The complexity of finding medians

PF(#P) is characterized in a manner similar to M.W. Krentel´s (1988) characterization of Pf(NP). If MidP is the class of functions that give the medians in the outputs of metric Turing machines, then it is shown that every function in PF(#P) is polynomial time 1-Turing reducible to a function in MidP and MidP⊆PF(#P); that is, PF(#P)=PF(MidP[1]). Intuitively, finding medians is as hard computationally as PF(#P); this forms a contrast to an intuitive interpretation of Krentel´s result that finding maxima (or minima) is as hard as PF(NP). Several applications of the result are shown