Stably updating mean and standard deviation of data

By considering the (sample) mean of a set of data as a fit to this data by a constant function, a computational method is given based on a matrix formulation and Givens transformations. The (sample) mean and standard deviation can be updated as data accumulates. The procedure is numerically stable and does not require storage of the data. Methods for dealing with weighted data and data removal are presented. When updating the mean and square of the standard deviation, the process requires no square roots.