How to Find the Median

How do you find the median of a large group of numbers? The first step is you have to list the numbers in order from least to greatest. Then we find the middle value, which is the median. Some times there is a catch. If there is an even amount of numbers in the set, that means two numbers are technically in the middle. So we have to take an average of those values by adding them and dividing them by two.

How to Find the Median

Finding the median can be tricky, because sometimes it’s straightforward and some times there is calculation involved. First we always put the numbers in order from smallest to largest. Then we can find the middle value several ways. The way that’s shown in the video above is to mark off the least and greatest numbers, and keep doing so until you get to the middle. You can also do a calculation.

Median of Even Set

When you have a set with an even amount of numbers, finding the median is harder. The way you find this is you take the total count of numbers in the set and divide by 2. This gives you only one of the two numbers that make up your median. You must also include the following number. Then you have to take the average of those two.

For instance, if you had a set of 8 numbers, and you had them listed in order. There will actually be two numbers in the middle of the list. To find out which numbers are in the middle you divide 8 by 2, which gives you 4. So if you start with the smallest number and count up, the middle numbers will be the fourth AND fifth (because you must also include the next one). So to find the median you would take numbers 4 and 5, add them, and then divide by two to find your median.

Median of Odd Set

Some times you will have an odd count of numbers. In this case you divide the total count of numbers by 2, and then round UP to the nearest number. This is your median number, because it is in the middle of the set.

For instance, if you had a group of 15 numbers in a set, to find the median you would divide 15 by 2. This gives you 7.5. To find the median we round this number up to 8. Make sure that the numbers are in order from smallest to largest. Your 8th number is in the middle, so it is the median.

Median Example Problem

How to Find the MedianLet’s find the median of this set of data:

10, 16, 19, 21, 13, 16, 25, 29, 10, 12, 18, 16, 20, 27, 11, 15

When we put these numbers in order from smallest to largest it looks like this:

10, 10, 11, 12, 13, 15, 16, 16, 16, 18, 19, 20, 21, 25, 27, 29

We count how many numbers are in the set, which is 16. Since this is an even number, we have to find the two numbers that are in the middle. We divide 16 by two, which gives us 8. We also include the NEXT number, which will be the 9th number. We start with the smallest number and find out what the 8th and 9th number are. Coincidentally they are both 16. This means automatically that our median is 16.

Remember, if those numbers had been different, we would have to add them and divide by two. Always remember this.

Another Median Example Problem

Let’s find the range of the following set:

57, 43, 65, 55, 39, 50, 65, 64, 52, 61, 49

We begin by putting the numbers in order from least to greatest, which is:

39, 43, 49, 50, 52, 55, 57, 61, 64, 65, 65

We count to see how many numbers are in the set and find out there are 11. We divide 11 by 2, which gives us 5.5. We round it up to the nearest number, which gives us 6. We begin counting from the smallest and see that our 6th number is 55. This is the median of the set.

To learn how to find other values of a set of numbers, check out the other articles in this series:

How to Find the Mean

How to Find the Mode

How to Find the Range

How to Find the Midrange

 

 

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