An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers.
If you were asked to find the class (arithmetic) average of test scores, you would simply add up all the test scores of the students, and then divide that sum by the number of students. For example, if five students took an exam and their scores were 60%, 70%, 80%, 90% and 100%, the arithmetic class average would be 80%.
This would be calculated as: (0.6 + 0.7 + 0.8 + 0.9 + 1.0) / 5 = 0.8.
The reason you use an arithmetic average for test scores is that each test score is an independent event. If one student happens to perform poorly on the exam, the next student's chances of doing poor (or well) on the exam isn't affected. In other words, each student's score is independent of the all other students' scores. However, there are some instances, particularly in the world of finance, where an arithmetic mean is not an appropriate method for calculating an average.
Consider your investment returns, for example. Suppose you have invested your savings in the stock market for five years. If your returns each year were 90%, 10%, 20%, 30% and 90%, what would your average return be during this period? Well, taking the simple arithmetic average, you would get an answer of 12%. Not too shabby, you might think.
However, when it comes to annual investment returns, the numbers are not independent of each other. If you lose a ton of money one year, you have that much less capital to generate returns during the following years, and vice versa. Because of this reality, we need to calculate the geometric average of your investment returns in order to get an accurate measurement of what your actual average annual return over the fiveyear period is.
To do this, we simply add one to each number (to avoid any problems with negative percentages). Then, multiply all the numbers together, and raise their product to the power of one divided by the count of the numbers in the series. And you're finished  just don't forget to subtract one from the result!
That's quite a mouthful, but on paper it's actually not that complex. Returning to our example, let's calculate the geometric average: Our returns were 90%, 10%, 20%, 30% and 90%, so we plug them into the formula as [(1.9 x 1.1 x 1.2 x 1.3 x 0.1) ^ 1/5]  1. This equals a geometric average annual return of 20.08%. That's a heck of a lot worse than the 12% arithmetic average we calculated earlier, and unfortunately it's also the number that represents reality in this case.
It may seem confusing as to why geometric average returns are more accurate than arithmetic average returns, but look at it this way: if you lose 100% of your capital in one year, you don't have any hope of making a return on it during the next year. In other words, investment returns are not independent of each other, so they require a geometric average to represent their mean.
To learn more about the mathematical nature of investment returns, check out Overcoming Compounding's Dark Side.

Can two numbers have the same arithmetic and geometric means?
Learn about the often complicated relationship between the geometric mean and arithmetic mean for a set of numbers, and which ... Read Answer >> 
How can investors benefit by understanding geometric means?
Discover why investors should know the difference between geometric and arithmetic means, and why the geometric mean is more ... Read Answer >> 
The ABC Global mutual fund exhibited the following rates of return over the last ...
The correct answer is: a) Arithmetic Mean = (15 + 7 + 6.5 + 11.3 + 32.7)/5 = 7.18% Geometric Mean =[(1.15 x 0.93 x 1.065 ... Read Answer >> 
What is a geometric mean in statistics?
Learn what the geometric mean is in statistics and how it is used to calculate various growth rates and returns by financial ... Read Answer >> 
How do you calculate the geometric mean to assess portfolio performance?
Learn how to calculate the geometric mean. Understand when the geometric mean should be used and how it differs from the ... Read Answer >> 
What are some examples of applications of the geometric mean?
Learn about applications of the geometric mean based on examples such as calculations of portfolio return, growth rates and ... Read Answer >>

Managing Wealth
Breaking Down The Geometric Mean
Understanding portfolio performance, whether for a selfmanaged, discretionary portfolio or a nondiscretionary portfolio, is vital to determining whether the portfolio strategy is working or ... 
Trading
Calculating the Arithmetic Mean
The arithmetic mean is the average of a sum of numbers. 
Markets
The Most Accurate Way To Gauge Returns: The Compound Annual Growth Rate
The compound annual growth rate, or CAGR for short, represents one of the most accurate ways to calculate and determine returns for individual assets, investment portfolios and anything that ... 
Investing
Explaining the Geometric Mean
The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. 
Investing
How To Calculate Your Investment Return
How much are your investments actually returning? Find out why the method of calculation matters. 
Investing
Calculating Annualized Total Return
The annualized total return is the average return of an investment each year over a given time period. 
Personal Finance
How High Is a 'Good' Credit Score?
How high of a credit score do you need to get a home mortgage or buy a car? Read on for some actual numbers. 
Investing
10 Ways Student Debt Can Destroy Your Life
If you're getting a student loan, think critically about how you will manage your loan. Student debt could have a profound negative impact on your life. 
Investing
Gauge Portfolio Performance By Measuring Returns
Calculate returns frequently and accurately to ensure that you're meeting your investing goals. 
Managing Wealth
The Uses And Limits Of Volatility
Check out how the assumptions of theoretical risk models compare to actual market performance.

Arithmetic Mean
A mathematical representation of the typical value of a series ... 
Mean
The simple mathematical average of a set of two or more numbers. ... 
Unweighted Index
A simple arithmetic or geometric average used to calculate stock ... 
Arithmetic Index
An index of securities that uses an arithmetic sum to determine ... 
Geometric Mean
The average of a set of products, the calculation of which is ... 
Simple Moving Average  SMA
A simple, or arithmetic, moving average that is calculated by ...