Unlike the arithmetic mean, the geometric mean uses the product of a set of numbers rather than their sum. The geometric mean is the \(n\)-th root of the product of \( n\) numbers.

Thus, the geometric mean of \( \{81, 1, \frac{1}{3} \} \) is \( \sqrt[3]{81\times 1 \times \frac{1}{3}} = \sqrt[3]{27} = 3 \).

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