Is there any way to find arithmetic mean “better” than sum()/N?

Question

Suppose we have N numbers(integers, floats, whatever you want) and want to find their arithmetic mean. Simplest method is to sum all values and divide by number of values:

Answer 1

If the array is floating-point data, even the "simple" algorithm suffers from rounding error. Interestingly, in that case, blocking the computation into sqrt(N) sums of length sqrt(N) actually reduces the error in the average case (even though the same number of floating-point roundings are performed).

For integer data, note that you don't need general "big integers"; if you have fewer than 4 billion elements in your array (likely), you only need an integer type 32 bits larger than that the type of the array data. Performing addition on this slightly larger type will pretty much always be faster than doing division or modulus on the type itself. For example, on most 32 bit systems, 64-bit addition is faster than 32-bit division/modulus. This effect will only become more exaggerated as the types become larger.