http://jonisalonen.com/2014/efficient-and-accurate-rolling-standard-deviation/

rolling_statistic.py

class RollingStatistic(object):

    def __init__(self, window_size, average, variance):
        self.N = window_size
        self.average = average
        self.variance = variance
        self.stddev = sqrt(variance)

    def update(new, old):
        oldavg = self.average
        newavg = oldavg + (new - old)/self.N
        self.average = newavg
        self.variance += (new-old)*(new-newavg+old-oldavg)/(self.N-1)
        self.stddev = sqrt(variance)