In order to carry out a k-means cluster analysis, we can use Minitab, JMP, or XLMiner. For example, consider using XLMiner to carry out a k-means cluster analysis of the sports perception data in Table 3.9, where we (somewhat arbitrarily) choose to use k = 5 clusters. In this case, the XLMiner output shown on page 192 gives the final members of the five clusters, the centroids of each cluster (that is, the six mean values on the six perception scales of the cluster€™s members), the average distance of each cluster€™s members from the cluster centroid, and the distances between the cluster centroids.

a. Use the output to summarize the members of each cluster.

b. By using the members of each cluster and the cluster centroids, discuss the basic differences between the clusters. Also, discuss how this k-means cluster analysis leads to the same practical conclusions about how to improve the popularities of baseball and tennis that have been obtained using the previously discussed hierachical clustering.   

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Average Rating of Each Sport on Each of the Six Scales o9 SportsRatings TABLE 3.9 (1) Easy to Play (7) Hard to Play (1) Comp Opp. (7) Comp Std. (1) Compl. (7) Simple (1) Fast Mvg. (7) Slow Mvg. (1) Team (7) Indv. (1) Ncon (7) Con. Sport Boxing 6.62 3.07 4.62 4.78 6.02 1.73 Basketball 1.84* 3.78 1.56* 3.82 4.89* 2.27* Golf 1.82 6.13 4.49 6.58 3.84 4.11 Swimming 2.87 5.02 5.29 3.64 2.22 4.36 Skiing Baseball 4.60 5.96 2.51 2.13 5.22 4.71 4.18 3.33 2.67/ 4.78/ 2.16/ 3.60/ Ping Pong Hockey 2.20 3.18 5.13 5.38 2.91 2.04 3.22 1.71* 1.82* 5.04 5.96* 2.49* Handball 2.31 2.53 4.67 4.78 3.71 2.78 Track & field 4.47 2.82 4.38 3.84 2.89 3.82 Bowling 5.16 5.07 5.40 3.11 1.60 3.73 Tennis 2.42X 2.89X 3.78 5.47X 4.09 2.16X Football 2.42* 2.76 1.44* 5.00 6.47* 2.33* Sport Cluster ID Dist. Clust-1 Dist. Clust-2 Dist. Clust-3 Dist. Clust-4 Dist. Clust-5 Boxing 5.64374 5.649341 4.289699 5.353059 2.382945 Basketball 4 3.350791 6.914365 4.599382 1.315692 5.130782 Golf 2 5.192023 0.960547 3.825935 7.91777 4.546991 Swimming 4.656952 3.138766 1.836496 6.290393 3.223697 Skiing 5.528173 4.049883 2.58976 6.107439 2.382945 Baseball 4.573068 3.76884 3.928169 5.052507 Ping-Pong 4.081887 3.115774 1.286466 6.005379 3.434243 Hockey 4 4.357545 7.593 5.404686 0.593558 5.110051 Handball 3.621243 3.834742 0.924898 4.707396 2.643109 Track & Field 3.362202 3.4311 1.201897 4.604437 2.647626 Bowling 4.088288 0.960547 2.564819 7.005408 4.257925 Tennis 4.171558 3.396653 1.349154 5.417842 2.710078 Football 4 4.387004 7.911413 6.027006 1.04255 5.712401 3.