Here in Texas the furthest shot I have made on one was about 260 yards, closest was about 55. Average has been about 125 yards, but I don't have a vast expanse of land to shoot at.
Your average shot distance is not so much determined by what part of the country you are in, but what type of land you are hunting on. If there is some brush and trees around, you will have closer shots. If you are out in an open field, be ready to take shots over 200 yards.