Geometric Average Formula
A mean or average indicates the central tendency of a set of numbers. The geometric average commonly referred to as geometric mean (or GM) is a very interesting type of special mean that indicates the central tendency of a set of numbers by using the product of their values. The geometric mean is an average but it is calculated in a special way. It is defined as the n^{th} root of the product of n numbers. Let us learn about the geometric average formula in detail.
What is the Geometric Average Formula?
The geometric average formula or geometric mean formula is calculated as we find out the product of the given numbers and then calculate the n^{th} root of the result. The geometric average formula or geometric mean formula is given as:
Geometric Mean or Geometric Average = \( \sqrt[n]{x_1·x_2·x_3·...·x_n}\)
where,
 n = Total number of terms
 x_{1},_{ }x_{2},_{ }x_{3}, . . . , x_{n} = Different n terms

Example 1: Find the geometric average of 2, 3, and 6 by using geometric average formula.
Solution:
To find: Geometric average for the given set.
Given:
Number of terms, n = 3
Terms = 2, 3, 6
Using Geometric Average or Geometric Mean Formula,
Geometric Mean = \( \sqrt[3]{2·3·6}\)
= 3.30
Answer: Geometric mean = 3.30

Example 2: Calculate the difference between the arithmetic mean and the geometric mean of numbers 2 and 32 by using the geometric average formula.
Solution:
To find: Difference between the arithmetic mean and geometric mean
Given:
Terms = 2, 32
Number of terms = 2
Arithmetic mean = (2 + 32)/2
= 17
Using Geometric mean Formula,
Geometric mean = \( \sqrt{2 \times 32}\)
= \( \sqrt{64}\)
= 8
Difference between arithmetic mean and geometric mean = 17  8
Answer: Difference between the arithmetic mean and geometric mean = 9