Note: For this question to be marked you must return the

entire exam paper question booklet together with your

answer sheet.

Your objective is to use the $K-$means clustering algorithm

to assign $7$ data points to $2$ clusters.

$($a$)$ In Step $1$ these data points are randomly assigned

to $2$ clusters. Complete Step $2$ on the diagram

by calculating the cluster centroids for the Class

A and $B$ data points. Clearly mark each cluster

centroid on the diagram with an $"A^{\text{'}}$ for the Cluster

A centroid, and a $"$B$"$ for the Cluster B centroid.

Also fill in the coordinates of each centroid in the

prowided space.

$($b$)$ Given the centroids of Step $2,$ complete Step $3$ on

the diagram by re$-$assigning the data points to the

appropriate cluster centroid. $($Note: For cluster A$,$

you can color in these points, for cluster B you can

leave the points as they are.$]$

$($c$)$ Complete Step $4$ on the diagram by re$-$calculating

the new cluster centroids. Clearly mark each

cluster centroid with an $"A^{\text{'}}$ or $"B^{\text{'}\text{'}}$ on the dlagram.

Also fill in the final coordinates of each centroid in

the provided space.