A) 0
B) \[\bar{x}\]
C) \[\bar{x}-(a-b)\]
D) \[\bar{x}+(a-b)\]
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 \[=\frac{{{x}_{1}}+(a-b)+{{x}_{2}}+(a-b)+...+{{x}_{n}}+(a-b)}{n}\] \[=\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{n}}}{n}+\frac{n(a-b)}{n}\] \[=\bar{x}+(a-b)\]
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