median

In the context of mathematics and statistics, the median is the middle number in a set of values when those values are arranged from smallest to largest. In contrast, the word mean refers to what’s informally called the average—the sum of a set of values divided by the number of values. The mode of a set of values is the most frequently repeated value in the set.

The word average is of course also very commonly used in more general ways. In math, though, it’s helpful to use more specific terms when determining the most representative or common value in a set of numbers.

To illustrate the difference, let’s look at an example set of seven values: 2, 3, 3, 4, 6, 8, 9.

To get the mean of this set, you’d add up all the values (2+3+3+4+6+8+9=35) and then divide that total by the number of values (7), resulting in a mean of 5. This is what most people are referring to when they refer to the average of some set of numbers.

To find the median, you have to find the one that’s sequentially in the middle. In a set of seven numbers arranged in increasing value, the median is the fourth number (since there are three before and three after). In this set (2, 3, 3, 4, 6, 8, 9), the median is 4. When a set has an even number of values, the median is the mean of the two middle values.

The mode is simply the value that shows up the most. In the example set, the mode is 3, since it occurs twice and all the other values occur only once.

Want to learn more? Read the full breakdown of the difference between median, mean, mode, and average.

Should median, mean, mode, or average be used in the following sentence?

The most frequently repeated test score is 80, so it’s the _____ of the set.