How much memory does PHP Statistics require?

This depends on how many hits your site gets. The data collection code is very light weight, however the reporting and statistics code can take a lot of memory to process. The longer you collect data for the more memory you will need to process it. At a bare minimum, a basic WordPress site with WP Statistics should have at least 32 meg of RAM available for a page load. Sites with lots of plugins and high traffic should look at significantly increasing that (128 to 256 meg is not unreasonable).