What does mean, median, and mode mean?
Let’s make the numbers make sense.
Published:
Jan 2025
Key takeaways
- • Mean is the average – Mean is the average of a set of numbers.
- • Median is in the middle – Median represents the rough middle point of a data set.
- • Mode is the most – Mode is the most common value in a set of numbers.
Table of contents
Numbers help us understand the world, and for young learners, that can be a bit of a head-scratcher. Mean, median, and mode are some of the first tools your student will learn to unpack the meaning behind a group of numbers.
Read on to help them master these fundamental math concepts.
What is Mean?
Mean, well, means the average of a set of numbers. You can use this average to understand what is “normal” in a data set.
For example you might have a list of cookie prices across all brands and grocery stores, and you want to know what the typical price is. Finding the average or mean of those prices lets you know what you could expect if you walked into a random store and checked the price.
How to Calculate the Mean
Mean is nice and simple to calculate:
- Step 1. Add up all of the numbers in the data set.
- Step 2. Once you have that total, divide it by the amount of numbers you just added up.
For instance, if you wanted the average of 15 numbers, you would add them up, one-by-one, and then divide the total by 15.
The number you are left with is your mean.
Examples of Mean Calculations
Let’s put this into practice.
Imagine that the following numbers are the ages of kids who watched a recent Sonic the Hedgehog movie in theaters. You want to find the mean to learn the typical age of a Sonic movie fan.
Ages: 12, 11, 7, 15, 6, 14, 12, 13, 14, and 10.
The first step is to add those ages all up. The order does not matter since the sum will be the same.
12 + 11 + 7 + 15 + 6 + 14 + 12 + 13 + 14 + 10 = 114
Great! Now the next and final step is to divide that total by the number of values in the data set, which is just a fancy way of saying the number of numbers we’re working with.
We have 10 numbers, so we will divide our sum, 114, by 10.
114 ÷ 10 = 11.4
That means the average age of Sonic moviegoers is 11.4 years old.
What is Median?
Sometimes sets of numbers have a lot of variation, lots of really high numbers or lots of really small numbers. When the numbers are all over the place, the mean can sometimes be misleading.
For example, if you have 100 numbers, and 99 of them are all lower than 10 but one is 1,000, the average of those numbers will make it look like most of the numbers are larger than they really are.
Median reveals the middle number in a set of numbers when you order them from smallest to largest. You can sometimes get a better sense of the “typical” number by using the median.
How to Calculate the Median
First we’re going to look at how to calculate the median with an odd set of numbers:
- Step 1. You need to arrange the numbers from smallest to largest.
- Step 2. Your median is the number in the middle of the data set. So, if you have 5 total numbers in your data set, the median will be the third number.
Finding the median of an even set of numbers is a little trickier since you don’t have one number right in the middle. Here’s how to find it:
- Step 1. Start by arranging your data set in ascending order, smallest to largest.
- Step 2. Divide the total set of numbers by two and count to the middle of the list.
- Step 3. You should have two numbers right in the middle of the data set. Next, add those numbers together and divide them by two.
The average of those two numbers is your median!
Examples of Median Calculations
Let’s look at those movie-goer ages from earlier and find the median.
Ages: 12, 11, 7, 15, 6, 14, 12, 13, 14, and 10.
Okay we need to rearrange these numbers first, ordering them from smallest to largest.
6, 7, 10, 11, 12, 12, 13, 14, 14, and 15.
There we go! Check to make sure you didn’t miss any numbers. All 10 numbers are there, so we’re good to go. Ten is an even number, so we’ll follow extra steps for this example.
Now we need to divide the number of numbers by two.
10 ÷ 2 = 5
Let’s now count five values in our number list.
6, 7, 10, 11, 12, 12, 13, 14, 14, and 15.
12 is the fifth number, and since we have an even number of values, we need the next number, too, which is also 12.
6, 7, 10, 11, 12, 12, 13, 14, 14, and 15.
Now you can probably guess that the median is 12 since both numbers are 12, but let’s go through the next step just for practice.
We need to add up those two numbers and then divide them by two.
12 + 12 = 24
24 ÷ 2 = 12
That means our median is 12!
What is Mode?
Mode is the most common value in a set of numbers.
You might want to know the mode to figure out the most typical number in a list. This can be helpful when looking at categories, like favorite color where figuring out the mean is either impossible or doesn’t make sense.
How to Identify the Mode
Mode is the easiest to figure out. Here’s how:
- Step 1. Order the numbers in ascending order.
- Step 2. After that, start counting! Look for which number appears the most.
- Step 3. Whatever number has the highest count is your mode.
Some data sets can have multiple modes or no mode at all depending on the numbers.
Examples of Mode Calculations
Let’s look at those movie-goer ages again. Here they are in ascending order.
6, 7, 10, 11, 12, 12, 13, 14, 14, and 15.
Now we simply count how many times each number appears. As you can see, we have two 12s and two 14s.
6, 7, 10, 11, 12, 12, 13, 14, 14, and 15.
No other number appears more often, so we have two modes for this set of numbers, 12 and 14.
A number set with two modes is considered bimodal. If we had three modes, that would be trimodal. Any number sets with more than three modes are considered multimodal.
Differences Between Mean, Median, and Mode
Mean, median, and mode are all different ways of looking at numbers, and each one fits its role.
Mean is great for getting a sense of what is average in large sets of numbers. Ages, product prices, etc. are examples of numbers where the mean is useful to know.
Median is a good option for number sets with a lot of variation where you want to know what the actual middle value is. If you want to look at what the typical worker earns in a company where the CEO makes millions but the beginning employees make minimum wage, the median could be helpful.
Mode is great for determining what is most typical in number sets where the same number is likely to pop up. If you wanted to know how many slices of pizza people want at one time, mode could be helpful if you asked everyone.
Conclusion
Numbers can be even more informative than words for understanding the world. Mean, median, and mode are important tools for starting your journey of learning how numbers reveal the world around us.
FAQs about Mean, Median, & Mode
You can find the mean of a number set by adding up all the numbers and dividing the sum by the total number of values.
You can find the mode by arranging your numbers in ascending order and counting the frequency of each number. The value with the most occurrences is the mode. Some data sets show multiple modes or no mode at all.
To find the median, arrange your numbers in ascending order. If you have an odd number of values, divide the total number of values by two and then count that many from the start of your number list. The value that comes after the counting is done is the very middle of the data set. For even numbers, find the two numbers in the middle and find the average of those two numbers.
