## What Is Mean?

A mean is the simple mathematical average of a set of two or more numbers. The mean for a given set of numbers can be computed in more than one way, including the arithmetic mean method, which uses the sum of the numbers in the series, and the geometric mean method, which is the average of a set of products. However, all of the primary methods of computing a simple average produce the same approximate result most of the time.

### Key Takeaways

- The mean is the mathematical average of a set of two or more numbers.
- The arithmetic mean and the geometric mean are two types of mean that can be calculated.
- Summing the numbers in a set and dividing by the total number gives you the arithmetic mean.
- The geometric mean is more complicated and involves multiplication of the numbers taking the nth root.
- The mean helps to assess the performance of an investment or company over a period of time, and many other uses.

#### Calculating The Means

## Understanding the Mean

The mean is a statistical indicator that can be used to gauge the performance of a company’s stock price over a period of days, months, or years, a company through its earnings over a number of years, a firm by assessing its fundamentals such as price-to-earnings ratio, free cash flow, and liabilities on the balance sheet, and a portfolio by estimating its average returns over a certain period.

An analyst who wants to measure the trajectory of a company’s stock value in the last, say 10 days, would sum up the closing price of the stock in each of the 10 days. The sum total would then be divided by the number of days to get the arithmetic mean. The geometric mean will be calculated by multiplying all of the values together. The nth root of the product total is then taken, in this case, the 10^{th} root, to get the mean.

## Arithmetic Mean vs. Geometric Mean

Let’s put this into practice by examining the stock price of Nvidia Corp. (NVDA) for a 10 day period in 2017. An investor that purchased NVDA on June 5^{th} for $148.01 wants to know how well his investment has fared after 10 days. The table below shows the price and returns from June 6^{th} to June 19^{th}, 2017.

The arithmetic mean is 0.67%, and is simply the sum total of the returns divided by 10. However, the arithmetic mean of returns is only accurate when there is no volatility, which is nearly impossible with the stock market.

The geometric mean factors in compounding and volatility, which makes it a better metric of average returns. Since it is impossible to take the root of a negative value, add one to all the percentage returns so that the product total yields a positive number. Take the 10^{th} root of this number and remember to subtract from one to get the percentage figure. The geometric mean of returns for the investor in the last five days is 0.61%. As a mathematical rule, the geometric mean will always be equal to or less than the arithmetic mean.

## Example

Proof that the geometric mean provides a better value is given in the table. When the arithmetic mean of 0.67% is applied to each of the stock prices, the end value is $152.63. But clearly, NVDA traded for $157.32 on the last day. This means that the arithmetic mean of returns is overstated. On the other hand, when each of the closing prices is raised by the geometric average return of 0.61%, the exact price of $157.32 is calculated. This is an example of why the geometric mean is an accurate reflection of the true return of a portfolio.

While the mean is a good tool to evaluate the performance of a company or portfolio, it should also be used with other fundamentals and statistical tools to get a better and broader picture of the investment's historical and future prospects.