In a computer implementation, as the three "s""j" sums become large, we need to consider round-off error, arithmetic overflow, and arithmetic underflow. The method below calculates the running sums method with reduced rounding errors. This is a "one pass" algorithm for calculating variance of "n" samples without the need to store prior data during the calculation. Applying this method to a time series will result in successive values of standard deviation corresponding to "n" data points as "n" grows larger with each new sample, rather than a constant-width sliding window calculation.