Jake Duffy is the e-commerce manager of a major electronics retailer. He is researching his company’s e-commerce competitors and wants to group the competitors based on their performance data. He has compiled a data set that contains the following four performance measures of the major competitors’ e-commerce operations: Annual Revenue (Revenue, in $), Growth Rate (in %), Monthly Visits (Visits), and Conversion Rate (in %). In order to avoid any personal bias in grouping these competitors, he decided to replace the names of the competitors with a code. A portion of the data set is shown in the accompanying table. 

a. Perform k-means clustering to group the competitors into five clusters using all four performance measures. Does the data set need to be standardized prior to cluster analysis? 

b. Plot the cluster membership using the cluster and silhouette plots. What is the average silhouette width? Describe the characteristics of each cluster. What are the size and cluster center values of the largest cluster of competitors?

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Website Revenue 3276000 2485716 B 484720000 1 2 ** 32 Growth Rate 13.6 9.6 1 23.44 Visits 78047136 28000000 B 872000 Conversion Rate 1.928 4 E 4.72