Sum of Withinss Over Number of Clusters

$k=2$

$\backslash$table$[[,$Inter$-$Cluster Distances$],[,$Cluster $1,$Cluster $2,],[$Cluster $1,0,5\mathrm{.}65,],[$Cluster $2,5\mathrm{.}65,0,],[,$Within$-$Cluster Summary,,$],[,$Size,Average Distance,$],[$Cluster $1,87,4\mathrm{.}003,],[$Cluster $2,91,4\mathrm{.}260,],[$Total$,178,4\mathrm{.}134,]]$

$k=3$

$\backslash$table$[[,$Inter$-$Cluster Distances$],[,$Cluster $1,$Cluster $2,$Cluster $3],[$Cluster $1,0,5\mathrm{.}247,6\mathrm{.}378],[$Cluster $2,5\mathrm{.}247,0,5\mathrm{.}832],[$Cluster $3,5\mathrm{.}378,5\mathrm{.}832,0]]$

$\backslash$table$[[,$Within$-$Cluster Summary$],[,$Size,Average Distance$],[$Cluster $1,62,3\mathrm{.}355],[$Cluster $2,65,3\mathrm{.}999],[$Cluster $3,51,3\mathrm{.}483],[$Total$,178,3\mathrm{.}627]]$

$k=4$

$\backslash$table$[[,$Inter$-$Cluster Distances$],[,$Cluster $1,$Cluster $2,$Cluster $3,$Cluster $4],[$Cluster $1,0,5\mathrm{.}245,6\mathrm{.}067,4\mathrm{.}253],[$Cluster $2,5\mathrm{.}245,0,5\mathrm{.}133,4\mathrm{.}289],[$Cluster $3,6\mathrm{.}067,5\mathrm{.}133,0,6\mathrm{.}034],[$Cluster $4,4\mathrm{.}253,4\mathrm{.}299,6\mathrm{.}034,0]]$

$\backslash$table$[[,$Within$-$Cluster Summary$],[,$Size,Average Distance$],[$Cluster $1,56,3\mathrm{.}024],[$Cluster $2,45,3\mathrm{.}490],[$Cluster $3,49,3\mathrm{.}426],[$Cluster $4,28,4\mathrm{.}580],[$Total$,178,3\mathrm{.}498]]$

Calculate the average of the ratios of the inter$-$cluster distances to the within cluster distances for the values $k=2,3,4.($Round your answers to two decimal places.$)k=2$

$k=2k=3k=4$

Which value of $k$ is the most appropriate to categorize these wines