user885: I'm not sure if there exists an average, but what could be considered an average rating range in these systems?

user70: While the numbers drift and have to be adjusted from time to time, the average USCF rating is supposed to be 1500.

user291: (I assume in the following discussion that by "average" you mean median, not mean.)
It depends on whether you are just looking at active players (who have played a tournament recently) or all players, and on whether you are just looking at just adults or players of all ages.
The latest rating distribution chart for the USCF I could find was from 2004 (here). You can see from it that at that time the 50th percentile was about 1050 for all players, or 1280 when just adults are considered. (USCF ratings have inflated a bit in the last decade so they are probably a bit higher now.) This is for all members, not just active ones; the median rating for active players would be higher, probably by 150 points or so from looking at the graph here.

user3552: An updated rating distribution graph:

The data is from the Golden Database.  It uses data from just current members with established (non provisional) ratings.  Note that only "regular" ratings are shown, not Quick ratings or blitz ratings.  
The overall shape of the graph, of course, is almost identical to the first one, with data from 2013.

user12: I took the following data from the September 2013 Golden Database1 and "active" players are players with a USCF membership expiration date later than January 1, 20132.  All ratings are regular ratings.  Note that players have an established rating after completing 25 games.
USCF Active Players

Established Ratings

46,574 Players
1315.99 Mean Rating
1390 Median Rating


Provisional Ratings

33,692 Players
537.09 Mean Rating
410 Median Rating

All USCF Rated Players

Established Ratings

252,989 Players
1165.77 Mean Rating
1148 Median Rating


Provisional Ratings

303,153 Players
631.46 Mean Rating
576 Median Rating

Distribution of active, established USCF ratings

Note that unrated players were discarded and that no checks were done on the data (duplicate entries, placeholders, etc.).
Distribution of ratings by age

This image comes from the uschess forums.
1: The Golden Database is a database provided to USCF affiliates and TD's that includes the names, ratings, and expiration dates.  It can be downloaded from the USCF website
2: I picked January 1, 2013 as an arbitrary cutoff date.  If there's a better and easy check for whether or not a player is active I'm happy to add additional data or update these stats.

885: <p>I'm not sure if there exists an average, but what could be considered an average rating range in these systems?</p>
 70: <p>While the numbers drift and have to be adjusted from time to time, the average USCF rating is supposed to be 1500.</p>
 291: <p>(I assume in the following discussion that by "average" you mean median, not mean.)</p>

<p>It depends on whether you are just looking at active players (who have played a tournament recently) or all players, and on whether you are just looking at just adults or players of all ages.</p>

<p>The latest rating distribution chart for the USCF I could find was from 2004 <a href="http://archive.uschess.org/ratings/ratedist.php" rel="nofollow">(here)</a>. You can see from it that at that time the 50th percentile was about 1050 for all players, or 1280 when just adults are considered. (USCF ratings have inflated a bit in the last decade so they are probably a bit higher now.) This is for all members, not just active ones; the median rating for active players would be higher, probably by 150 points or so from looking at the graph <a href="http://www.eddins.net/steve/chess/2008/06/06/131" rel="nofollow">here</a>.</p>
 3552: <p>An updated rating distribution graph:</p>

<p><img src="https://i.stack.imgur.com/5y7MX.png" alt="enter image description here"></p>

<p>The data is from the Golden Database.  It uses data from just current members with established (non provisional) ratings.  Note that only "regular" ratings are shown, not Quick ratings or blitz ratings.  </p>

<p>The overall shape of the graph, of course, is almost identical to the first one, with data from 2013.</p>
 12: <p>I took the following data from the September 2013 Golden Database<sup>1</sup> and "active" players are players with a USCF membership expiration date later than January 1, 2013<sup>2</sup>.  All ratings are regular ratings.  Note that players have an established rating after completing 25 games.</p>

<h3>USCF Active Players</h3>

Established Ratings

<pre><code>46,574 Players
1315.99 Mean Rating
1390 Median Rating
</code></pre>

Provisional Ratings

<pre><code>33,692 Players
537.09 Mean Rating
410 Median Rating
</code></pre>

<h3>All USCF Rated Players</h3>

Established Ratings

<pre><code>252,989 Players
1165.77 Mean Rating
1148 Median Rating
</code></pre>

Provisional Ratings

<pre><code>303,153 Players
631.46 Mean Rating
576 Median Rating
</code></pre>

<h3>Distribution of active, established USCF ratings</h3>

<p><img src="https://i.stack.imgur.com/BWjat.png" alt="Active USCF ratings"></p>

<p>Note that unrated players were discarded and that no checks were done on the data (duplicate entries, placeholders, etc.).</p>

<h3>Distribution of ratings by age</h3>

<p><img src="https://i.stack.imgur.com/zflWp.png" alt="enter image description here"></p>

<p>This image comes from the uschess forums.</p>

<p>1: The Golden Database is a database provided to USCF affiliates and TD's that includes the names, ratings, and expiration dates.  It can be downloaded from the USCF website<br>
2: I picked January 1, 2013 as an arbitrary cutoff date.  If there's a better and easy check for whether or not a player is active I'm happy to add additional data or update these stats.</p>
