# Arithmetic Mean

## What is the Arithmetic Mean?

The **arithmetic mean** is the average of a series of numbers.

## How Does the Arithmetic Mean Work?

The formula for calculating the *arithmetic mean* is:

Arithmetic mean = (X1 + X2 + X3 + ... +XN) / N

where X1, X2, X3, XN are the values of the observations being averaged and N equals the number of observations

Let's assume that you would like to find the arithmetic mean of stock prices of Company XYZ over the last four years. Here are the stock prices from each of the last four years:

Year 1: $10

Year 2: $15

Year 3: $20

Year 4: $25

Using the formula above, we can calculate the arithmetic mean price of Company XYZ to be:**($10+$15+$20+$25)/4 = $17.50**

The arithmetic mean always lies between the smallest and the largest of the numbers in the set.

## Why Does the Arithmetic Mean Matter?

The arithmetic mean allows investors to gain some insight into stock prices, economic data, and a host of other information. For instance, if Company XYZ's stock price is trading above its arithmetic mean, it could be that the stock is overvalued.

It is important to note that arithmetic means are not very useful if the underlying data is erratic. One "outlier" could artificially increase or decrease an arithmetic mean to where it no longer reflects the nature of the bulk of the underlying data. This is one reason some analysts prefer to use weighted averages in certain circumstances.