Several exploratory data techniques -- including principal component analysis, minimum and maximum hierarchical clustering methods and Minimum Spanning Trees and their graphical representations -- are presented and discussed using data obtained by optical emission spectroscopic chemical analyses of Mycenaean ceramic specimen from 33 sites, augmented by similar chemical data about ceramic groups from Chania and Thebes. Comparable analyses are given of electron microprobe data measuring the major chemical elements (or their oxides) of local and Aegean imported ceramic materials from Tell Gemmeh. The correspondence between raw clay specimen and locally made pottery is also noted. The Minimum Spanning Tree as a alternative to the minimum hierarchical clustering method and the potentialities of the maximum hierarchical clustering method are illustrated and discussed. Such informal techniques for evaluating the quality of different clustering schemes as the t -statistic and the circle diagram are described using Mycenaean ceramic chemical data. Both increasing the number of chemical variables quantitatively analyzed along with analyzing raw clay specimen from beds near archaeological sites may further enhance the precision with which Mycenaean pottery provenances can be identified.