Geometric Mean Formula
Before beginning with the geometric mean formula, let us recall what is the geometric mean. The geometric mean is the central tendency of a set of numbers calculated using the product of their values. It can be defined as the n^{th} root of the product of n numbers. The geometric mean is also known as geometric average. Let us learn the geometric mean formula with a few solved examples.
Formula to Find Geometric Mean
Suppose we have n observation values: \(x_1, x_2, ..., x_n\). Geometric mean formula can be calculated as,
\[\text{Geometric Mean} = \sqrt[n]{x_1 x_2 ... x_n}\]
Solved Examples Using Geometric Mean Formula

Example 1:
Find the geometric average of 2, 4, and 8?
Solution:
The number of observations, n = 3
Using the geometric mean formula,
\(\begin{align}\text{Geometric Mean} &= \sqrt[3]{2 \times 4 \times 8}\\&=\sqrt[3]{64}\\&=4\end{align}\)
Answer: Geometric mean of given observations = 4.

Example 2:
Find the sum of geometric mean and the arithmetic mean of 9 and 4.
Solution:
Using the geometric mean formula,
\(\begin{align}\text{Geometric Mean} &= \sqrt{9 \times 4}\\&=\sqrt{36}\\&=6\end{align}\)
Using the arithmetic mean formula,
\(\begin{align}\text{Arithmetic Mean} &= \frac{9 + 4}{2}\\&=\frac{13}{2}\\&=6.5\end{align}\)
Geometric Mean + Arithmetic Mean = 6 + 6.5 = 12.5Answer: Sum of geometric mean and the arithmetic mean of 9 and 4 = 12.5.