Median vs Mean

It’s come to our attention that some of you may be having a bit of a problem. You don’t know when to use mean vs median. Now, while we’re generally easy people to get along with, there are a few things that bug us.

We’re firm believers that less and fewer are not interchangeable. We think that everyone over the age of 12 should know the difference between there, their and they’re. And we do think that everyone should know how to find and correctly use a mean and a median. It’s really basic math, guys.

We understand that the words themselves can refer to different concepts. That’s a matter of context, and you can probably figure that out pretty easily. We’ll cover it here just in case. But as for the math terms, let’s just set the record straight, once and for all. Here is the complete rundown on how to use mean vs median.

Mean vs Median: What is Mean?

Mean is one of those words that can be used in a variety of ways. Here are three sentences to demonstrate this fun fact.

  • You’re so mean!
  • The mean of 1, 2, 4, 5 and 20 is 6.4.
  • “Away put your weapon, I mean you no harm!” ~Yoda, 1980
  • What does that word mean?

You see? The word mean, in these sentences, is used to describe disposition, a math concept, intent and definition, respectively. Isn’t the English language great?

But most of you seem to have trouble with the word mean in a mathematical context. That would be the second sentence. So, we’ll start with a definition.

The mean is the average of all the numbers in a set. It is a calculated central value, derived by totaling the value of the numbers and subsequently dividing by the sum by the quantity of the numbers in the set.

In other words, it’s the average. And if you took math in grade school, you probably learned how to find an average. If you did not, we’re here to help. Let’s look at the numbers in our sample sentence.

1, 2, 4, 5 and 20. Add those numbers together. The sum of those numbers is 32. Now, determine the quantity of numbers in the set. There are 5, so you’ll next want to divide 32 by 5. The answer is 6.4. And there you have it – the mean!

Mean vs Median: What is Median?

Mean vs Median
He’s laughing at you for using median. Cats hate median.

Alright, so now you know what a mean is. What’s a median? No, it’s not that guy who talks to your dead relatives. That’s a medium and a completely different website.

You can use the word median in a few ways, too. Let’s look at a few sentences.

  • She crossed the median because she was texting and driving.
  • Pete firmly believed that, in a past life, he’d been the ruler of the Median Empire.
  • The median of 1, 2, 4, 5 and 20 is 4.

The words in these sentences describe a location, a bit of Middle Eastern history, and a math concept. Again, we’re going to look at the math concept.

The definition of median is the following:

The middle number of an ordered data set or the average of the two middle numbers in an ordered data set with an even number of data.

The median is literally the number in the middle. In our set, there are 5 numbers; they are 1, 2, 4, 5 and 20. We’re lucky because these numbers are already in order from lowest to highest value. So we’ll just pluck the guy out of the middle, the number 4. That’s our median.

If there were an even quantity of numbers, we’d take the two in the center and find the mean of them. You remember how to do that, right? That mean is our median.

Mean vs Median: Who Really Cares?

Median vs Mean
This cow doesn’t care, so why should you?

We use averages and medians all the time. Have you ever seen a news article which mentions the median demographic? Or which announces the average SAT score? These are two very different ways of gathering information.

In politics, the median is very frequently used. Think about it. Let’s say there’s a town with 100 citizens. Within that town, there are 98 citizens with an annual income of $20,000. And then there’s the mayor and his wife, who each earn $1 million.

To average the salaries to determine the demographics of that town would be foolish. The average would be derived as follows: 98 residents earning $20,000 per year = $1,960,000. Add the mayoral contribution of $2M and you get a total of $3,960,000. Divide this number by 100, which is the total number of residents. The answer you’d get is $39,600. That number is much higher than the lowly townspeople actually get paid.

Instead, researchers use the median. There are an even number of residents within the town, so we’d need to find the two numbers in the middle. Incidentally, they’re both $20,000. Find the mean of those, and you’ve got your median salary. It’s much more representative of the population.

So when should you find an actual average? We use averages in other ways. We look at the average incidences of gun violence, or the average temperature of a city. The average cost of a three bedroom home can be an indicator of an area’s wealth. Even our example of salary can be used, if it’s used in a more specific scope. For example, the national average hourly rate of a tig welder is $18.10.

Mean vs Median: Which Should You Use?

As a rule of thumb, if you’re looking at statistics, it’s best to go with the median. The median isn’t affected much by outliers, like the mayor and his wife. If you’re looking at something more specific, like the average number of kids per household in the city of Pittsboro, use the mean.

Say what you mean, and mean what you say. (You see what we did there?) Now that you know the definitions of mean and median, it ought to be pretty simple for you to determine which to use.

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