Finding the Mean, Median, Mode, Range, and Outlier of a Set of Numbers

Hello Again!

Today, I will be teaching you how to find the mean, median, mode, range, and outlier of a set of numbers! First, I would like to share with you really quickly what those words mean. So mean is the same thing as the average number in a set of numbers, median is the number in the middle, and mode is the number that appears the most.

For example, say we had the numbers:

10     12     20     14     35     27     21     9     17     16     15      32     54

What are we supposed to do with those numbers? Well, usually I would start with putting them in order, because my OCD would go crazy otherwise. Also, putting the numbers in order is required to help us find some of the information we need a little bit later. So this is what those numbers would look like in order:

9     10     12     14     15     16     17     20     21     27     32      35     54

That's better! Now then, first lets get the hardest thing out of the way- the mean. Some would say that it is called the mean because it is the hardest one to find. The way you find the mean (or average) is by adding all of numbers together, and then dividing the total that you get by how many numbers there are. So, 9 + 10 + 12 + 14 + 15+ 16 + 17 + 20 + 27 + 32 + 35 + 54 = 261. Now, we count how many numbers there are, and we know that there are 12 numbers. So now we take that 261 total that we got, and divide it by 12. So 261 ፥ 12= 21.75. That means that our mean for the whole set of numbers is 21.75.

Next, we are going to find the median. This is a very simple thing to do. This is where you would have needed to put the numbers in order, if you haven't already. The easiest way to find the median is to cross out numbers on either side until you reach the middle, like this:

9     10     12     14     15     16     17     20     21     27     32      35     54

9     10     12     14     15     16     17     20     21     27     32      35     54

9     10     12     14     15     16     17     20     21     27     32      35     54

9     10     12     14     15     16     17     20     21     27     32      35     54

9     10     12     14     15     16     17     20     21     27     32      35     54

9     10     12     14     15     16     17     20     21     27     32      35     54

After crossing out all of the numbers, we can see that 17 is the number in the middle, or the median. Easy right? In this case, we had an odd amount of numbers, so our median was only one number, but if you had an even amount of numbers you would have two numbers that you didn't cross out. In that case, you would just add the two numbers together and divide by 2. That would then be your median!

On to the mode! This is probably the easiest of them all! Since I told you earlier that mode means the number that appears the most, you would just look for the number that shows up the most amount of times. However, in our case, each number only appears once, so there is no mode. There can be situations where there is more than one mode though, when there is more than one number that appears the same amount of times. 

Next there is the range. This is another simple one. All you do in this case is subtract the highest number and the lowest number. The highest number is 54, and the lowest number is 9, so we would do 54 - 9 which equals 45. That means 45 is the range!

Finally, on to the outlier. The outlier is that one number that is way off from the rest of them. In this case, all of these numbers are pretty close to each other, except for 54. That would mean that 54 is our outlier. An outlier is important in situations where maybe there is a class of test scores, and someone scores much lower or much higher than the rest of the class. That number that is way off would affect the mean, so usually you wouldn't include it just so the numbers stay more fair.

If you would like to know more, please visit this website! Mean, Median, Mode and Range

I hope my explanations were thorough enough! Please leave me a comment if you have any questions. Until next time!