Central Tendency

Weighted Mean

Compute the weighted mean: sum each value multiplied by its weight, then divide by the total weight. Values with larger weights pull the mean toward them more than values with smaller weights. By hand, accumulate the weighted sum and total weight in a loop. With numpy, np.average(values, weights=weights) does both steps in one call.

By hand

With the library

np.average(values, weights=weights) computes the weighted sum and divides by the total weight in one vectorised call. float() converts the numpy scalar to a plain Python float before printing.

naive.py 
values  = [10, 20, 30, 40, 50]
weights = [1, 2, 3, 2, 1]
w_sum = 0.0
total_w = 0.0
for i in range(len(values)):
    w_sum = w_sum + values[i] * weights[i]
    total_w = total_w + weights[i]
mean = w_sum / total_w
print('RESULT:', round(mean, 10))
library.py 
import numpy as np
from dalib.display import set_display
set_display()

values  = [10, 20, 30, 40, 50]
weights = [1, 2, 3, 2, 1]
wmean = float(np.average(values, weights=weights))
print('np.average:', wmean)
print('RESULT:', round(wmean, 10))

np.average: 30.0
RESULT: 30.0

Implementation notes

  • When all weights are equal, the weighted mean reduces to the arithmetic mean. With weights=[1,1,1,1,1] on this data the result would be 30.0 — the same answer, because the values are symmetric around 30.
  • np.average raises ZeroDivisionError if the weights sum to zero; the naive half has the same failure mode at mean = w_sum / total_w.
  • Cross-reference: arithmetic-mean (this chapter) for the equal-weight special case and the balance-point property.