Statistics And Probability Question 402
Question: Let $ \bar{x} $ be the mean of n observations $ x_1,x_2,…x_{n}, $ if $ (a-b) $ is added to each observation, then what is the mean of new set of observations?
Options:
A) 0
B) $ \bar{x} $
C) $ \bar{x}-(a-b) $
D) $ \bar{x}+(a-b) $
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Answer:
Correct Answer: D
Solution:
[d] Let $ \bar{x} $ is the mean of n observation $ x_1,x_2,…x_{n}. $
$ \Rightarrow \bar{x}=\frac{x_1+x_2+x_3+…+x_{n}}{n} $ Now (a - b) is added to each term.
$ \therefore $ New mean $ =\frac{x_1+(a-b)+x_2+(a-b)+…+x_{n}+(a-b)}{n} $ $ =\frac{x_1+x_2+…+x_{n}}{n}+\frac{n(a-b)}{n} $ $ =\bar{x}+(a-b) $
BETA
