The Mining skill allows the operation of mines and, at higher levels, increases the amount of ore yielded on each pull.
In effect, then, the ranges are UP TO:
Level 1 - 7 ore/pull.
Level 2 - 11 ore/pull.
Level 3 - 14 ore/pull.
Level 4 - unknown. (15?)
Level 5 - 16 ore/pull.
Level 6 and up - Unknown (needs spading)
Whether or not higher levels also result in a better rate of gem drop is hard to say. That also needs testing.
One must first learn Ore Extraction from the University of Architecture in order to learn Mining.
School of Architecture: