Colleges and universities are often interested in identifying their peer institutions. The file named Colleges.xlsm that accompanies this book contains a number of (artificial) metrics for 307 higher education institutions in the United States.

a. Use k-means clustering to create 4 clusters for this data (use normalized input data and 100 iterations).

b. How many schools are in each cluster?

c. How would you characterize each of the clusters?

d. Use hierarchical clustering (with Ward’s method) for this data and produce a dendrogram.

e. If four clusters are desired, how many schools would be in each cluster?

f. Which clustering technique would you recommend be used and why?