Consider the following set of one$-$dimensional points: $\{5,7,16,18,24,26,34,38\}.$

Suppose we apply k$-$means clustering to obtain three clusters, A$,$ B$,$ and C$.$ If the three initial centroids are located at $(15,25,31),$ respectively, show the clustering results after assigning each point to their closest centroid.

Based on your answer in part $($a$),$ recompute the new locations of the centroids for A$,$ B$,$ and C$.$ Compute also their overall SSE.