+33614 The geometric mean only applies to positive numbers.
It has a geometric interpretation. Image a rectangle with sides 10 and 30. It has an area of 300. A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.
Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths 3√(u*v*w), etc.
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+128407 The geometric mean of N numbers is just the Nth root of their product.....so, since we have two numbers, we have....
√(10 * 30) = √300 = 10√3
+118608 SO
The geometric mean of 7,6,8 and 2
is it $$\sqrt[4]{7*6*8*2}$$
$${\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}^{\left({\mathtt{0.25}}\right)} = {\mathtt{5.091\: \!459\: \!790\: \!043\: \!661}}$$
what happen if there is negative numbers?
+33614 The geometric mean only applies to positive numbers.
It has a geometric interpretation. Image a rectangle with sides 10 and 30. It has an area of 300. A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.
Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths 3√(u*v*w), etc.
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