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.

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

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

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

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

Key Differences

• The arithmetic mean is known as additive mean and are used in the everyday calculation of returns. Geometric Mean is known as multiplicative mean and is a little complicated and involves compounding.
• The main difference in both these means is the way it is calculated. The  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 arithmetic mean is (Return1 + Return2 + Return3 + Return4)/ 4.
• can only be calculated for positive numbers and is always less than geometric meanwhile, arithmetic mean can be calculated for both positive and negative numbers and is always greater than the geometric mean.
• A most 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 260.75. The effect is clearly highlighted. 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 set 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 mean to describe the size of the bacterial population. For example, the bacterial population can be 10 in one day and 10,000 on others. Income distribution can also be calculated 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. how the wealth and by how much wealth of an individual has increased or decreased.

Conclusion

The use of geometric mean is appropriate for percentage changes, volatile numbers, and data that exhibit correlation, especially for . 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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