A) \[\frac{\overline{X}}{\alpha }\]
B) \[\frac{\overline{X}+10}{\alpha }\]
C) \[\frac{\overline{X}+10\,\alpha }{\alpha }\]
D) \[\alpha \overline{X}+10\]
Correct Answer: C
Solution :
Let\[{{x}_{1}},{{x}_{2}},...{{x}_{n}}\]be n observations. Then, \[\overline{X}=\frac{1}{n}\Sigma {{y}_{i}}\] Let\[{{y}_{i}}=\frac{{{x}_{i}}}{\alpha }+10\](according to the given condition) Then, \[\overline{Y}=\frac{1}{n}\Sigma {{y}_{i}}\] \[=\frac{1}{n}\Sigma \left( \frac{{{x}_{i}}}{\alpha }+10 \right)\] \[=\frac{1}{\alpha }\left( \frac{1}{n}\Sigma {{x}_{i}} \right)+\frac{1}{n}(10n)\] \[=\frac{1}{\alpha }\overline{X}+10\] \[\Rightarrow \] \[\overline{Y}=\frac{\overline{X}+10\alpha }{\alpha }\]
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