🚀 go-pugleaf

In article <3SEP199213440863@utkvx2.utk.edu>, menees@utkvx2.utk.edu (Menees, Bill) writes:
> 	I'm a senior math major taking my first p&s course, and this problem
> has come up and it intrigues me.  My prof. has a proof for it, but he said it
> was way over my head.  Does anyone know of a proof suitable for a senior 
> undergrad?  Thanks in advance.
This reminds me of an interesting approach to several
common location statistics. I'll state it for samples
to avoid technicalities.

Suppose we have a sample x_1, x_2, . . .,x_n.
Given a positive real number p define m to minimise

  Sum |x_i - m|**p

then we get

  p --> 0         mode
  
  p = 1           median
  
  p = 2           mean
  
  p --> infinity  midrange
  
Neat, eh?  
-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'