Sample variance in a single pass

online_variance.py

def online_mean_variance(iterable):
    mN = 0
    mM = 0.0
    mS = 0.0

    for x in iterable:
        mN += 1
        nextM = mM + (x - mM) / mN
        mS += (x - mM) * (x - nextM)
        mM = nextM

    mean = mM
    var = mS / (mN - 1) if mN > 1 else 0.0

    return mean, var

if __name__ == '__main__':
    import numpy as np

    data = np.random.random(1000)
    print (np.mean(data), np.var(data))
    print online_mean_variance(data)