Why is geometric mean used

Since the return in each year impacts the absolute return in the next year, a geometric mean is a better way to calculate the annualized return on investment.

When one needs to calculate the average of variables that are not dependent on each other, Arithmetic means a suitable tool to calculate the average. The 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. 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 The arithmetic mean does not take into account the impact of compounding, and therefore, it is not best suited to calculate the portfolio returns.

The geometric mean takes into account the effect of compounding, therefore, better suited for calculating the returns. Accuracy The use of Arithmetic means to 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 the data set, a geometric mean is more effective and more accurate. Application The arithmetic mean is widely used in day to day simple calculations with a 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 The arithmetic mean is relatively easy to use in comparison to the Geometric mean. The geometric mean is relatively complex to use in comparison to the Arithmetic mean. Mean for the same set of numbers The 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 both finds their application in economics , finance, statistics, etc. The geometric mean is more suitable for calculating the mean and provides 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. This has been a guide to the top difference between Geometric Mean vs Arithmetic Mean. Here we also discuss the Geometric Mean vs Arithmetic Mean key differences with infographics and comparison table. You may also have a look at the following articles to learn more. Submit Next Question. By signing up, you agree to our Terms of Use and Privacy Policy. Forgot Password?

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Develop and improve products. List of Partners vendors. In statistics, the geometric mean is calculated by raising the product of a series of numbers to the inverse of the total length of the series. The geometric mean is most useful when numbers in the series are not independent of each other or if numbers tend to make large fluctuations.

Applications of the geometric mean are most common in business and finance, where it is frequently used when dealing with percentages to calculate growth rates and returns on a portfolio of securities.

It is also used in certain financial and stock market indexes, such as the Financial Times' Value Line Geometric index. The geometric mean is used in finance to calculate average growth rates and is referred to as the compounded annual growth rate. The geometric mean of the growth rate is calculated as follows:.

The geometric mean is commonly used to calculate the annual return on portfolio of securities. The geometric mean is also occasionally used in constructing stock indexes. Many of the Value Line indexes maintained by the Financial Times employ the geometric mean. The index is calculated by taking the geometric mean of the proportional change in price of each of the stocks within the index.

The geometric mean was first conceptualized by Greek philosopher Pythagoras of Samos and is closely associated with two other classical means made famous by him: the arithmetic mean and the harmonic mean. The geometric mean is also used for sets of numbers, where the values that are multiplied together are exponential. Examples of this phenomena include the interest rates that may be attached to any financial investments, or the statistical rates if human population growth.

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