The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.

You are watching: Geometric mean of 8 and 18


Example: What is the Geometric Mean of 2 and 18?

First we multiply them: 2 × 18 = 36Then (as there are two numbers) take the square root: √36 = 6

In one line:

Geometric Mean of 2 and 18 = √(2 × 18) = 6

It is like the area is the same!

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Example: What is the Geometric Mean of 10, 51.2 and 8?

First we multiply them: 10 × 51.2 × 8 = 4096Then (as there are three numbers) take the cube root: 3√4096 = 16

In one line:

Geometric Mean = 3√(10 × 51.2 × 8) = 16

It is like the volume is the same:

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Example: What is the Geometric Mean of 1, 3, 9, 27 and 81?

First we multiply them: 1 × 3 × 9 × 27 × 81 = 59049Then (as there are 5 numbers) take the 5th root: 5√59049 = 9

In one line:

Geometric Mean = 5√(1 × 3 × 9 × 27 × 81) = 9

I can"t show you a nice picture of this, but it is still true that:

1 × 3 × 9 × 27 × 81 = 9 × 9 × 9 × 9 × 9


Example: What is the Geometric Mean of a Molecule and a Mountain

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Using scientific notation:

A molecule of water (for example) is 0.275 × 10-9 mMount Everest (for example) is 8.8 × 103 m

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Example: you want to buy a new camera.

One camera has a zoom of 200 and gets an 8 in reviews,The other has a zoom of 250 and gets a 6 in reviews.

Comparing using the usual arithmetic mean gives (200+8)/2 = 104 vs (250+6)/2 = 128. The zoom is such a big number that the user rating gets lost.

But the geometric means of the two cameras are:

√(200 × 8) = 40√(250 × 6) = 38.7...

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So, even though the zoom is 50 bigger, the lower user rating of 6 is still important.