It varies based on time of day. For example, you'd expect to see more people in the US online at 7pm than 3am. I've seen activity measured at 15-minute intervals throughout the day and then averaged throughout the week.
If you've got 5k invites and each person is online for 1 hour per day, randomly distributed, then you'd expect to see in the 200-300 player range at any given time of day. So really if you want to analyze the invite-to-active-player ratio you'd need more information:
- Total number of beta keys used (that
is, invitees who logged in at least
- Average amount of time spent per play session?
- Average number of logins per day (or week) per account?
If you're just trying to ask instead, how many players to invite for beta... depends on whether your beta is more for bug-hunting purposes (keep it small and among trusted friends so you get good reports but you're not flooded with them), playtesting/balance purposes (mid-sized, large enough to get good playtest data but small enough that you don't generate too much bad press for your game if the players initially decide it sucks), or marketing purposes (bigger is better).