Calculate mean and standard deviation using batch updates

batch_stats.py

import numpy as np
x = np.arange(100)
N = 0
mean = 0
std = 0
for i in range(11):
    batch = x[10*i:10*(i+1)]
    k = len(batch)
    N += k
    old_mean = mean
    batch_mean = batch.mean()
    old_std = std
    batch_std = batch.std()

    # Mean update
    new_mean = (N - k) / N * old_mean + k / N * batch_mean
    
    # Variance update
    new_var = (
        (N - k) / N * (old_std**2 + old_mean**2)
        + k / N * (batch_std**2 + batch_mean**2)
        - new_mean**2
    )
    
    mean = new_mean
    std = np.sqrt(new_var)
    
print(f"Mean: {x.mean()} | Running mean: {mean}")
print(f"Std: {x.std():.03f} | Running std: {std:.03f}")
# Mean: 50.0 | Running mean: 50.0
# Std: 29.155 | Running std: 29.155

Based on this blog post: http://notmatthancock.github.io/2017/03/23/simple-batch-stat-updates.html