 # Geometric Mean and its characteristics

• November 1, 2021

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## Geometric Mean:

It is about finding the average from a set of numbers. The main fundamental of the geometric mean is to multiply the numbers or parts and then find out the square root of the total number of parts, i.e., n. It is used to find the mean of a data set which is later measurable in different units. The formula of Geometric Mean can be written as:

(nπi=1ai)1/n or simply as N√(x1*x2*x3*x4….xn)

## Arithmetic Mean:

The arithmetic mean is also the same as Geometric Mean but different in calculating the process. Arithmetic Mean is simply defined as adding up the total numbers or parts and dividing it by the total numbers or parts depicted within the problem. The formula can be written as:

1/n.nΣi=1ai

## Harmonic Mean:

The Harmonic Mean is generally the same as the Arithmetic Mean but has two more extra steps. It is finding the multiplicative inverse of each number, i.e., for x, it would be 1/x or x-1. After that, we have to add up and divide the same as we did in the arithmetic mean. After that, we have to take that inverse too. The formula of Harmonic Mean can be written as:

(1/n.nΣi=1ai-1)-1

### Calculating Geometric Mean with the help of an example

Let us calculate the Geometric Mean of a set of numbers: 1, 5, 9, 13 and 27

Solution: The Geometric Mean of the set of numbers 1, 5, 9, 13, and 27 can be known using the formula: N√(x1*x2*x3*x4….xn)

Thus, there are 5 numbers, and the Geometric Mean of the set is 6.91.

## What are the benefits of using Geometric Mean?

The different benefits of the Geometric Mean are as follows.

• Fixed Value – It always has a fixed value. They are not quite flexible and have rigid values. Since they follow the geometric mean method, the values remain fixed.
• Dependent on Observations – The method is generally dependent on numbers and different observations of number series.
• Low Impact Level – With different values oversampling, the fluctuations don’t have a major impact on the Geometric Mean.
• Helps in the easy calculation – Geometric Mean helps in easily identifying the changes. This, in general, helps in finding out the average concerning ratios and percentages.
• Mathematical Interpretation – Geometric Mean is useful in finding out calculations based on algebra or different mathematical concepts.
• Major preference over small values – Using Geometric Mean, the higher level of importance is given to smaller numbers, whereas the larger numbers are given no significance.
• Multiple Usages - It is used in multiple calculations. For, e.g., it helps in finding out percentages, ratios, and averages. It can also be used for calculation over the rise and fall of growth rates.

## Drawbacks of using Geometric Mean

There are a few drawbacks of using Geometric Mean, and they are as follows.

• Difficult in Calculating due to high complexity – This method is quite difficult to follow. Individuals must have good knowledge of logarithms, ratios, and percentages to figure out the calculations. It is a less-used method due to all the complicated processes involved with it. Thus, individuals should have a good grasp of mathematical concepts for utilizing this method.
• Cannot use negative value or zero – Geometric Mean cannot be utilized using numbers that have a negative value or are zero. Eventually, we also cannot use this method where the negative values are also odds.

These are a few basic points regarding Geometric Mean. To find out more about Geometric Mean or Arithmetic Progression, do get in touch with Cuemath. It is an online platform that excels in teaching maths and coding.