These are procedures for revealing trends in scatter diagrams by determining typical values based on observation of successive small intervals of the explanatory variable. Simple examples are provided by the running mean and running median. For a data set, y1, y2, y3,…, ordered by the corresponding values of the explanatory variable, the three-point running means are given by while, denoting the median of yi−1, yi, and yi+1 by M(yi), for i > 1, the three-point running median values would be M(y2), M(y3), M(y4),…. These ideas can be extended by calculating, for example, M(M(yj). More sophisticated alternatives are kernel methods, loess, and the use of splines. See also generalized additive model.
Subjects: Probability and Statistics.