Updating averages

Question

Hello,

I'm analyzing some data and calculating averages. Basically what im doing is calculating the average ranges of gps coordinates from a central location. My issue is that I want to update said ranges with new data without having to keep a record of the old data. Is this possible if so please assist?

Answer 1

In theory yes!

If µ(n) = ∑ⁿ₁ (x_n) /n is the average for the first n terms, then µ(n+1) = ( x_n+1 /(n+1) ) + n µ(n) /(n+1).

So by storing previous n-term average and n+1-th term x_n+1 you may calculate n+1-th average µ(n+1).