Mathematics - Statistics Question with Solution | TestHub

Let $x_1, x_2,\dots ,x_n$ be $n$ observations.

Then, $\overline{X}=\frac{1}{n}\Sigma x_i$

Let $y_i=\frac{x_i}{\alpha }+10$

Then. $\frac{1}{n}\sum _{i=1}^n{y}_i=\frac{1}{\alpha }\left(\frac{1}{n}\Sigma x_i\right)+\frac{1}{n}\left(10n\right)$

$\Rightarrow {\overline{X}}_{\text{new}}=\frac{1}{\alpha }\overline{X}+10=\frac{\overline{X}+10\alpha }{\alpha }$

Hence option (c) is correct.