PageLever offers pretty extensive statistical analysis for Facebook Pages. They have recently come out with a free Facebook Analytics tool called Minilytics:
http://minilytics.pagelever.com/start/500888614#who-are-my-fans
It will tell you a few details that will make it easier to interact in the right way with your Facebook Fans, including:
- The best time to post
- How many fans you are reaching
- Best type of post
- Who are your fans
It’s info you could glean from Facebook insights – but it’s quick and easy so in my book, it’s even better.
One quick reminder – this is for a Page, not for your personal/user account.