A) \[\bar{x}+n\]
B) \[\bar{x}+\frac{n}{2}\]
C) \[\bar{x}+\frac{n+1}{2}\]
D) None of these
Correct Answer: C
Solution :
Let \[{{x}_{1}},{{x}_{2}},\]....... \[{{x}_{n}}\] be n items. Then, \[\bar{x}=\frac{1}{n}\Sigma {{x}_{i}}\] Let \[{{y}_{1}}={{x}_{1}}+1,\ {{y}_{2}}={{x}_{2}}+2,\ {{y}_{3}}={{x}_{3}}+3,..,{{y}_{n}}={{x}_{n}}+n\] Then the mean of the new series is \[\frac{1}{n}\Sigma {{y}_{i}}=\frac{1}{n}\sum\limits_{i=1}^{n}{({{x}_{i}}+i)}\] \[=\frac{1}{n}\sum\limits_{i=1}^{n}{{{x}_{i}}}+\frac{1}{n}(1+2+3+.....+n)\] \[=\bar{x}+\frac{1}{n}.\frac{n(n+1)}{2}\]\[=\bar{x}+\frac{n+1}{2}\].
You need to login to perform this action.
You will be redirected in
3 sec
