Statistics-And-Probability Question 605
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
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:
[b] $ M=\frac{x_1+x_2+x_3…x_{n}}{n} $ $ nM=x_1+x_2+x_3+…+{x_{n-1}}+x_{n} $ i.e., $ nM-x_{n}=x_1+x_2+x_3+…+{x_{n-1}} $ $ \frac{nM-x_{n}+x’}{n}=\frac{x_1+x_2+x_3+…{x_{n-1}}+x’}{n} $
$ \therefore $ New average $ =\frac{nM-x_{n}+x’}{n} $
BETA
