Average Player Rating? It Depends.
Many people ask, "What is an average player rating?" Well, there are many answers to that, but here I'll present just two possible measures. You can decide if these are representative and helpful.
The first of these is a snapshot of the ratings distribution for USCF rated tournament players, taken from 2005 data. Surely the demographics have changed somewhat in the past four years; but from what I understand, this distribution is somewhat representative of the data after the great influx of junior players. The mean for adults is between 1500 and 1600, which rings true with what most USCF members would recall. The junior players are more like 600. Thus, the strong bimodal distribution. The USCF uses a proportional formula for estimating the strength of an incoming unrated player: 50 x Age, up to 26, then 1300 from there on. See the chart directly below for the distribution.
Here, on chess.com, the incoming rating is set at 1200 for everyone, regardless of age. Since there is no way to verify age in any case, but with the understanding that most incoming players are relatively young, the 1200 number certainly seems reasonable. Additionally, most new players entering chess.com are NOT adult tournament players like the population in the second hump in the chart above. So, it's not surprising to see the mean rating near 1200, what with it being biased towards 1200 by the incoming set point anyway. See chart below, for recent data on Live Chess Blitz ratings at chess.com.
Many would insist that ratings are meaningless. While I would suggest something less polarized than that, far too many new players get obsessed with their rating when it's chess improvement that should be sought. Ratings will follow.