How to calculate efficiently the variance or standard deviation given a counter of numbers?

Question

Given for example the next histogram and the bins:

import numpy as np
hist = np.array([1,1,2,1,2])
bins = np.array([0,1,2,3,4 ])

¿What is the most efficient way to calculate the variance? One way would be to recreate the array and pass it to the np.var function:

import numpy as np
np.var(np.array([0, 1, 2, 2, 3, 4, 4]))

However, I think this is not very efficient.

Answer 1

So you can just rewrite the formula:

counts  = hist.sum()
mean = (hist*bins).sum() / counts

sum_squares = (bins**2 * hist).sum()
var = sum_squares/counts - mean ** 2

# test
np.isclose(var, np.var(np.repeat(bins, hist)))

Output True.