The Geometric mean is a special types of average where we calculate the root of the product of a value of a set of observations. It is usually used to define various types of growth rates such as population growth, interest rates etc.
Formula of geometric mean
By definition, the formula is as below,
G.M =
![{displaystyle left(prod _{i=1}^{n}x_{i}right)^{frac {1}{n}}={sqrt[{n}]{x_{1}x_{2}cdots x_{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/026cae6801f672b9858d55935ec7397183dc3a36 "geomatric mean formula")
Where, G.M=geometric mean
n=number of observations
Mathematical example
What is the geometric mean of 2, 3, and 6?
First, multiply the numbers together and then take the cubed root (because there are three numbers) = (2*3*6)1/3 = 3.30
Note: The power of (1/3) is the same as the cubed root 3√. To convert a nth root to this notation, just change the denominator in the fraction to whatever “n” you have. So,
- 5th root = to the (1/5) power
- 12th root = to the (1/12) power
- 99th root = to the (1/99) power.…….
The situation where we use geometric mean
The geometric mean is the most appropriate measure of location when,
It is appropriate for averaging the ratios of change, for average of proportions, etc.
Advantages
There are some merits as following,
- Geometric mean is least affected by extreme values.
- It is based on all observations of the set.
- It is suitable for further algebraic treatment.
Disadvantages
There are some demerits as following,
- Geometric mean calculation is somewhat complicated.
- It cannot be calculated if any of the values in the set is zero.
- If any one or more values are negative, either it will not be calculable, or an absurd value will be obtained.