gistfile1.py

def mean(*xs):
    return sum(xs) / float(len(xs))

def naive(*xs):
    m = mean(*xs)
    return sum((x-m)**2 for x in xs) / float(len(xs))

def update(x, prior):
    s, n, m = prior
    m_ = float(m*n + x) / (n + 1)
    s_ = s + n * abs(m_-m)**2
    return (s_ + (x - m_)**2, # new sum
            n + 1,            # new count
            m_)               # new mean

def running(*xs):
    if len(xs) <= 1:
        return (naive(*xs),
                len(xs),
                mean(*xs))
    return update(xs[0], running(*xs[1:]))

def var(*xs):
    return running(*xs)[0] / len(xs)

def std(*xs):
    return sqrt(var(*xs))

if __name__ == "__main__":
    from sys import argv
    xs = [float(n) for n in argv[1:]]
    print "naive:", naive(*xs)
    print "running:", var(*xs)