Problem $1$ K$-$Means Clustering$(20$ Points$)$:

Given the following table with $8$ examples and use K$-$Means for $K=3$ to cluster the given points. The initial seeds are $(1,1\mathrm{.}5),(3\mathrm{.}5,4\mathrm{.}5)$ and $(5,6).$ Compute the average purity and Entropy for each cluster and the average of each.

$\backslash$table$[[$Individual$,$Variable $1,$Variable $2],[1,1\mathrm{.}0,1\mathrm{.}0],[2,1\mathrm{.}5,2\mathrm{.}0],[3,3\mathrm{.}0,4\mathrm{.}0],[4,5\mathrm{.}0,7\mathrm{.}0],[5,3\mathrm{.}5,5\mathrm{.}0],[6,4\mathrm{.}5,5\mathrm{.}0],[7,3\mathrm{.}5,4\mathrm{.}5],[8,5\mathrm{.}0,5\mathrm{.}5$