Geometric Mean vs Arithmetic Mean

Differences Between Geometric and Arithmetic Mean

Geometric mean is the calculation of mean or average of series of values of product which takes into account the effect of compounding and it is used for determining the performance of investment whereas arithmetic mean is the calculation of mean by sum of total of values divided by number of values.

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The geometric mean is calculated for a series of numbers by taking the product of these numbers and raising it to the inverse length of the series. Arithmetic Mean is simply the average and is calculated by adding all the numbers and divided by the count of that series of numbers.

Geometric Mean vs. Arithmetic Mean Infographics

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Source: Geometric Mean vs Arithmetic Mean (wallstreetmojo.com)

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For eg:
Source: Geometric Mean vs Arithmetic Mean (wallstreetmojo.com)

Key Differences

Comparative Table

BasisGeometric MeanArithmetic Mean
MeaningGeometric Mean is known as the Multiplicative Mean.Arithmetic Mean is known as Additive Mean.
Formula{[(1+Return1) x (1+Return2) x (1+Return3)…)]^(1/n)]} – 1(Return1 + Return2 + Return3 + Return4)/ 4
ValuesThe geometric mean is always lower than the arithmetic means due to the compounding effect.The arithmetic mean is always higher than the geometric mean as it is calculated as a simple average.
CalculationSuppose a dataset has the following numbers – 50, 75, 100. Geometric mean is calculated as cube root of (50 x 75 x 100) = 72.1Similarly, for a dataset of 50, 75, and 100, arithmetic mean is calculated as (50+75+100)/3 = 75
DatasetIt is applicable only to only a positive set of numbers.It can be calculated with both positive and negative sets of numbers.
Usefulness Geometric mean can be more useful when the dataset is logarithmic. The difference between the two values is the length.This method is more appropriate when calculating the mean value of the outputs of a set of independent events.
Effect of OutlierThe effect of outliers on the Geometric mean is mild. Consider the dataset 11,13,17 and 1000. In this case, 1000 is the outlier. Here, the average is 39.5The arithmetic mean has a severe effect of outliers. In the dataset 11,13,17 and 1000, the average is 260.25
UsesThe geometric mean is used by biologists, economists, and also majorly by financial analysts. It is most appropriate for a dataset that exhibits correlation.The arithmetic mean is used to represent average temperature as well as for car speed.

Conclusion

The use of geometric mean is appropriate for percentage changes, volatile numbers, and data that exhibit correlation, especially for investment portfoliosInvestment PortfoliosPortfolio investments are investments made in a group of assets (equity, debt, mutual funds, derivatives or even bitcoins) instead of a single asset with the objective of earning returns that are proportional to the investor's risk profile.read more. Most returns in finance are correlated like stocks, the yield on bonds, and premiums. The longer period makes the effect of compounding more critical and hence also the use of a geometric mean. While for independent data sets, arithmetic means is more appropriate as it is simple to use and easy to understand.

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