Pseudo–median

In statistics, the pseudomedian is a measure of centrality for data-sets and populations. It agrees with the median for symmetric data-sets or populations. In mathematical statistics, the pseudomedian is also a location parameter for probability distributions.

In descriptive statistics, the pseudomedian of a data-set is measure of centrality, similar to a sample median. Other centrality statistics include the sample mean and a mode.

In inferential statistics, the pseudomedian of a finite populations is the location parameter computed by the Hodges–Lehmann statistic. It coincides with a population median when the population is symmetric.

In the statistical theory of probability distributions, the pseudomedian is the location parameter that is estimated by Hodges–Lehmann statistic. When the distribution is symmetric about a median, its pseudomedian coincides with that median. For nonsymmetric distributions, the pseudomedian is defined as the median of all of the midpoints of pairs of observations. Like the set of medians, the pseudomedian is well defined for all probability distributions, even for the many distributions that lack modes or means.

In Signal Processing there is another definition of pseudomedian filter for discrete signal. For a window of width 2N+1 pseudomedian defined as the average of the maximum of the minima and the minimum of the maxima of the N+1 sliding subwindows of length N+1.

...
Wikipedia