In article <firstname.lastname@example.org>, David W. Cantrell <DWCantrell@sigmaxi.net> wrote:
>Well, as Achava correctly pointed out, it depends on the variable with >respect to which the mean is calculated.
>> Recall the "string and pins" method of drawing an ellipse, which >> depends on the fact that the sum of the distances from a point on the >> ellipse to the two foci of that ellipse is the major axis of that >> ellipse. Since the sum of those two distances is always the major >> axis, the sum of their means is the major axis.
This is true regardless of the variable.
>> By symmetry, the >> means of these distances are the same.
So the mean will be the semi-major axis provided the variable varies symmetrically wrt to the two foci.
(Which it doesn't for time in orbit.)
-- Richard -- Please remember to mention me / in tapes you leave behind.