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Given a straight road with n towns x1, x2, ... xn where x is the location of the city determine the best place for a

Given a straight road with n towns x1, x2, ... xn where x is the location of the city determine the best place for a shop.

Show how to determine the best location that minimizes the average distance between the shop and the towns.

Ex. A ... B ....... C .... D .. E (each . is 1 mile, find the best location for the shop so that the average distance between the towns is the smallest it can be).

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