To calculate geometric mean for a set of numbers, multiply the numbers together, and take the nth root of this product. Only calculate the geometric mean when all of the numbers in a set are nonzero and positive.
- Multiply the numbers in the data set together
Multiply the numbers in the data set together. Consider the example of a set of numbers: 5, 8, 2, 8, and 10. Multiply these five numbers together for a product of 6,400.
- Take the nth root of the product
Count the numbers in the set of data (in the example, there are five). Take the nth root of the product that you calculated in Step 1. Take the fifth root of 6,400 to find the geometric mean of the set of numbers in the example, which is 5.771.
- Use the geometric mean for appropriate applications
Calculate the geometric mean for sets of data that involve items you want to multiply together. Use the geometric mean to find average rates of return and other numbers helpful in investment scenarios, because those numbers are generally percentages rather than reflections of counting. Use the arithmetic mean (in which you add numbers and divide by the number of data present) for items involving counting rather than multiplying.