import numpy as np

Not a bad idea to solve this one in pieces/two functions.

def mean(x):
    s = 0.0
    N = np.size(x)
    for n in range(N):
        s += x[n]
    return s / N

def var(x):
    s = 0.0
    N = np.size(x)
    m = mean(x)
    invN = 1 / N # minimizing division is a good idea, even if ineffective here
    for n in range(N):
        d = x[n] - m
        s += d * d # multiplication is faster than powers
    return s * invN

rng = np.random.default_rng()
x = rng.normal(size = 100)
np.isclose(np.var(x), var(x))

True