Geometric mean facts for kids

The geometric mean is a special type of average that helps represent a group of numbers. You find it by multiplying all the numbers together and then taking the "nth root" of that product. The "nth root" means if you have 3 numbers, you take the third (cube) root; if you have 5 numbers, you take the fifth root, and so on.

Most people think of the arithmetic mean when they hear "average." That's where you add all the numbers and divide by how many there are. The geometric mean is almost always smaller than the arithmetic mean, but sometimes they can be the same. This type of average is often used in subjects like finance and statistics.

When to Use the Geometric Mean

The geometric mean is super useful when you're dealing with things that grow or change over time, like interest rates or population growth. It gives you a good idea of the typical growth factor.

When Not to Use It

It doesn't make sense to calculate the geometric mean if any of your numbers are zero. That's because if you multiply by zero, the whole product becomes zero, and the root of zero is always zero, which doesn't tell you much about the other numbers.

It's also usually not a good idea to use it with negative numbers. And you won't use it for complex numbers, because finding the root of a complex number can have more than one answer, which makes the geometric mean unclear.

Images for kids

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  Example of the geometric mean: l_g (red) is the geometric mean of l_1 and l_2.

See also

In Spanish: Media geométrica para niños