On the expected difference between mean and median

Abstract

Mean and median are both estimators of the central value of statistical distributions. For a given sampled continuous probability distribution function the equations for the influence of one sample are used to derive the known expressions for the standard deviation of mean and median and the novel expression for the expectation value of the squared differerence between mean and median. The usefulness of this result is illustrated on a dataset, where the difference between mean and median serves as an outlier detection and as a tool for deciding whether to use the mean or median as an estimator.