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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?
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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
$\log \mathrm{G}=\frac{\mathrm{n}_{2} \log \mathrm{G}_{1}+\mathrm{n}_{1} \log \mathrm{G}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
$\log \mathrm{G}=\frac{\mathrm{n}_{2} \log \mathrm{G}_{1}+\mathrm{n}_{1} \log \mathrm{G}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
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