GH-102670: Use sumprod() to simplify, speed up, and improve accuracy of statistics functions

[rhettinger]

• Use sumprod() which is faster, simpler, and more accurate than rounding each multiplication before summation.
• For an additional speed-up and simplification, compute the (x_xi - bar) only once instead of multiple times.
• For Spearman's rank correlation, we can skip the (x_xi - bar) step because the ranks are centered around zero.

Baseline timing

% ./python.exe -m timeit -r11 -s 'from random import expovariate as r' -s 'from statistics import correlation' -s 'n=100' -s 'data = [r() for i in range(n)]' -s 'weights = [r() for i in range(n)]' 'correlation(data, weights)' 10000 loops, best of 11: 21 usec per loop 

Timing with PR

% ./python.exe -m timeit -r11 -s 'from random import expovariate as r' -s 'from statistics import correlation' -s 'n=100' -s 'data = [r() for i in range(n)]' -s 'weights = [r() for i in range(n)]' 'correlation(data, weights)' 50000 loops, best of 11: 8.92 usec per loop 

• Issue: Use sumprod() to simplify, speed up, and improve accuracy of statistics functions #102670

[alexanderGerbik]

Is this a typo or some kind of black magic?