Please help - get average

[Robin Becker]

Cliff Wells wrote:
......
> 
> total = 0.0
> count = 0
> number = None
> 
> while number not in ('q', 'Q'):
>     number = raw_input("Enter a number (or Q to quit): ")
>     try:
>         number = float(number)
>     except ValueError:
>         continue
>     total += number
>     count += 1
> 
> print "The average is:", total / count
> 
...... interestingly the standard algorithms for means/deviations are 
numerically poor. As an example

 >>> (1.e30+1-1.0e30)/3
0.0

Where we have total loss of information in one of the terms.


There are better algorithms involving recursion,

eg

    mu[n] = (data[n]+(n-1)*mu[n-1])/n

The error in the existing estimate, mu[n-1], gets multiplied by the 
number (n-1)/n which is less than one (ie the errors are damped).

However, in the case of widely differing magnitudes I think you need to 
accumulate the sums specially.
-- 
Robin Becker