Question $1$: Consider a one$-$dimensional dataset with three natural clusters. The first cluster contains consecutive integers $\{1...5\}.$ The second cluster contains consecutive integers $\{8...12\}.$ The third cluster contains data points $\{24,28,32,36,40\}.$ Apply the k$-$means algorithm with initial centers of $1,11,$ and $28.$ Does the algorithm determine the correct clusters?

Question $2$: As in Question $1,$ if the initial center is changed to $1,2,$ and $3,$ will the algorithm find the correct clusters? what does this tell you?