263,428 plays over 53,632 songs = 5 plays of each song on average. (updated after comment below)

I haven't "scrobbled" in many years, but checked now that I in 2007 (when I was 16) had 12,377 plays with only 153 unique songs. An average of playing each song 78 times. However, most of the songs I only listened to a few times, so there is basically just ~20+ songs I listened to 250-500 times each that year.

So I guess I was a typical teenager that got obsessed with some songs/artists and listened to them non stop, heh.