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Unlike a arithmetic mean, the geometric mean takes the product of the values and then the $n$th root, where $n$ is the number of values. $\text{Mean}=\sqrt[n]{a_1\cdot a_2\cdot ...\cdot a_n}$ For example, the geometric mean of $2,$ $4$ and $8$ is: $\sqrt[3]{2\cdot4\cdot8}=\sqrt[3]{64}=4.$ When calculating the geometric mean of two values, it can be interpret as a rectangle and square with the same area.
The side length of the square can be calculated by taking the square root of the area. $s=\sqrt{2\cdot4.5}=\sqrt{9}=3$ Therefore, the geometric mean of $2$ and $4.5$ is $3.$