Ron Guth: All 1892-S Quarter Dollars have the mintmark centered on the reverse between the eagle's tail and the R of QUARTER. Apparently, this position was too tight and led to die chipping, thus the mintmark was moved further to the right on later S-Mint issues.
Sources and/or recommended reading:
"Those Shifty Mintmarks" by David Lange, The Numismatist, September 2010, pp. 21-22
Stack's/Bowers 8/15/2013:2053, $9,165