def prod_signs(arr):
    if not arr: return None
    prod = 0 if 0 in arr else (-1) ** len(list(filter(lambda x: x < 0, arr)))
    return prod * sum([abs(i) for i in arr])
from typing import List
def mean_absolute_deviation(numbers: List[float]) -> float:
    mean = sum(numbers) / len(numbers)
    return sum(abs(x - mean) for x in numbers) / len(numbers)