  A Banach space X has the average distance property (ADP) if there exists a
unique real number r such that for each positive integer n and all x_1,...,x_n
in the unit sphere of X there is some x in the unit sphere of X such that
  1/n \sum_{k=1}^n ||x_k-x|| = r.
  We show that l_p does not have the average distance property if p>2. This
completes the study of the ADP for l_p spaces.
