Mean vs. average!

In mathematics or statistics, you are very likely to come across two terms, average and mean. They are often used interchangeably, and many people aren’t sure whether these two words refer to the same thing or not. If you feel confused as well, don’t feel bad.

After reading this post, your mean vs. average dilemma will be solved.

## Mean vs. Average

In statistics, some of the measures that are used are Median, Mode, and Mean. *Mean* refers to the central point of a specific list of values and, in order to find it, you need to add all of the values together and then divide the result by the number of values.

For example, if the set of values is 3, 7, 8:

**Mean** = (3 + 7 + 8) / 3 = 18 / 3 = 6

In mathematics, you can find yourself talking about *average*, and this is the middle point of all the numbers that you have. So, if the numbers that you have are 3, 7, 8:

**Average** = (3 + 7 + 8) = 18 / 3 = 6

## Mean vs. Average Difference

The method used and the result found are the same, so what’s the difference? The answer is very simple: only the terminology is different. The number that statisticians call *mean* is the same as the number that mathematicians call *average*.

And yet, there’s one thing you need to keep in mind: while you can always say that *average* is a synonym to *mean*, you can’t always say that *mean* is a synonym to *average*. This is because, even though *mean* refers to the same thing as *average* by default, there are other forms of it, such as the **geometric** or **harmonic mean**. What we call *mean* and can call *average*, is also known as the **arithmetic mean**.

The **geometric mean** is the number that you get when you multiply all the values in the list and then find the square root (if you have 2 numbers), cube root (if you have 3 numbers), etc, of this number. So, if you have numbers 4 and 16, the **geometric mean** will be 8 (the square root of 4 * 16, or the square root of 64).

To find the **harmonic mean**, you need to find the arithmetic mean at first. The reciprocal of this number of the sum of reciprocals of the given set of values will give you the harmonic mean. So, if your numbers are 1, 2, 3:

**Arithmetic mean** = (1 + 2 + 3) / 3 = 6 / 3 = 2

**Harmonic mean** = Arithmetic mean / (1/1) + (1/2) + (1/3) = 2 / (11/6) = 12/11