Let A(4, 7, 8), B(2, 3, 4) and C(2, 5, 7) be the vertices of $∆\mathrm{ABC}.$ The length of the median AD is 

The midpoint of $BC$ is $\left(\frac{2+2}{2},\frac{3+5}{2},\frac{4+7}{2}\right)=\left(2,4,\frac{11}{2}\right)$

The distance between $A$ and $D$ is length of the median is $AD$ is $\sqrt{{\left(2-4\right)}^2+{\left(4-7\right)}^2+{\left(\frac{11}{2}-8\right)}^2}=\sqrt{4+9+\frac{25}{4}}=\frac{\sqrt{77}}{2}$