Though we commonly use the word average in everyday life when discussing the number that’s the most “typical” or that’s “in the middle” of a group of values, more precise terms are used in math and statistics. Namely, the words mean, median, and mode each represent a different calculation or interpretation of which value in a data set is the most common or most representative of the set as a whole.
In this article, we’ll answer these questions and more:
- Is there a difference between mean and average?
- What’s the difference between mean, median, and mode?
- How do you find the mean, median, and mode?
⚡ Quick summary
You find the mean (informally called the average) by adding up all the numbers in a set and then dividing by how many values there are. When you arrange a set of values from smallest to largest, the median is the one in the middle. The mode is simply the value that occurs the most in the set.
mean vs. average
In math, the word mean refers to what’s informally called the average. They mean the same thing, but in the context of math and statistics, it’s better to use the word mean to distinguish from other things that might be casually referred to as “average” values in a general sense (meaning values that are the most representative or common within the set).
What is the mean, median, and mode?
The mean is the number you get by dividing the sum of a set of values by the number of values in the set.
In contrast, the median is the middle number in a set of values when those values are arranged from smallest to largest.
The mode of a set of values is the most frequently repeated value in the set.
To illustrate the difference, let’s look at a very simple example.
How to find the mean, median, and mode
Here’s an example set of seven values: 2, 3, 3, 4, 6, 8, 9.
To find the mean: 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: find the value 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 (in other words, you find the median by adding the two middle numbers together and dividing by two).
To find the mode: simply look to see which value shows up the most. In the example set, the mode is 3, since it occurs twice and all the other values occur only once.
Of course, this set of values is very simple compared to data sets you’re likely to encounter in real life. In cases when there is too much data to look at all at once, there are often special tools (such as those used in spreadsheet software) that you can use to determine the mean, median, and mode.
