A direct shear test was performed on three identical samples of dry sand. The sample in the shear box has a diameter of $2$ inches. The results are shown in the table below. $($a$)$ Plot the results on a Mohr diagram and determine the Mohr$-$Coulomb strength parameters for the soil. $($b$)$ Based on the results to part a were the samples loose or dense? Explain.

$\backslash$table$[[$Test$,$Normal load $($lb$),$Shear load at failure $($lb$)],[$A$,200,120],[$B$,400,225],[$C$,600,330]]$