Geometric mean of $$$12$$$, $$$15$$$
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Find the geometric mean of $$$12$$$, $$$15$$$.
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 $$$\left(12\right)\cdot \left(15\right) = 180$$$.
Therefore, the geometric mean is $$$\sqrt{180} = 6 \sqrt{5}$$$.
Answer
The geometric mean is $$$6 \sqrt{5}\approx 13.416407864998738$$$A.