iter_avg.py

from itertools import count
from functools import reduce

def iter_mean(iterable):
    """
    Caluculate the arithmetic mean of an iterable *without* loading the entire collection
    into memory or knowing the legnth apriori.
    """
    return reduce(
        lambda c, i: (c * (i[1] - 1) + i[0]) / i[1], zip(iterable, count(1)), 0
    )

IPython %timeit examples:

In [1]: from statistics import mean

In [2]: %timeit mean(list(range(10 **6)))                                                                      
355 ms ± 11.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [3]: %timeit iter_mean(range(10**6))
153 ms ± 371 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)