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Where shall we meet?

Suppose that a group of friends live along a straight road and that they wish to meet somewhere on that road. They wish to choose the meeting place so that they do not have to travel too far; there are several criteria which they could use: (1) Make the total distance travelled as small as possible. (2) Make the greatest distance any individual travels as small as possible. (3) Minimise the total of the squares of the distances travelled.