# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Averaging**

**From:**Alexandre Eremenko

**Date:**2004 Nov 3, 14:32 -0500

Dear Herbert, I am really surprised that after such long discussion on the "Averaging", you still say: On Wed, 3 Nov 2004, Herbert Prinz wrote: > Simple averaging of the altitudes is always wrong. My impression was that in this long discussion I managed to convince everybody that just the opposite is true: Simple averaging of altitudes is almost always RIGHT. (almost=except few situations which were explicitly described before). Your "math argument" is correct, of course, but if you complete it to the end you will see that it gives EXACTLY the same answer that I propose:-) Just do it. You want to find the line y=ax+b of the best fit say from 3 observations (x_1,y_1), (x_2,y_2), (x_3,y_3). Just do the "least square procedure" as you described, and find a and b. Then compute the averages x=(x_1+x_2+x_2)/3 and y=(y_1+y_2+y_3)/3. And then plug the averages to the equation y=ax+b. If you do all your computations correctly, you will see that they fit:-) So the "method" you propose, in the case of a linear function, gives EXACTLY the same answer as simple averaging. Alex.