In a set of 2n observations the geometric mean of first 'n' observations is 81 and the geometric mean of remaining n-observations is 16 then the geometric mean of all 2n observations is
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If two groups have the same number of observations, their combined Geometric Mean is simply the Geometric Mean of their individual Geometric Means: $G = \sqrt{G_{1} \cdot G_{2}}$. This shortcut saves you from dealing with $n$ and $2n$ during the exam.