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 the constituent schools. The file FBS contains data on schools belong to the Football Bowl Subdivision (FBS). Each row in this file contains information on a school. The variables include football stadium capacity, latitude, longitude, athletic department revenue, endowment, and undergraduate enrollment.

Refer to the Appendix for instructions on how to perform a given hierarchical clustering method using JMP Pro. In the Clustering JMP Pro dialog box, in the Options area, in the Method section check Single in the first analysis (Average in the second analysis), select Data as usual, and check Standardize Data. When the Data Hierarchical Cluster JMP Pro dialog results box appears, click the red triangle next to Hierarchical Clustering, choose Number of Clusters and enter 10.

A. Apply hierarchical clustering with 10 clusters using latitude and longitude as variables. Compute the cluster sizes, as well as the minimum and maximum of the latitude and longitude of single linkage method. If required, round your answers to one decimal places. If your answer is negative, use minus sign.

Cluster Id 1 2 3 4 5 6 7 8 9 10

Cluster Size, Min of Latitude, Max of Latitude, Min of Longitude, Max of Longitude

School	StadiumCapacity	Latitude	Longitude	AthleticRevenue ($)	Endowment ($000)	Enrollment
Air Force Falcons	52480	38.8632	-104.759899	39823782	56600	4413
Akron Zips	30000	41.0804	-81.521499	25583730	171513	27470
Alabama Crimson Tide	101821	33.2377	-87.540979	124498616	995147	31647
Arizona State Sun Devils	73379	33.38835	-111.930639	55294113	514724	72254
Arizona Wildcats	57803	32.195816	-110.891717	59663128	552351	39236
Arkansas Razorbacks	76000	36.0718	-94.155684	91768112	788668	23199
Arkansas State Red Wolves	30964	35.821828	-90.685768	13374507	39479	13900
Army Black Knights	40000	41.362343	-74.027317	34342038	73190	4624
Auburn Tigers	87451	32.5929	-85.480322	103982441	471851	25469
Ball State Cardinals	22500	40.115904	-87.842539	20483476	140275	22147