Given the building energy usage data from Table $1($see below$)$

Perform k$-$means clustering on 'Energy Usage Index' versus 'Year Built'. Implement the k$-$means cluster technique for $2$ clusters, $3$

clusters $,4$ clusters, and $5$ clusters. Use the Elbow method to identify the optimal number of clusters. To receive full credit, you must

show your detailed work for both the initialization step for $2$ cluster $(k=2),$ and also show your detailed fork for the $1$st iteration of

centroids movement. Then, you should summarize the remaining steps and final result.

Table $1$: Building energy use and attributes data