# How to Find the Median

This tutorial explains how to find the median with an example.

If you want to find the median in Excel, refer to the article below:

How to find the median in Excel

### How do you find the median?

You can find the median in the following three steps:

• Arrange data in order of smallest to largest
• Find out if the number of items is even or odd
• Find the middle value

### Find the median

Let’s try to solve the following example:

The list below shows the data of 10 students’ records of the shot-put throw in a junior high school.

• Student A: 7 m
• Student B: 4 m
• Student C: 5 m
• Student D: 9 m
• Student E: 11 m
• Student F: 3 m
• Student G: 4 m
• Student H: 11 m
• Student I: 6 m
• Student J: 7 m

Step 1. Sort by size

Let’s reorder the data.

Sort the data in ascending order.

It looks like this.

• Student G: 3 m
• Student F: 3 m
• Student B: 4 m
• Student C: 5 m
• Student I: 6 m
• Student J: 7 m
• Student A: 7 m
• Student D: 9 m
• Student E: 11 m
• Student H: 11 m

Step 2. Is the number of data odd or even?

Let’s count the number of data.

Is the number of data odd or even?

The data in the example are the records of 10 students in the shot put, right?

So that means there are 10 data in total.

That means the number of data is even.

Step 3. Search for the data in the middle

The median is the middle value when sorted in ascending (or descending) order.

You can sort the data and select the middle one.

But be careful. However, note that the way you select the middle value depends on whether the number of data is odd or even.

If the number of data is even, you should take the average of the two middle values.

The values in the middle are:

• Student J: 7 m
• Student I: 6 m

If we take the average of these two, we get

= (7 + 6) ÷ 2

= 6.5

That’s the median.

### What do you do when the number of data is odd?

What do you do when the number of data is odd?

In the previous example, let’s say that Student F is absent due to a cold.

Then, the number of students who threw the shot would be 9.

So, the number of data is odd.

When the number is odd, it’s easier than when it’s even.

The number in the middle is the median as it is.

In the above example, “7” is right in the middle is the median.

### Summary: There are two ways to get the median

There are two ways to get the median when the number of data is even and odd.

• Sort the data in ascending order
• Find out if the number of data is even or odd
• Find the middle value

Mastering these three steps will help find the median quickly and easily.