Differences Between Geometric and Arithmetic Mean

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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 series length of the series. The arithmetic mean is the average calculated by adding all the numbers and dividing by the count of that series of numbers.

Geometric Mean vs. Arithmetic Mean Infographics

Key Differences

  • The arithmetic mean is known as the additive mean and is used in the everyday calculation of returns. The geometric mean is known as the multiplicative mean and is a little complicated and involves compounding.The main difference in both these means is the way to calculate. The arithmetic meanArithmetic MeanArithmetic mean denotes the average of all the observations of a data series. It is the aggregate of all the values in a data set divided by the total count of the observations.read more is calculated as the sum of all the numbers divided by the number of the dataset. The geometric mean is a series of numbers calculated by taking the product of these numbers and raising it to the inverse of the length of the series.Formula for geometric mean is {[(1+Return1) x (1+Return2) x (1+Return3)…)]^(1/n)]} – 1, and for the arithmetic mean is (Return1 + Return2 + Return3 + Return4)/ 4.The Geometric meanGeometric MeanGeometric Mean (GM) is a central tendency method that determines the power average of a growth series data. read more can only be calculated for positive numbers and is always less than the geometric ones. Meanwhile, the arithmetic mean can be calculated for positive and negative numbers and is always greater than the geometric mean.A common problem with having a dataset is the effect of outliers. In a dataset of 11, 13, 17, and 1000 the geometric mean is 39.5, while the arithmetic means is 260.75. The effect highlights. The geometric mean normalizes the dataset, and the values are averaged out. Hence, no range dominates the weights, and any percentage does not significantly affect the data set. The geometric mean is not influenced by skewed distributions as the arithmetic average is.The arithmetic mean is used by statisticians but for data sets with no significant outliers. This type of mean is useful for reading temperatures. It is also helpful in determining the average speed of the car. On the other hand, the geometric mean is useful in cases where the dataset is logarithmic or varies by multiples of 10.Many biologists use this type of means to describe the size of the bacterial population. For example, the bacterial population can be 10 in one day and 10,000 in others. One can also calculate income distribution using a geometric average. For example, X and Y make $30,000 yearly, while Z makes $300,000 annually. In this case, the arithmetic average will not be useful. Portfolio managers highlightPortfolio Managers HighlightA portfolio manager is a financial market expert who strategically designs investment portfolios.read more how an individual’s wealth has increased or decreased.

Comparative Table

Conclusion

The geometric mean is appropriate for percentage changes, volatile numbers, and correlation data, especially 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 financial returns correlate with stocks, bond yield, and premiums. The longer period makes the compounding effect more critical and hence 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.

This article is a guide to Geometric Mean vs. Arithmetic Mean. Here, we discuss the top 9 differences between geometric and arithmetic mean, infographics, and a comparison table. You may also have a look at the following articles: –

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