jmc

The least member of the set is either $\frac{3}{7}$ or $\frac{6}{16}$, since these two members are the only ones smaller than 1. Since $\frac{3}{7}=\frac{6}{14}$, $\frac{6}{16}$ is the smaller of the two. The greatest member is either $\frac{4}{3}$ or $\frac{11}{8}$. Since $\frac{4}{3}=\frac{32}{24}$ and $\frac{11}{8}=\frac{33}{24}$, $\frac{11}{8}$ is the larger of the two. Thus, the desired difference is $\frac{11}{8}-\frac{6}{16}=\frac{22}{16}-\frac{6}{16}=\boxed{1}$.