I definitely don't have hardcore stats off hand, nor do I know of a chart that displays them. However, if you take the LSAT in December you should get your scores by the end of that month. For the most part, schools have special scholarship deadlines, some of which are December 1st or December 15th, although a few are January 1st/15th. With that said, some scholarships simply won't be available to you if you wait for the December LSAT score.
I do know that some schools that run rolling admissions state that they give out merit scholarships simply after viewing your application, and while this is true you have to take into account that the more admitted students there are, the less scholarship money that's available.
So, bottom line--earlier applications are always more advantageous. That is, unless you're going to bomb the October LSAT, in which case waiting until December is definitely preferable.
Best of luck! I hope everything works out for you!
P.S. You might want to check out
http://www.lawschoolnumbers.com, it will show you people who were admitted and sometimes they list their scholarship amounts. You might be able to compare the dates they sent off their apps to their scholarship amounts. I'm sure it would give you a better idea of what to expect than you have now!