Geometric Mean vs Arithmetic Mean

Difference Between Geometric Mean vs Arithmetic Mean

The Arithmetic mean and Geometric mean are the tools widely used to calculate the returns on investment for investment portfolios in the world of finance. People use the arithmetic mean to report the higher returns which are not the correct measure of calculating the return on investment. Since the return on investment for a portfolio over years is dependent on returns in previous years, Geometric mean is the correct way to calculate the return on investment for a specific time period. Arithmetic mean is better suited in the situation wherein variables being used for calculation of average are not dependent on each other.

Example: Suitability use of Geometric mean vs Arithmetic mean

1. Let’s take an example of return on investment for an amount of $100 over 2 years. Suppose the returns in two years were -50% and +50% in the 1^st and 2^nd Average return calculation by using arithmetic mean will be 0% (Arithmetic mean = (-50%+50%) /2 = 0%)

Which gives a wrong impression that the investor is breaking even on its investment and there is no loss or profit. However, a closer analysis gives the entire different picture of the scenario.

From the above table, we can see that the investment of $100 after -50% and +50% return in year 1 and 2, will be close to $75.Therefore, the investor is not breaking even on its investment as suggested by the arithmetic mean average but he has incurred a loss of $25 after 2 years on its investment. Which is well reflected by using Geometric mean to calculate the return on the investment over 2 years as below:

The geometric mean of returns

Which means the annualized return on the portfolio had been negative 13.40%. The investment position after two years is as below:

Therefore, the Geometric mean shows the true picture of investment that there is a loss in investment with an annualized negative return of -13.40%. Since the return in each year impact the absolute return in next year, geometric mean is a better way to calculate the annualized return on investment.

2. When one needs to calculate the average of variables which are not dependent on each other, Arithmetic means a  suitable tool to calculate the average. Average of marks of a student for 5 subjects can be calculated by the arithmetic mean as scores of the student in different subjects are independent of each other.

Head to Head Comparison between Geometric Mean vs Arithmetic Mean (Infographics)

Below is the top 8 difference between Geometric Mean vs Arithmetic Mean

Key Differences between Geometric Mean vs Arithmetic Mean

Let us discuss some of the major differences between Geometric Mean vs Arithmetic Mean:

• Both Geometric Mean vs Arithmetic Mean are the tools to calculate the returns on investment in finance and also used in other applications such as economics, statistics.
• Arithmetic mean is calculated by dividing the sum of the numbers by number count. However, Geometric means takes into account the compounding effect while calculation.
• The geometric mean is the correct way to calculate the return on investment for a specific time period Since the returns on investment for a portfolio over years are interdependent. However, Arithmetic mean is better suited in the situation wherein variables being used for calculation are not dependent on each other.
• Arithmetic mean is more useful and accurate when it is used to calculate the average of a data set where numbers are not skewed and not dependent on each other. However, in the scenario where there is a lot of volatility in a data set, a geometric mean is more effective and more accurate.
• Arithmetic mean is relatively easier to calculate and use in comparison to Geometric mean, which is relatively complex to calculate.
• The geometric mean is very widely used in the world of finance specifically in a calculation of portfolio returns. However, an Arithmetic mean is not an appropriate tool to use in return calculation.
• The Arithmetic mean of two numbers is always higher than the Geometric mean of the same numbers.

Geometric Mean vs Arithmetic Mean Comparison Table

Let’s look at the top 8 Comparison between Geometric Mean vs Arithmetic Mean

The Basis Of  Comparison Arithmetic Mean vs Geometric Mean	Arithmetic Mean	Geometric Mean Finance for Non Finance Managers Training Course 7 Online Courses | 25+ Hours | Verifiable Certificates | Lifetime Validity Watch The Course Preview
Definition	The arithmetic average of a series of number is the sum of all the numbers in the series divided by the total numbers counts in the series.	Geometric means takes into account the compounding effect during the calculation period. This is calculated by multiplying the numbers in a series and taking the nth root of the multiplication. Where n is the numbers count in series.
Formula	If there are two numbers X and Y in the series than Arithmetic mean = (X+Y)/2	If there are two numbers X and Y in the series than Geometric mean = (XY)^(1/2)
Suitability of Use	Arithmetic means shall be used in a situation wherein the variables are not dependent on each other and data sets are not varying extremely. Such as calculating the average score of a student in all the subjects.	Geometric mean shall be used to calculate the mean where the variables are dependent on each other. Such as calculating the annualized return on investment over a period of time.
Effect of Compounding	Arithmetic mean does not take into account the impact of compounding and therefore it is not best suited to calculate the portfolio returns.	Geometric mean takes into account the effect of compounding, therefore, better suited for calculating the returns.
Accuracy	Use of Arithmetic mean provide more accurate results when the data sets are not skewed and not dependent on each other.	Where there is a lot of volatility in data set, a geometric mean is more effective and more accurate.
Application	Arithmetic mean is widely used in day to day simple calculations with more uniform data set. It is used in economics and statistics very frequently.	The geometric mean is widely used in the world of finance specifically in calculating portfolio returns.
Ease of Use	Arithmetic mean is relatively easy to use in comparison to Geometric mean.	The geometric mean is relatively complex to use in comparison to Arithmetic mean.
Mean for the same set of numbers	Arithmetic mean for two positive numbers is always higher than the Geometric mean.	The geometric mean for two positive numbers is always lower than the Arithmetic mean.

Conclusion – Geometric Mean vs Arithmetic Mean

Geometric Mean vs Arithmetic Mean both find their application in economics, finance, statistics etc. according to their suitability. Geometric mean is more suitable in calculating the mean and provide accurate results when the variables are dependent and widely skewed. However, an Arithmetic mean is used to calculate the average when the variables are not interdependent. Therefore, these two should be used in a relevant context to get the best results.

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