geothmetic_meandian.py

import math
import operator

from functools import reduce
from itertools import combinations
from typing import Union

Number = Union[int, float]

def all_close(*values: Number):
    return all(math.isclose(a, b) for a, b in combinations(values, 2))

def gmdn(*values: Number, iteration: int = 1):
    n = len(values)

    if n <= 1:
        raise TypeError(f"Not enough values provided, expected at least 2, got {len(values)}.")
    a_mean = sum(values) / n
    g_mean = reduce(operator.mul, values) ** (1 / n)
    median = values[math.floor((n + 1) / 2)]
    if all_close(a_mean, g_mean, median):
        return a_mean, iteration
    return gmdn(a_mean, g_mean, median)

# testing
def test_xkcd_value():
    value, iterations = gmdn(1, 1, 2, 3, 5)
    assert math.isclose(value, 2.089)