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

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 article, 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 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

Difference between Average vs. Mean | Picture

Mean vs. AveragePin

Mean vs. Average: What’s the Difference?

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austin
austin
1 year ago

this is the best math ever better than ms sochacki´s

miek
miek
6 months ago
Reply to  austin

BODMAS

  • Brackets/Off/Multiply/Divide/ Add/Supstract

a rather old rule

alfred
alfred
10 months ago

If we assume that: (3 + 7 + 8) = 18 / 3 = 6
we get: 18=6

There’s something wrong with this equation.

carson
carson
9 months ago
Reply to  alfred

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.

Carson
Carson
9 months ago

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… Read more »

carson
carson
9 months ago

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… Read more »

jay
jay
4 months ago

this is soooooooooooooooooooooooooooooooooooooo easy

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