Geometric mean of $$$7$$$, $$$21$$$

Find the geometric mean of $$$7$$$, $$$21$$$.

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 $$$\left(7\right)\cdot \left(21\right) = 147$$$.

Therefore, the geometric mean is $$$\sqrt{147} = 7 \sqrt{3}$$$.

The geometric mean is $$$7 \sqrt{3}\approx 12.124355652982141$$$A.