Bargraphs are lattice paths in $\mathbb{N}_0^2$ that start at the origin and end upon their first return to the $x$-axis. Each bargraph is represented by a sequence of column heights $\pi_1\pi_2\cdots\pi_m$ such that column $j$ contains $\pi_j$ cells. In this paper, we study the number of bargraphs with $n$ cells and $m$ columns according to the distribution for the statistic that records the number of times a given shape lies entirely within a bargraph for various small shapes.