Let $G$ be a graph and let $f:V(G)\rightarrow \{1,2,\dots,n\}$ be a function such that the label of the edge $uv$ is $\frac{f(u)+f(v)}{2}$ or $\frac{f(u)+f(v)+1}{2}$ according as $f(u)+f(v)$ is even or odd and $f(V(G))\cup \{f^*(e):e\in E(G)\}\subseteq \{1,2,\dots,n\}$. If $n$ is the smallest positive integer satisfying these conditions together with the condition that all the vertex and edge labels are distinct and there is no common vertex and edge labels, then $n$ is called the super mean number of a graph $G$ and it is denoted by $S_m(G)$. In this paper, we find the bounds for super mean number of some standard graphs.