wanders over a large range, depending on how many satellites are currently overhead, whether there are line-of-site obstructions such as trees or buildings, or signal reflections from nearby surfaces. The best you can do is average your position for a long time (days) and even then the average has some uncertainty AND inaccuracy, which gets smaller the longer you average. Beware of the difference between the terms “accuracy” and “precision”, they mean different things.
In general you can’t expect one centimeter accuracy from a simple GPS receiver, no matter how long you average. In some situations, you can’t even expect one meter accuracy. A number of web pages describe various tests of GPS accuracy, you can start here: http://www.doylesdartden.com/gis/gpstest.htm