A) \[\overline{X}+n\]
B) \[\overline{X}+\frac{n}{2}\]
C) \[\overline{X}+\frac{n+1}{2}\]
D) None of these
Correct Answer: C
Solution :
(c): \[\overline{X}={{x}_{1}}+{{x}_{2}}+{{x}_{3}}+....+{{x}_{n}}\](given) According to question New Mean=\[\frac{\left( {{x}_{1}}+1 \right)+\left( {{x}_{2}}+2 \right)+\left( {{x}_{3}}+3 \right)+...+\left( {{x}_{n}}+n \right)}{n}\] \[=\frac{{{x}_{1}}+{{x}_{2}}+.....+{{x}_{n}}}{n}+\frac{1+2+3+.....+n}{n}=\overline{X}+\left( \frac{n+1}{2} \right)\]
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