(Personal opinion below, and does not necessarily represent the views of chess.com management or anyone else with authority or insight.)
Not many minutes go by in Live Chess chat without some player asking the question: "Is a premium membership worth it?"
There is no single answer to that question, I suppose. One's personal financial situation and other interests must be weighed against one's interest in chess enjoyment and improvement and how one imagines the myriad features offered on the chess.com site contributing to those interests.
One thing is clear, if you look at the readily available data: higher rated players opt for premium memberships more frequently than lower rated players. The following chart was built from ratings and membership status data readily available using the full stats feature:
Each datum was obtained on August 7, 2009 by sampling roughly 250 to 450 players information centered around nominal rating values, spaced every 100 rating points (except for the lowest two and highest one datum).
Clearly, there is a strong correlation between premium membership and player rating. Immediately, I must point out that this is a correlation, not necessarily a cause-and-effect relationship.
Indeed, there are many possible explanations that might yield such a correlation. One that pops to mind quickly is that older players are typical higher rated AND might have more ready access to funds to pay for the premium benefits. Another possible explanation is that higher rated players more readily see the value of the premium membership features. Still another possible effect is that premium membership features help raise the ratings of players who procure and use those features.
The cause-and-effect possible of these explanations cannot be determined from these raw data. All three explanations, and even others unmentioned, could be at play. However, knowing what I know about my personal chess learning experience, what I value as a player, and what has helped me grow as a player, I'm guessing that the latter two explanations above are surely in the mix.
Now, if I'd only take even better advantage of premium features, I'm sure I could improve by another hundred ratings points by the holidays.