Equation for Rapid Calculation of the Standard Deviation

Abstract

This paper proposes rapid standard deviation equation for determining the standard deviation of variable-size data. The novel method calculates the standard deviation in an accumulative way: it requires only new observation to be included, instead of using whole data, in calculation. The method has the running time of O(N) instead of the traditional O(N²). The proposed rapid standard deviation equation depends on the following factors: new observation(x_N), the amount of current data size (N), the average of the value of current data (), and standard deviation of previous data set ('). The equation is in a compact form, easy to understand and apply to data sets.