I'd quote the 75 percentile ...
As an exercise - lets say you want to buy a car. You walk into the dealership and find one for $35,000 MSRP. You want to buy it for $30,000. You tell the salesman "I'll take it! Here's $30k". Now you've started negotiations, and you set the floor at $30k, and they set the ceiling at $35k, You're probably going to meet somewhere in the middle. If you set the floor at $27k, realizing you want to settle out at $30k, you're more likely to do so.
Obviously you won't get anywhere if you set your expectation too high, which is why I typically pick the 75th percentile. The recruiter knows the 50th and 75th percentile too, and if you're way too high for the job they'll tell you. They don't want to waste your time or theirs, so if you say "I want $250k" and they say "We couldn't pay you any more than $225k" then you can decide if you want to continue with the interview, realizing that maybe $225k was actually your ideal number. If you go in asking for $225k, don't be surprised if you get less, despite $225 being their ceiling.
All of this is moot if you're interviewing with a group with standard salaries however.