Regression to the mean

main.py

import random
from collections import Counter


def regression_to_the_mean(n):
    data = [random.randint(1, 10) for x in range(n)]
    return sum(data) // len(data)

# 10
Counter([regression_to_the_mean(10) for x in range(50)]).most_common()
>>> [(5, 23), (4, 14), (6, 6), (7, 4), (3, 3)]

# 100
Counter([regression_to_the_mean(100) for x in range(50)]).most_common()
>>> [(5, 41), (4, 5), (6, 4)]

# 1_000
Counter([regression_to_the_mean(1_000) for x in range(50)]).most_common()
>>> [(5, 50)]

The more data points, the less variance in the mean.