"... I was wondering if anyone has compiled the data to determine the mean age of winners."
The Wikipedia article below, about
the contestants who have appeared on Jeopardy, includes the birth dates for a good number of them, so it provides a start to an answer and at least gives a general picture of their ages.
One would have to go through the individual biographies listed, collect the birth dates provided and then do the math, to get an average: https://en.wikipedia.org/wiki/list_of_jeopardy!_contestants
Chronic prostatitis (age 60 on)
BPH w/ urinary obstruction, 6/2011
Ongoing high PSA, 7/2011-12/2011
Biopsy, 12/2011: positive 3/12 (90%, 70%, 5%)
Gleason 6(3+3), T1c
No mets, PCa likely still organ contained
IMRT w/ HT (Lupron), 4/2012-6/2012
PSAs (since post-IMRT): 0.1 to 0.3 range