Consider the following dataset, consisting of fifteen instances A$..\mathrm{.}0$ each represented with two numeric attributes $(x_1,x_2),$ shown on the left, and plotted on the right:

$A$:$(1,4),B$:$(2,4),C$:$(3,4)$

$D$: $(1,6),E$:$(2,6),F$:$(3,6)$

$G$: $(1,7),H$:$(2,7),$I:$(3,7)$

$J$:$(1,8),K$:$(2,8),L$:$(3,8)$

$M$:$(1,9),N$:$(2,9),0$:$(3,9)$

$($a$)$ Explain how the $K-$means clustering method works. Run the $K-$means al$-$

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