dynamical list problem

[peacecalc]

Hello folks,

I have a problem for you, but no solution. We have a growing list, in every cycle a new element is appended to the list. Let us say, every second a new value is generated and which series of elements have the highest average. The sum of values of such a sequence should obey a certain value:

Here a example: sum value is 5

1 {1}
2 {1 2}
3 {1 2 1}
4 {1 2 1 3} Now the first time for building an averge value: m = (4 + 1)/(3 + 1/3) = 3/2
5 {1 2 1 3 2} m = (3+2)/(1+1) = 5/2. Statically it would be not calculated because the sum value is not 5 (only 2+2). I hope this explain a little bit the problem. A more difficult situation occurs when the not only one but more values in the "past" must be included in the new average caluation.

From where I get this dynamical problem? My fitness watch told me after a jogging tour that was my fastest mile. I've the impression, the watch works statically. It takes the time after the first miles, then after the second mile and so on. And at the end, it tells me, ok your fith mile was my record (= fastest) mile. But what is, when my record milstones lies in between?

Greetings
peacecalc