Glossary term
Arithmetic Mean
Arithmetic mean is the simple average found by adding values together and dividing by the number of values.
Updated
Read time
What Is the Arithmetic Mean?
The arithmetic mean is the simple average of a set of numbers. It is calculated by adding all the values together and dividing by the number of values. In finance, it is often used to describe average returns, average prices, average balances, or average economic data points.
The arithmetic mean is easy to understand, but it can be misleading when returns compound over time. For investment growth, the geometric mean often gives a better picture of the actual compound result.
Key Takeaways
- The arithmetic mean is the simple average.
- It adds values and divides by the number of observations.
- It is useful for summarizing a set of equal-weighted numbers.
- It can overstate investment growth when returns are volatile.
- For compound returns, geometric average or annualized return may be more useful.
Arithmetic Mean Formula
x1 through xn are the values in the data set. n is the number of values. The formula gives each observation equal weight.
How It Works in Investing
Suppose an investment returns 20% in one year and -10% the next. The arithmetic mean return is 5%, because 20% plus -10% divided by two equals 5%. But the actual compound result is not exactly the same as earning 5% per year.
The difference comes from the way investment returns build on prior values. A loss after a gain applies to a larger or smaller base than the original investment. Volatility pulls compound returns below the simple average when returns vary.
The arithmetic mean can still be useful for describing a set of returns. It answers a straightforward question: what was the average period's return? The problem comes when that answer is treated as the same thing as the rate at which wealth actually compounded.
Arithmetic Mean Versus Other Averages
Measure | What it does | Best use |
|---|---|---|
Arithmetic mean | Simple average of values | Equal-weighted summary of observations |
Geometric mean | Compound average growth rate | Multi-period investment returns |
Median | Middle value in an ordered set | Data with outliers or skew |
Weighted average | Average using different weights | Portfolio returns or index calculations |
When the Simple Average Helps
The arithmetic mean is useful because it is simple and transparent. It can summarize monthly spending, average account balances, average annual returns, or economic data points. It is often the first average people learn and the easiest to calculate.
But investors should know when not to lean on it. For long-term performance, a simple average return may make the path look smoother and stronger than the actual compounded result.
Outliers are another reason to be careful. If most monthly returns are modest but one month is unusually strong, the arithmetic mean can rise even though the typical month did not feel that strong. In skewed data sets, the median or a weighted measure may give useful additional context.
What the Average Can Hide
The arithmetic mean can be distorted by outliers. One unusually large value can pull the average away from the typical experience. It can also hide sequence risk in portfolios, especially when withdrawals are involved.
The measure is not wrong; it is just answering a specific question. It tells the simple average of values, not necessarily the typical value, the compound growth rate, or the investor's dollar-weighted result.
The Bottom Line
The arithmetic mean is the simple average of a set of numbers. It is useful for clear summaries, but investors should be careful when using it for multi-period returns because compounding and volatility can tell a different story.