which cluster is the densest? Type the within-cluster average distance of that cluster ($average.distance). round 2 decimal places.

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What is the ratio of the average between-cluster distance to the average within-cluster distance for the smallest cluster (by cluster size)? use the average between cluster distance of the smallest cluster and the largest cluster ($avg.between.matrix). the ratio should be between-cluster/within the cluster. round answer to 3 decimal places.

> #display the structure of the 4-means clustering object > str (k4) List of 9 $ cluster : int [1:1470] 2 2 2 2 2 2 2 2 2 2 ... $ centers : num [1:4, 1] 1. 299 -1. 298 0.435 -0.431 . .- attr(*, "dimnames")=List of 2 ..$ : chr [1:4] "1" "2" "3" "4" . . ..$ : chr "X.1" $ totss : num 1469 $ withinss : num [1:4] 22.9 23 22.9 23 $ tot. withinss: num 91.8 $ betweenss : num 1377 $ size : int [1:4] 367 368 367 368 $ iter : int 2 $ ifault : int 0 - attr(*, "class")= chr "kmeans" > > #display information on 4-means clustering > k4 K-means clustering with 4 clusters of sizes 367, 368, 367, 368 Cluster means : X. 1 1 1. 2991854 2 -1. 2980075 3 0. 4346323 4 -0. 4310987$cluster.size [1] 367 368 367 368 $min.cluster.size [1] 367 $noisen [1] o $diameter [1] 0.8621974 @.8645531 0.8621974 0.8645531 $average.distance [1] 0.288969% @.2897549 0.2889696 0.2897549 $median.distance [1] 0.2544189 0.2544189 0.2544189 0.2544189 $separation [1] 0.002355731 0.002355731 0.002355731 0.002355731 $average.toother [1] 1.731462 1.731462 1.154571 1.154047 $separation.matrix [,1] [,2] [,3] [,4] [1,] 0.000000000 1.733817706 @.002355731 0.866908853 [2,] 1.733817706 0.000000000 @.869264583 0.002355731 [3,] 0.002355731 0.869264583 0.000000000 @.002355731 [4,] 0.866908853 0.002355731 0.002355731 @.000000000 $ave.between.matrix [,1] [,2] [,3] [,4] [1,] 0.0000000 2.5971930 0.8645531 1.7302841 [2,] 2.5971930 0.0000000 1.7326398 0.8669089 [3,] 0.8645531 1.7326398 0.0000000 @.8657310 [4,] 1.7302841 0.8669089 0.8657310 0.0000000 $average.between [1] 1.442885 $average . between [1] 1. 442885 $average . within [1] 0. 2893628 $n. between [1] 810337 $n. within [1] 269378 $max . diameter [1] 0. 8645531 $min. separation [1] 0. 002355731 $within. cluster . ss [1] 91.81237 $clus . avg . silwidths 1 2 3 4 0. 6257182 0. 6257210 0. 5163134 0.5153247 $avg. silwidth [1] 0.570769 $92 NULL $93 NULL $pearsongamma [1] 0. 6117471 $dunn [1] 0. 002724796