# Arithmetic: Mean, Median, Mode, and Range: What's the Difference?

By Keren Perles

We all know what an average is. But did you know there are three different types of averages - the mean, median, and mode? These terms are different ways that mathematicians describe groups of values.

## Finding the Mean

The term “mean,” sometimes called “arithmetic mean,” describes what we would normally call an “average.” To find the mean of a group of values, you would add up the values and divide the result by the number of values.

For example, to find the mean of 6, 4, 5, 4, and 11, you would add the values (6 + 4 + 5 + 4 + 11 = 30) and then divide the result by 5, which is the number of values (30 / 5 = 6). The mean, in this case, would be 6.

## Finding the Median

The median of a group of values is the middle value when the values are placed in numeric order. In other words, to find the median of the group of values above, you would have to place them in order like this: 4, 4, 5, 6, 11. The middle value in the group is 5, so the median of the group of values is 5.

## Finding the Mode

The mode of a group of values is the number that is listed most often in the group. In other words, in the example above, there are only one of each of the following values: 5, 6, and 11. There are two 4s, however. Therefore, the mode of the group of values would be 4, because there are more 4s than any other values in the group.

In some groups of values there is no mode. For example, if the list read 6, 4, 5, 4, 6, there would be no mode. Although there are still two 4s, there are also two 6s, so there is no one value that is repeated more than the other values.

## Finding the Range

The range of a group of values is the difference between the largest and the smallest value. For example, in the list of numbers above, the largest value is 11 and the smallest value is 4. Therefore, the range would be 11 – 4 = 7.