Geometric mean of $$$5$$$, $$$16$$$

Find the geometric mean of $$$5$$$, $$$16$$$.

The geometric mean of data is given by the formula $$$\left(\prod_{i=1}^{n} x_{i}\right)^{\frac{1}{n}}$$$, where $$$n$$$ is the number of values and $$$x_i, i=\overline{1..n}$$$ are the values themselves.

Since we have $$$2$$$ points, $$$n = 2$$$.

The product of the values is $$$\left(5\right)\cdot \left(16\right) = 80$$$.

Therefore, the geometric mean is $$$\sqrt{80} = 4 \sqrt{5}$$$.

The geometric mean is $$$4 \sqrt{5}\approx 8.944271909999159$$$A.