Mine have varied from day tours to a 3-month tour. If I were to calculate an average, it would probably be some length of time that doesn't match any of the tours I've done, and would be meaningless.

As for getting ready for a cross-country trip, first it would depend which country you're planning to cross. You could cross some of the European ones in a week-long tour. But if you're planning to do a 3-month or 6-month tour, as mev says, you really don't need 10-15 week-long tours to get ready for an extended tour. But definitely do some shorter tours so that you can sort out your equipment needs etc., and definitely do lots of cycling in general.