A) \[\overline{x}\]
B) \[na\,\overline{x}+nb\]
C) \[a\,\,\overline{x}\]
D) \[a\,\,\overline{x}+b\]
Correct Answer: D
Solution :
Required mean \[=\,\,\frac{(a{{x}_{1}}+b)+(a{{x}_{2}}+b)+...+(a{{x}_{n}}+b)}{n}\] \[=\,\,\,\,\frac{a({{x}_{1}}+{{x}_{2}}+.....+{{x}_{n}})+nb}{n}\] \[=\,\,a\overline{x}+b,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( \because \,\,\,\frac{{{x}_{1}}+{{x}_{2}}+....+{{x}_{n}}}{n}=\overline{x} \right)\]
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