Geometric mean of $$$2$$$, $$$19$$$

Find the geometric mean of $$$2$$$, $$$19$$$.

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 $$$\left(2\right)\cdot \left(19\right) = 38$$$.

Therefore, the geometric mean is $$$\sqrt{38}$$$.

The geometric mean is $$$\sqrt{38}\approx 6.164414002968976$$$A.