Definition
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. By formula,
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)
Where, G.M=geometric mean
n=number of observations
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 of geometric mean
There are some merits of the geometric mean-
- 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 of geometric mean
There are some demerits of the geometric mean-
- 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 geometric mean will not be calculable, or an absurd value will be obtained.
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