A) \[M-{{x}_{n}}+x'\]
B) \[\frac{nM-{{x}_{n}}+x'}{n}\]
C) \[\frac{(n-1)M+x'}{n}\]
D) \[\frac{M-{{x}_{n}}+x'}{n}\]
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 \[=\frac{nM-{{x}_{n}}+x'}{n}\]
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