Geometric mean of $$$8$$$, $$$16$$$
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Find the geometric mean of $$$8$$$, $$$16$$$.
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 $$$\left(8\right)\cdot \left(16\right) = 128$$$.
Therefore, the geometric mean is $$$\sqrt{128} = 8 \sqrt{2}$$$.
Answer
The geometric mean is $$$8 \sqrt{2}\approx 11.31370849898476$$$A.