Proxyhub is right, but he didn't say why. Alexa is dependent on people installing its SPYWARE onto their computers to track which sites they go to. Which means the data isn't accurate as far as the general population and their surfing habits is concerned.
You need not be online for a particular amount of time, you simply need visitors with the Alexa toolbar
Alexa is an statistic algorithm, and as such, prone to errors. I would say you would have to be on the fist 100,000 to have some real valuable data
Alexa is really useless, you can move up in rankings 100 fold by just having the toolbar yourself, I never pay any attention to it.