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Question: Answered & Verified by Expert
If $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$ are the sizes, $\mathrm{G}_{1}$ and $\mathrm{G}_{2}$ the geometric means of two series respectively, then which one of the following expresses the geometric mean (G) of the combined series?
MathematicsStatisticsNDANDA 2008 (Phase 1)
Options:
  • A $\log \mathrm{G}=\frac{\mathrm{n}_{1} \mathrm{G}_{1}+\mathrm{n}_{2} \mathrm{G}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
  • B $\log \mathrm{G}=\frac{\mathrm{n}_{2} \log \mathrm{G}_{1}+\mathrm{n}_{1} \log \mathrm{G}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
  • C $\mathrm{G}=\frac{\mathrm{n}_{1} \log \mathrm{G}_{1}+\mathrm{n}_{2} \log \mathrm{G}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
  • D None of the above
Solution:
1230 Upvotes Verified Answer
The correct answer is: $\log \mathrm{G}=\frac{\mathrm{n}_{2} \log \mathrm{G}_{1}+\mathrm{n}_{1} \log \mathrm{G}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
Geometric Mean of combined series is given by the expression
$\log \mathrm{G}=\frac{\mathrm{n}_{2} \log \mathrm{G}_{1}+\mathrm{n}_{1} \log \mathrm{G}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$

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