Well, there are 52 choose 5=2,598,960 possible 5 card hands that you can be dealt. I'll cheat on the computations and refer to
http://www.math.sfu.ca/~alspach/comp18/
There are 10,200 straights, 5108 flushes, 3744 full houses, 624 four-of-a-kinds (I am going to count these as pat hands, although somebody with pat quads will probably draw 1 to trick you), and 40 straight flushes, for a total of 19716 pat hands that are a straight or better, 19092 if we disregard quads.
So we see that a little over half of the pat hands are straights, so the median pat hand is going to be a fairly strong straight. There are 10 choices (A,K,Q,J,T,9,8,7,6,5) for the top card in the straight. So counting quads, the median pat hand would be approx. a king-high straight if my rough back-of-the-envelope calculations are correct.
Just as an aside, I once folded a pat hand in a pot-limit draw tournament. UTG opened with a raise, I had a pat ten-high straight and raised the pot. The next player (an extremely weak-tight passive player who virtually never raises-the kind of player who check-calls high trips) re-raised the pot. UTG calls the 2 pot-sized raises, putting himself all-in. I figure there are at least one, if not two, pat hands against me and I put the rock on at least a high flush. I fold. UTG draws two and shows down unimproved AAA. Rock shows Ace-high flush.