Statistics And Probability Question 320
Question: The mean of n times is $ \overline{x} $ . If the first terms is increased by 1, second by 2 and so on, then new mean is
Options:
A) $ \bar{x}+n $
B) $ \bar{x}+\frac{n}{2} $
C) $ \bar{x}+\frac{n+1}{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] 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}+\frac{1}{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}. $
BETA
