Statistics And Probability Question 49
Question: The average of n numbers $ x_1,,x_2,,x_3,,……,,x_{n} $ is M. If $ x_{n} $ is replaced by $ {x}’ $ , then new average is
[DCE 2000]
Options:
A) $ M-x_{n}+{x}’ $
B) $ \frac{nM-x_{n}+{x}’}{n} $
C) $ \frac{(n-1)M+{x}’}{n} $
D) $ \frac{M-x_{n}+{x}’}{n} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ M=\frac{x_1+x_2+x_3……x_{n}}{n} $ i.e., $ \underset{n}{\mathop{\underline{\begin{matrix} nM \\ nM-x_{n} \\ nM-x_{n}+{x}’ \\ \end{matrix}}}},\begin{matrix} = \\ = \\ = \\ \end{matrix}\underset{n}{\mathop{\underline{\begin{matrix} x_1+x_2+x_3+……{x_{n-1}}+x_{n} \\ x_1+x_2+x_3+……{x_{n-1}}\ \ \ \ \ \\ x_1+x_2+x_3+……{x_{n-1}}+{x}’ \\ \end{matrix}}}}, $ \ New average $ =\frac{nM-x_{n}+{x}’}{n} $ .
BETA
