Statistics And Probability Question 1
Question: The mean of n items is $ \bar{x} $ . If the first term is increased by 1, second by 2 and so on, then new mean is
[DCE 1998]
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:
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} $ .
BETA
