A) \[\frac{{\bar{x}}}{\alpha }\]
B) \[\frac{\bar{x}+10}{\alpha }\]
C) \[\frac{\bar{x}+10\alpha }{\alpha }\]
D) \[\alpha \bar{x}+10\]
Correct Answer: C
Solution :
Let\[{{x}_{1}},\,\,{{x}_{2}},\,\,...,\,\,{{x}_{n}}\]be \[n\] observations. Then, \[\bar{x}=\frac{1}{n}\Sigma {{x}_{i}}\] let \[{{y}_{i}}=\frac{{{x}_{i}}}{\alpha }+10\] Then, \[\frac{1}{n}\sum\limits_{i=1}^{n}{\frac{1}{\alpha }}\left( \frac{1}{n}\Sigma {{x}_{i}} \right)+\frac{1}{n}(10n)\] \[\Rightarrow \] \[\bar{y}=\frac{1}{\alpha }\bar{x}+10\] \[\Rightarrow \] \[\bar{y}=\frac{\bar{x}+10\alpha }{\alpha }\]
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