Geometric mean of $$$19$$$, $$$27$$$

Find the geometric mean of $$$19$$$, $$$27$$$.

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 $$$\left(19\right)\cdot \left(27\right) = 513$$$.

Therefore, the geometric mean is $$$\sqrt{513} = 3 \sqrt{57}$$$.

The geometric mean is $$$3 \sqrt{57}\approx 22.649503305812249$$$A.