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## What is the Arithmetic Mean?

The arithmetic mean is the mean or the simplest and most widely used measure of the mean. It simply involves taking the sum of a group of numbers and then dividing that sum by the number of numbers used in the series. For example, consider the numbers 34, 44, 56, and 78. The total is 212. The arithmetic mean is 212 divided by 4 (53).

People also use some other type of mean, such as geometric mean and harmonic mean. These work in certain financial and investment situations. Another example is the trimmed mean used when calculating economic data such as the consumer price index (CPI) and personal consumption expenditure (PCE).

Important point

- The arithmetic mean is a simple mean, or the sum of a series of numbers divided by the count of the series of numbers.
- In the financial world, arithmetic mean is usually not the right way to calculate the mean, especially if a single outlier can significantly distort the mean.
- Other averages more commonly used in finance include geometric mean and harmonic mean.

## How the Arithmetic Mean works

Arithmetic mean maintains its position in finance as well. For example, the average return estimate is usually the arithmetic mean. Suppose you want to know the average earnings expectations of 16 analysts covering a particular stock. Sum all the estimates and divide by 16 to get the arithmetic mean.

The same is true when calculating the average closing price of a stock for a particular month. Let’s say you have 23 trading days in the month. Simply get all the prices, add them up and divide by 23 to get the arithmetic mean.

Arithmetic mean is simple and most people with any financial and math skills can calculate it. It is also a useful measure of central tendency, as it tends to provide useful results even with large groups of numbers.

## Arithmetic mean limit

Arithmetic mean is not always ideal. This is especially true if a single outlier can significantly distort the mean. Let’s say you want to estimate the capacity for a group of 10 children. Nine of them receive an allowance between $ 10 and $ 12 a week. The 10th child will receive a $ 60 allowance. One outlier is the arithmetic mean of $ 16. This is not very representative of the group.

In this particular case, a median tolerance of 10 may be a better measurement.

Arithmetic mean is not very good when calculating the performance of an investment portfolio, especially when compounding interest or involving reinvestment of dividends and returns. It is also not typically used to calculate current and future cash flows that analysts use to make estimates. Doing so will almost certainly lead to misleading numbers.

important

Arithmetic mean can be misleading if there are outliers or if you look at past returns. The geometric mean is best suited for series that show series correlation. This is especially true for investment portfolios.

## Arithmetic mean and geometric mean

In these applications, analysts tend to use the geometric mean, which is calculated differently. The geometric mean is best suited for series that show series correlation. This is especially true for investment portfolios.

Most financial returns are correlated, including bond yields, equity returns, and market risk premiums. The longer the period, the more important compound interest calculations and geometric mean use will be required. For volatile numbers, the geometric mean provides a much more accurate measure of true return by taking into account compound interest over the previous year.

The geometric mean takes the product of all series numbers and raises it to the reciprocal of the series length. It’s a lot of work to do manually, but it’s easy to calculate using the GEOMEAN function in Microsoft Excel.

The geometric mean is calculated differently from the arithmetic mean or the arithmetic mean because it takes into account the compound interest that occurs over each period. For this reason, investors typically consider the geometric mean to be a more accurate measure of return than the arithmetic mean.

## Examples of Arithmetic Mean and Geometric Mean

Let’s say the stock returns for the last five years are 20%, 6%, -10%, -1%, and 6%. The arithmetic mean is simply the sum of them divided by 5 to give an average annual rate of return of 4.2%.

Instead, the geometric mean is calculated as (1.2 x 1.06 x 0.9 x 0.99 x 1.06).^{1/5} -1 = Average annual rate of return 3.74%. Note that in this case the geometric mean, which is a more accurate calculation, is always smaller than the arithmetic mean.