from math import sqrt
def ave_error(arr):
    M = len(arr)
    assert(M>0)
    if M == 1:
        return (arr[0], 0.)
    else:
        average = sum(arr)/M
        variance = 1./(M-1) * sum( [ (x - average)**2 for x in arr ] )
        error = sqrt(variance/M)
        return (average, error)