Consider any set of observations ${\mathrm{x}}_1,{\mathrm{x}}_2,{\mathrm{x}}_3,\dots ,{\mathrm{x}}_{101}$. It is given that ${\mathrm{x}}_1<{\mathrm{x}}_2<{\mathrm{x}}_3<\dots <{\mathrm{x}}_{100}<{\mathrm{x}}_{101}$; then the mean deviation of this set of observations about a point k is minimum when k equals

Mean deviation is minimum when it is considered about an item equidistant from the beginning and the end, i.e., the median. In this case, the median is $\frac{101+1}{2}$ th, i.e., 51 st item, i.e., x₅₁.