Imagine you and your friends are comparing how many minutes it takes to bike to school. Most of you say it takes about 10, 12, or 15 minutes. But then your buddy Jake chimes in:
“It takes me 60 minutes!”
Whoa. Jake’s time is way different.
That kind of number makes you stop and wonder. It doesn’t quite match the rest, and in math, we call that kind of number an outlier.
In this guide, we’ll explore what outliers are, how to find them, and why they matter. You’ll also see how outliers can affect averages, test your skills with a quick quiz, and get answers to some of the most common questions students ask about these numbers.
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In math, an outlier is an extreme value, either much smaller or much larger than others in the dataset. In other words, it is a value that lies outside the rest.
Let’s take a look at this dataset:
8, 9, 10, 11, 45
Now, think about this:
Which number is much farther away from the others when you compare their values?
If you picked 45, you’re absolutely right! It’s much higher than the others, which are all pretty close together. That makes 45 an outlier.
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To find an outlier in a dataset, we look for a number that stands out as an extreme value, which will be either much smaller or much larger than the rest.
Let’s look at this dataset:
6, 8, 12, 15, 75
Most of these numbers are relatively close together. Then there’s a big jump from 15 all the way up to 75. Since 75 is much greater than the other values in the set, it is the outlier.
We can also see this on a number line:
The numbers from 6 to 15 are grouped near the beginning. The large gap between 15 and 75 on the number line shows us that 75 is the outlier.
Let’s look at another dataset:
7, 62, 65, 69, 75
Most of the numbers are between 60 and 75 and are fairly close together. But 7 is much smaller than the rest. Since 7 is much less than the other values in the set, it is the outlier.
This is how it appears on a number line:
The large gap between 7 and the rest of the numbers shows us that 7 is the outlier.
Sometimes, when we look at a group of numbers, we want to understand what’s typical for that group. This helps us make better decisions, notice patterns, or get a clearer picture of what’s going on.
For example:
To answer questions like these, we use something called measures of central tendency—ways to find the center of a dataset.
For example, in a dataset 6, 8, 10, 12, we calculate the mean like so:
(6 + 8 + 10 + 12) ÷ 4 = 36 ÷ 4 = 9
Another way is by finding the median. The median is the middle number when all the values are arranged from smallest to largest.
If there’s an odd number of values, the median is the number in the center. For example, in dataset 5, 7, and 9, the median is 7.
If there’s an even number, we find the two middle numbers and take their average. For example, in dataset 6, 8, 10, 12, we’d find the median like so:
(8 + 10) ÷ 2 = 18 ÷ 2 = 9
This is as straightforward as it gets. But how about when there’s an outlier involved? How would that affect the mean and median?
Let’s take a closer look.
To see how outliers affect the mean, we will start with a dataset that includes an outlier:
5, 7, 9, 11, 50
Let’s find the mean:
(5 + 7 + 9 + 11 + 50) ÷ 5 = 82 ÷ 5 = 16.4
Now, let’s see what happens when we remove the outlier (50):
5, 7, 9, 11
We’d get a new mean:
(5 + 7 + 9 + 11) ÷ 4 = 32 ÷ 4 = 8
So let’s ask ourselves:
What happened to the mean when we took out the outlier?
We went from 16.4 down to 8. That’s a big change!
This shows that the mean is very sensitive to outliers, as just one extreme number can shift it a lot.
To see how outliers affect the median, we’ll look at the same data set with the outlier of 50.
5, 7, 9, 11, 50
The middle number is 9, so the median is 9.
Without the outlier, we have:
5, 7, 9, 11
The two middle numbers are 7 and 9:
(7 + 9) ÷ 2 = 16 ÷ 2 = 8
The median changed slightly, from 9 to 8.
This shows that the median is less affected by an outlier than the mean.
Outliers don’t just show up in math class; they appear all around us in real life. And when they do, they can change how we understand what’s typical.
Imagine a teacher looking at these test scores:
78, 82, 85, 88, 32
All the scores are in the 70s and 80s, except one. That 32 is much lower than the rest.
That makes 32 an outlier.
If the teacher calculates the mean, that one low score pulls the average down. The result doesn’t represent how most students performed.
In this case, the median would show a result that’s closer to what’s typical for the group.
Here are a few more examples of outliers in everyday life:
Ready to practice what you’ve learned? Try our flash quiz and see how well you understand outliers.
When you’re done, check your answers at the bottom of the guide!
1. What is an outlier?
A) The most common number in a dataset
B) A number that is much higher or lower than the rest of the values
C) The number in the middle
D) A number that appears more than once
2. Which number is the outlier in this dataset?
6, 9, 11, 12, 44
A) 6
B) 12
C) 44
D) 9
3. What happens to the mean when an outlier is added to a dataset?
A) It usually stays the same
B) It becomes equal to the median
C) It can change a lot
D) It always decreases
4. In this dataset, what is the median?
3, 5, 6, 7, 42
A) 3
B) 5
C) 6
D) 42
5. Why might a teacher prefer to use the median instead of the mean when there’s an outlier in test scores?
A) The median is always higher
B) The median is not affected by any data
C) The median gives a better idea of what most students scored
D) The mean is harder to calculate
6. Which of these is most likely to be an outlier in a dataset of daily temperatures in March?
A) 68°F
B) 70°F
C) 65°F
D) 92°F
Learning about outliers often raises dilemmas among students. We've compiled a list of questions we usually get at Mathnasium of Highlands, along with answers to clear up any confusion.
Most students are introduced to outliers in upper elementary or middle school, often around grades 5 or 6. It’s usually taught when students begin working with mean and median, so they can understand how a single value can affect a dataset.
Yes. A dataset can have more than one outlier. If two or more numbers are much higher or lower than the rest, they can all be considered outliers.
For example, in the dataset 5, 7, 9, 50, 90, both 50 and 90 are much higher than the other values, so they would both be considered outliers.
In middle school math, if a number clearly stands apart from the rest, either much higher or much lower, it’s usually safe to call it an outlier. More advanced methods to define outliers will come later.
Outliers almost always affect the mean because they change the total. The median is based on position, not size, so it might not change, or only slightly.
Mathnasium of Highlands is a math-only learning center in Denver, CO, offering personalized math tutoring to K-12 students of all skill levels.
Our specially trained tutors use the Mathnasium Method™ to deliver face-to-face instruction in a caring group environment, helping students master topics like outliers, typically covered in 5th and 6th grade math.
Each student begins their Mathnasium journey with a diagnostic assessment that allows us to understand their specific strengths and knowledge gaps. Guided by assessment-based insights, we create personalized learning plans that will put them on the best path toward math mastery.
Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment and enroll at Mathnasium of Highlands today!
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If you’ve given our quiz a try, see how you did below:
1. What is an outlier?
B) A number that is much higher or lower than the rest of the values
2. Which number is the outlier in this dataset?
C) 44
3. What happens to the mean when an outlier is added to a dataset?
C) It can change a lot
4. In this dataset, what is the median?
C) 6
5. Why might a teacher prefer to use the median instead of the mean when there’s an outlier in test scores?
C) The median gives a better idea of what most students scored
6. Which of these is most likely to be an outlier in a dataset of daily temperatures in March?
D) 92°F
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