Here's a general idea that I found on previous forums. They don't give out the exact numbers to prevent people from advancing, don't know why you wouldn't want to move up to a higher rank....
Amateur : Average Score 85? (Around 5 games)
Pro : Average Score 78 (About 15-20 games)
Tour Pro: 72 (Unknown games)
Master : 67 (Unknown games)
All except the amateur average score are accurate (not too sure about Amateur) the games, where given are estimates
Cheers,
mn