From: ben.usenet@bsb.me.uk   
      
   Mike Terry  writes:   
      
   > ... But actually the balancing line idea wasn't my proper thinking -   
   > that was that we "counter-balanced" the circle by adding a new weight   
   > somewhere on the circle.  There is a unique such place where such a   
   > weight can go, and a unique weight that works.   
      
   Or just find the point in the (weightless) disc where it balances.   
   That's the vector average.   
      
   > The "average" for the   
   > x_i is then directly OPPOSITE the counter weight.  This is all   
   > assuming we don't start with an exactly balancing sample!   
   > The mass of   
   > the counter-weight is the magnitude of your vector sum, indicating the   
   > "strength" of the average...   
      
   The distance from the centre is then a measure of the strength of the   
   average.   
      
   I like the physical metaphor of a balanced disc, but I prefer the idea   
   of finding the balance point directly rather than the mass and location   
   (on the circumference) of a counterweight.   
      
   --   
   Ben.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)