Geometric mean of $$$14$$$, $$$30$$$
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Find the geometric mean of $$$14$$$, $$$30$$$.
Solution
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 $$$\left(14\right)\cdot \left(30\right) = 420$$$.
Therefore, the geometric mean is $$$\sqrt{420} = 2 \sqrt{105}$$$.
Answer
The geometric mean is $$$2 \sqrt{105}\approx 20.493901531919197$$$A.