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Sep 24, 2024

Whether you're just starting to learn about the median, preparing for a standardized exam, or looking to get ahead in your statistics course, you are in the right place.

We’ve put together this easy-to-follow guide to help you **understand the median** with simple explanations, simple instructions, real-life examples, and practical exercises.

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The median is the middle value in a set of numbers arranged from smallest to largest.

To put it simply, if you have a set of numbers and you organize them from the smallest to the largest, the median separates the upper half from the lower half.

Suppose you have the numbers 12, 3, 5, 14, and 8.

You arrange them in order from smallest to largest: 3, 5, 8, 12, and 14.

In this case, the middle is 8, which is the median.

As you begin to learn about the median, you will also encounter a few related concepts that help us understand the data in our dataset:

**Mean:**The average of a set of numbers**Mode:**The number that appears most frequently in a set**Range****:**The difference between the highest and lowest numbers in a set

How Do We Use the Median in Real Life?

Although we learn about the median in the classroom, we use this concept frequently in real life. Here are a few examples:

**Age in a Group:**If you have a group of people and you want to know the middle age, you could find the median. For example, if you have ages 12, 14, 15, 16, and 48, the median age is 15.**Player Performance:**In sports like basketball or soccer, coaches might use the median to understand a player's typical performance. For example, if a soccer player has scored in 7 different games with the following goals: 1, 0, 2, 2, 1, 7, 2, the median number of goals is 2. This means that half the games had more than 2 goals, and half had fewer. The median gives a better idea of the player's usual performance, without being skewed by an unusually high or low number of goals in one game.**Home Prices:**When buying or selling a house, the median home price is often used to show what a typical house costs in an area. This is more reliable than the average because it isn’t skewed by extremely high or low prices.**Traffic Speeds:**In traffic studies, the median speed is used to understand typical driving speeds. It’s the speed at which half the cars are going faster and half are going slower, giving a better sense of usual traffic flow.

To find the median, we follow these steps:

**Arrange the Numbers:**We put the numbers in order from smallest to largest.**Find the Middle:**If there is an odd number of values, the median is the one in the middle. For an even number of values, the median is the average of the two middle numbers.

Let’s start with an example where there is an odd number of values:

**Find the median of the numbers 4, 7, 1, 9, and 5.**

If we follow the steps listed above, we will:

- Arrange the numbers in order: 1, 4, 5, 7, 9.
- Since there’s an odd number of values (5), the median is the middle number:
**5**.

Now, let’s look at an example with an even number of values:

**Find the median of the numbers 2, 8, 3, and 5.**

- Arrange the numbers in order: 2, 3, 5, 8.
- Since there’s an even number of values (4), the median is the average of the two middle numbers:

(3 + 5) ÷ 2 = 4.

And that’s how we find the median! But don’t stop here—let’s explore some tougher examples to sharpen our skills.

Since you’ve learned how to find the median, let’s try some examples that require a bit more work to solve.

Find the median of these numbers: 12, 8, 35, 5, 20.

1) Arrange the numbers from smallest to largest: 5, 8, 12, 20, 35

2) Find the Middle: With 5 numbers (an odd number), the median is the number in the middle: **12**.

Find the median of these numbers: 22, 8, 15, 30, 25, 18.

1) Arrange the numbers: 8, 15, 18, 22, 25, 30

2) Find the middle: With 6 numbers, the median is the average of the two middle numbers, 18 and 22.

(18 +22) ÷ 2 = 20

So, the median is 20.

Find the median of these numbers: 50, 32, 45, 60, 25, 40, 70, 55, 30.

1) Arrange the Numbers: 25, 30, 32, 40, 45, 50, 55, 60, 70

2) Find the Middle: With 9 numbers, the median is the middle number: 45.

Find the median of these numbers: 9, 14, 11, 7, 12, 12, 10, 15.

1) Arrange the numbers: 7, 9, 10, 11, 12, 12, 14, 15

2) Find the middle: With 8 numbers, the median is the average of the two middle numbers, 11 and 12.

(11 + 12) ÷ 2 = 11.5

The median is 11.5

Now that you've seen how it's done, it's your turn! Test your skills with these median exercises.

Find the median of these numbers: 14, 29, 21, 8, 33, 18, 26.

Find the median of these numbers: 42, 55, 38, 29, 47, 50, 33, 46.

Find the median of these numbers: 7, 15, 22, 12, 19, 31, 25, 17, 10.

Find the median of these numbers: 13, 27, 22, 18, 32, 29, 24, 16, 30, 19.

We’ve put together answers to some common questions students have while learning about the median.

Students typically learn about the median in middle school, usually around 6^{th} grade. It’s part of understanding basic statistics, which also includes concepts like the mean, mode, and range.

The median can be more useful when there are outliers, or extreme values, in a data set.

Let’s see why with an example.

Imagine five friends comparing their weekly allowance: $5, $10, $10, $12, and $50.

To find the **mean**, we add them all up and divide by 5.

(5 + 10 + 10 + 12 + 50) ÷ 5 = $17.40

To find the **median**, we line the numbers up in order and pick the middle one.

$5, $10, $10, $12, $50 → The median is $10.

Here, the mean is $17.40, but that doesn’t really represent what most friends are getting. The outlier, that big $50 allowance, makes the mean higher than what’s typical. The median of $10, however, shows the middle value and gives a better idea of what most of the friends receive.

So, when there are outliers, the median can give a better picture of what’s typical, while the mean includes the effect of every value, even the extreme ones.

** **

When you add a new number to a data set, the median can change depending on where the new number falls within the order.

If the new number is added to the middle of the set, it might become the new median.

If the set is even, adding a new number will make it odd, meaning the median will now be the middle number in the new set.

Yes, the median can be a negative number. For instance, in the set -8, -5, -3, 2, 1, there is an odd number of values, and the median is the middle number, **-3**.

Yes, the median can be a decimal. For example, in the set 2, 4, 7, 10, the median is average of 4 and 7, which is** 5.5**.

Mathnasium’s specially trained math tutors work with middle school students of all skill levels to help them understand and excel in any math class and topic, including the median.

Explore our approach to middle school tutoring:

At Mathnasium, we assess each student’s current skills and consider their unique academic goals to create personalized learning plans that will put them on the best path towards math excellence.

Whether you are looking to catch up, keep up, or get ahead in your math class, find a Mathnasium Learning Center near you, schedule an assessment, and enroll today!

If you have completed the 4 examples in the exercise, check your answers here:

- Answer 1: 21

- Answer 2: 46.5
- Answer 3: 17
- Answer 4: 22

How did you do?

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