The Football Bowl Subdivision (FBS) level of the National Collegiate Athletic Association (NCAA) consists of over 100 schools.

Most of these schools belong to one of several conferences, or collections of schools, that compete with each other on a regular basis in collegiate sports. Suppose the NCAA has commissioned a study that will propose the formation of conferences based on the similarities of constituent schools. If the NCAA cares only about geographic proximity of schools when determining conferences, it could use hierarchical clustering based on the schools’ latitude and longitude values and Euclidean distance to compute dissimilarity between observations. The following charts and tables illustrate the 10-cluster solutions when using various linkage methods (group average, Ward’s, complete, and single) to determine clusters of schools to be assigned to conferences using hierarchical clustering. Compare and contrast the resulting clusters created using each of these different linkage methods for hierarchical clustering.

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Group Average Linkage Clusters 54 54 40 49 44 39 34 29 29 T T 24 19 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 Cluster 1 Cluster 2 Cluster 6 Cluster 7 Cluster 3 Cluster 4 Cluster 5 Cluster 8 Cluster 9 Cluster 10