Mean vs. Average: Confusing Math and Statistics Terms

In mathematics or statistics, you are very likely to come across two terms, mean vs. average. 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 reference, your mean vs. average dilemma will be solved.

Mean vs. Average: Understanding the Basics

Key Takeaways

  • Mean is a specific method of finding the central value by summing all numbers and dividing by the count.
  • Average is a broader term that can refer to the mean, median, mode, or range.
Mean vs. Average
Mean vs. Average – Created by 7ESL

Mean vs. Average: the Definition

Defining Mean

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.

Let’s break it down in simpler terms:

  • Imagine you have a set of numbers.
  • You add those numbers together to get a sum.
  • You then divide the sum by how many numbers are in the set.

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

Mean = (3 + 7 + 8) / 3 = 18 / 3 = 6

Defining Average

In mathematics, you can find yourself talking about average, and this is the middle point of all the numbers that you have.

To find your average, you’ll do a simple calculation:

  • Sum up all the numbers: Add all values together to get a total.
  • Count the values: Determine how many numbers are in your set.
  • Divide the total sum by the number of values: This will give you the average.

So, if the numbers that you have are 3, 7, 8:

Average = (3 + 7 + 8) = 18 / 3 = 6

Mean vs. Average: the Difference

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

Aspect Mean Average
Definition Sum of values / number of values Can include mean, median, or mode
Common Usage Statistical analysis Day-to-day conversation
Example Usage “The mean temperature for July.” “The average score of the students.”

Related Confused Words with Mean or Average

Mean vs. Median

Mean and median are both measures of central tendency used in statistics to describe the central position of a dataset, but they do so in different ways:

Mean (often referred to as the average) is calculated by adding up all the numbers in a dataset and then dividing by the count of those numbers. It represents the ‘average’ value of the dataset.

Median is the middle value in a dataset when the numbers are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle numbers. The median is less affected by outliers and skewed data than the mean.

Average vs. Median

The term “average” usually refers to the arithmetic mean, which is the sum of all numbers in a dataset divided by the count of those numbers. It represents the typical value of the dataset.

The median, on the other hand, is the middle value in a dataset when the numbers are arranged in order. If there’s an even number of observations, the median is the average of the two middle numbers.

The key difference is that the average can be heavily influenced by extreme values or outliers, whereas the median gives a better representation of the center of a dataset that may not be symmetrical or may have outliers. The median is often used in such cases because it provides a more robust measure of central tendency.

Latest posts by Liam Daniel (see all)