A) \[\frac{{\bar{x}}}{a}\]
B) \[\frac{\bar{x}+10}{a}\]
C) \[\frac{\bar{x}+10a}{a}\]
D) \[a\bar{x}+10\]
Correct Answer: C
Solution :
[c] 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, \[\frac{1}{n}\sum\limits_{i=1}^{n}{{{y}_{i}}}=\frac{1}{\alpha }\left( \frac{1}{n}\sum\limits_{i=1}^{n}{{{x}_{i}}} \right)+\frac{1}{n}(10n)\] \[\Rightarrow \bar{y}=\frac{1}{\alpha }\bar{x}+10=\frac{\bar{x}+10\alpha }{\alpha }\]
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