Solve this using RStudio code:

Consider the following data set with $n=9$ observations and $p=4$ variables. The data set is given next

as well as the distance matrix using the "Euclidean" metric. The symbol $x$ in the matrix below is to be calculated later.

A$)$ In the distance matrix there is a missing distance $x.$ Compute its value and write it$.$

B$)$ Consider two arbitrary clusters GH and ABCDEFI. Compute and write the dissimilarity between these clusters under "average" linkage.

C$)$ Using the above data $x,$ the $R$ command $,$ centers$=3)$ was run, with the following output

$>$ KM$cluster

$[1]2,1,2,2,3,3,1,3,3$

There is interest in determining the center of the cluster identified with the label $1.$ By computing this center manually or otherwise, identify which of the following is the correct centroid of this

cluster

D$)$ Still using the above data $x,$ the $R$ command pam $(x=x,k=3)PM$ was run, with the following output:

$>$ PM$id$.$med

$[1]1,7,6$

Identify correctly the medoids yielded by this cluster analysis.