Interpreting Data: What's the Median?

Lesson Plan - Get It!

Audio:

In the first part of this Interpreting Data series, you learned how to find the mean for a set of data.

Before you begin learning about median, let's practice finding the mean. Find the mean for the following set of data. Check your answer with a calculator:

13, 27, 6, 13, 22

The mean for this set of data is 16.2. If you did not get 16.2 for your answer, you may want to go back and review the Related Lesson on mean in the right-hand sidebar before moving on. You will need to know how to find the mean to complete this lesson.

Now, you will learn another way to analyze and interpret data: finding the median.

• When you hear the word median, what comes to mind?

Median means middle, and when determining the median of a group of numbers, you are just looking for the middle number.

Let's find the median of a series of numbers you saw in the previous lesson. You found the mean, or average, number of goals scored per game for Josie's soccer team.

• What is the median, or middle number, for this set of data?

• Did you say 2 is the median for this set of data?

If you said the answer is 2, you are incorrect.

Although it is in the middle, there is one thing you must do before simply finding the middle number like you did in the beginning of the lesson.

Before you can find the median for any set of data, you must first put the numbers in order from least to greatest. Make sure to write all the numbers, including those that are used more than once.

When you put the goals scored at each of Josie's soccer games in order, it should look like this:

2, 2, 3, 3, 5

• What is the median is for this set of data?

Did you say 3 is the median for this set of data? That is correct!

When you put the numbers in order from least to greatest, 3 is the middle number.

Remember, the middle number should have the same amount of numbers on each side of it. For example, in this problem, there are two numbers before the 3 and two numbers after the 3.

Unfortunately, the median is not always as easy to find as it was in the problem with Josie's soccer team. Anytime you have an odd amount of data, there is a clear middle number. When you have an even amount of data, there are two middle numbers.

For example, Tom's soccer team scored the following goals at each game this season.

• What is the median for this set of data?

1, 1, 2, 3, 3, 6

When you put the data in order from least to greatest, you can see there are two middle numbers; 2 and 3.

• Does that mean 2 and 3 are both the median?

No, only one number can be the median for a set of data. If only one number can be the median for a set of data, how do you think you would go about finding the median?

To find the median for an even set of data, you must find the mean (average) for the two middle numbers. Use this information to help you find the median for the number of goals that Tom's soccer team scored.

2 + 3 = 5

5 ÷ 2 = 2.5

The median number of goals that Tom's soccer team scored is 2.5. When you add the two middle numbers (2 and 3) together, you get 5. 5 divided by 2 (the total amount of data that was added) is 2.5.

Sometimes, when you divide, the quotient may have a never-ending decimal. When this is the case, round to the nearest hundredths place.

This information may seem confusing when it is first introduced, but once you get the hang of it, finding the median is easy.

Move on to the next section to continue reviewing how to find the median for a set of data.