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

• A

  ${\mathrm{x}}_1$

• B

  ${\mathrm{x}}_{51}$

• C

  $\frac{{\mathrm{x}}_1+{\mathrm{x}}_2+\cdots +{\mathrm{x}}_{101}}{101}$

• D

  ${\mathrm{x}}_{50}$