Arithmetic average, or arithmetic mean, or just mean, is the very basic statistical measure. It provides quick and easy information about general level of values in a data set ? it is one of the measures of central tendency.
Why Use Arithmetic Average
When you have a set of data, it is sometimes difficult to tell what the values are in general (you can't see the forest for the trees). For example, you have 10 stocks. Their annual returns in the last year were: 11%, -5%, 17%, 1%, -9%, 21%, 4%, -6%, 7%, and -1%.
The information provided in this form will tell you the details, but you will have to think for a while to get an idea regarding the annual return of this group of stocks as a whole. When the arithmetic average is provided in addition to this information, it can save you the thinking. The mean (arithmetic average) return of our basket of 10 stocks in the last year was 4%. This information is already quite clear and easy to work with.
Arithmetic Average Calculation
The calculation of arithmetic average is straightforward. You sum up all the values and then divide the sum by the number of values. Let's use the example above to illustrate the calculation of mean:
- First you sum up the annual returns: 11% + (-5%) + 17% + 1% + (-9%) + 21% + 4% + (-6%) + 7% + (-1%) = 40%
- Then you divide the sum (which is +40%) by the number of observations (which is 10), and you get the arithmetic average, which is +4% in this case.
Calculating Arithmetic Average in Excel
Though the calculation is very simple, it can be boring and prone to errors when you work with large sets of data (imagine calculating the average return of the 500 stocks in S&P500 like this). Computers calculate arithmetic average for us. In Microsoft Excel, you can use the function AVERAGE. The parameter is the area of the cells where you have the individual values.
Limitations of Arithmetic Average
Though arithmetic average is easy and elegant for the first quick information about a data set, it has weaknesses and sometimes it is better to use one of the other measures of central tendency, like geometric average, weighted average, median, or mode.
Furthermore, knowing the general level of values is often not enough. You may also want to measure volatility or dispersion (using standard deviation or variance) and many other characteristics.
You can easily calculate arithmetic average, median, variance, standard deviation and other measures using the Descriptive Statistics Excel Calculator.