$4.[$Clustering$,$ K$-$means$]$

We want to cluster the following dataset into K $=3$ clusters using the K$-$means

algorithin:

I $(2)=10,2(3)=16,$

x $(4)=20,$

x $(5)=26,$

where each $2*)$ is an one$-$dimensional data point.

$($a$)$ Please analyze how K$-$means updates the centroids of the clusters if we initialize

the centroids of the K $=3$ clusters by: f$1=2,$ H$2=3,$ and us $=4.$ What

values would the centroids $(41,$ M$2,|3)$ converge to when K$-$means determines?

Please show the centroid locations at each iteration of K$-$means. $($If no points are assigned to a cluster at a given iteration, do NOT update$$its$$centroid$).$