Mean vs. Average: Interesting Difference between Average vs. Mean

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 article, 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 Pin

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 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.

In summary, the mean is sensitive to extreme values, while the median provides a better measure of central tendency for skewed datasets or those with outliers.

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.

Frequently Asked Questions

How can you calculate the mean of a dataset?

To calculate the mean, sum up all the numbers in your dataset and then divide by the total count of values you have. This gives you the average value that represents the dataset.

What are the distinctions between mean, median, and mode in statistics?

The mean is the sum of all values divided by their number, the median is the middle value when a dataset is ordered from least to greatest, while the mode is the most frequently occurring value in a dataset.

In Excel, what is the procedure for finding the mean of a set of values?

In Excel, you can find the mean by selecting a cell and typing =AVERAGE(range) where ‘range’ is your set of cells containing the values you wish to average.

Why might someone choose to use the median over the mean in certain datasets?

You might opt for the median over the mean when your dataset includes outliers or skewed data because the median is less affected by exceptionally high or low values and can give a better central tendency measure for such data.

Can you explain the concept of average in mathematical terms?

The term ‘average’ can refer to a measure of central tendency and is often used interchangeably with mean. However, it can also pertain to the median and mode, depending on the context.

Are there situations where the mean might be considered more informative than the mode of a dataset?

The mean might be more informative than the mode when the dataset has values with small variations and no extreme outliers, as it considers all data points to provide a balanced measure of centrality.

8 thoughts on “Mean vs. Average: Interesting Difference between Average vs. Mean”

  1. r is occuring at “18 / 3”. It is not an error in the arithmetical division of 18 by 3 equalling 6. No; that would be okay. The error is based on wrong sequences. In its grammatical equivalent,

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  2. NO WAY!! Determining the “mean” is not at all the same as “averaging”. I’m surprised you made this claim! Averages are easily skewed. Means reflect much more reliable data via “bell curves.” If you live in a neighborhood where people can afford to buy cars no more expensive than, say, $5,000 each–and then one Mr. Rich moves in with his million-dollar SuperZaz car, you will discover the “average” person in your area now owns a vehicle many times more valuable than $5,000–even though that isn’t true! And, no matter how insurance costs are calculated, “averages” will lead all the “ordinary poor folk” to be GREATLY SUBSIDIZING the insurance costs of Mr. Rich’s SuperZaz car. In using MEANS, we avoid those pitfalls.

    Reply
    • I think you are thinking about the median, which can reduce the effect of outliers. The arithmetic mean is calculated exactly the same as what we normally call the “average”, and it would go up when Mr. Rich moves in. How much it goes up depends on how many people there are in the neighborhood (at some point the neighborhood can be so full of $5000 cars that one million dollar car won’t move the needle much, but that sized neighborhood might better be called a “city”) and by how different the cost is of Mr. Rich’s car vs. the others.

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  3. Your means and averages are very important in having been used to create a very unfortunate myth about age expectancies. We do NOT “live longer” as generally believed. The error is through using AVERAGES for length of life, rather than MEANS. In many socities, there are a great number of deaths among infants (say, between newborn and about age 5). THAT is why those societies, when ages are AVERAGED, indicate, “Oh Goody! We are living longer and longer lifetimes!” But, on visiting such societies, one sees there are about the same number or prevalence or “well, my graddad lived to be 103 years old” testimonies as anywhere else.

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    • Your error is occuring at “18 / 3”. It is not an error in the arithmetical division of 18 by 3 equalling 6. No; that would be okay. The error is based on wrong sequences. In its grammatical equivalent, the use of commas, semicolons, or else sentence completions and new sentences begun (ie clauses, actually) saves the day.

      Reply

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