The geometric mean ratio is calculated by following these steps:
1. Calculate the Product:
- Multiply all the values together. This gives you the product of all the numbers in your dataset. For example, if you have the numbers 2, 8, and 16, their product is 2 8 16 = 256.
2. Calculate the Nth Root:
- Find the nth root of the product. Here, 'n' represents the total number of values you multiplied together. In our example, we multiplied three values (2, 8, and 16), so n = 3. We need to find the cube root (third root) of 256. The cube root of 256 is approximately 6.35.
Here's a summarized breakdown in a table:
| Step | Description | Example (2, 8, 16) |
|---|---|---|
| 1. Product | Multiply all the values together. | 2 8 16 = 256 |
| 2. Nth Root | Find the nth root of the product (where n is the number of values). | ∛256 ≈ 6.35 |
Practical Insights
- The geometric mean is especially useful when dealing with rates or ratios that are multiplied together, like growth rates or percentage changes.
- Unlike the arithmetic mean, the geometric mean is not heavily affected by extreme values, so it can be more representative for datasets with outliers.
Example
Let's say you have percentage increases of 10%, 20%, and 30%. To use the geometric mean, first you need to express them as numbers: 1.10, 1.20, and 1.30.
- Multiply them: 1.10 1.20 1.30 = 1.716
- Find the cube root (since there are 3 numbers): ∛1.716 ≈ 1.196
The average percentage increase in this case is approximately 19.6%, calculated from the root (1.196 - 1)*100.
