Young and Cramer's Recursive Variance Algorithm in Python

variance.py

from typing import List, Union
import random 


def recursive_sum_of_squares(
    x: List[Union[float,int]], 
    checked: bool = False
) -> float:
    n = len(x)

    if not checked:
        if not all(
            this_x is not None and isinstance(
                this_x, 
                (float, int)
            ) for this_x in x
         ):
            raise ValueError(
                'Sample contains null values'
            )

        if n == 0:
            raise ValueError(
                'Sample variance cannot be computed for a sample size of 0.'
            )

    if n == 1:
        return 0

    term_variance = (n*x[-1] - sum(x))**2/(n*(n-1))
    return recursive_sum_of_squares(x[:-1], True) + term_variance

if __name__ == "__main__":
    sample = [
        random.randint(0, 100) 
        for _ in range(0,100)
    ]
    n = len(sample)
    variance = recursive_sum_of_squares(sample) / (n - 1)
    print(variance)