51.

$$\begin{gathered} \mathrm{If} \sum _{\mathrm{i} = 1}^{\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}} - \mathrm{a}\right) = \mathrm{n} \mathrm{and} \sum _{\mathrm{i} = 1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}} - \mathrm{a}\right)}^2 = \mathrm{na}, \left(\mathrm{n}, {\mathrm{a}}_1 > 1\right) \mathrm{then} \mathrm{the} \mathrm{standard} \mathrm{deviation} \mathrm{of} \mathrm{n} \\ \mathrm{observations} {\mathrm{x}}_1, {\mathrm{x}}_2, ... {\mathrm{x}}_{\mathrm{n}} \mathrm{is} : \end{gathered}$$

• a - 1

• $\sqrt{\mathrm{n}\left(\mathrm{a} - 1\right)}$

• $\mathrm{n}\sqrt{\left(\mathrm{a} - 1\right)}$

• $\sqrt{\left(\mathrm{a} - 1\right)}$