How to Find the Median of a Series of Numbers

The median of a series of numbers is, simply put, the number that divides the group of numbers into two equal parts when the numbers are listed in order from least to greatest. Exactly half the data will be below the median number of the series and exactly half the data will be above the median number. The median is called a measure of central tendency and is used in analyzing data. The process of finding the median varies slightly depending on whether the series contains an even or odd number of numbers.

Things You'll Need

• Pencil and paper
• Calculator, optional
• Basic arithmetic skills

Instructions

1. List the numbers in the series in order from least to greatest. If a number is repeated list it as many times as it occurs.

2. Count the total number of entries in the series of numbers. Again, if a number is repeated count it as many times as it occurs.

3. Suppose the total number of numbers in the series is an odd number. The median is the number exactly in the middle of all the numbers listed. Here's an example to illustrate. Suppose the series of numbers is 21, 22, 22, 25, 26, 28, 28, 29, 31. The total number in the series is nine, which is an odd number. The number in the middle is 26, so that is the median for this series of numbers. Notice that there four numbers below 26 and four numbers above 26.

4. Now suppose the total number of entries in the series is an even number. Because there is not just one number that is in the exact middle, to find the median you take the average of the two middle numbers. Remember, finding the average means you add those two numbers and divide the sum by two. Here's another example to illustrate. Suppose the numbers in the series are 1, 2, 2, 3, 4, 4, 5, 7, 10, 10, 10, 11. When you count all the numbers in the series, you get 12, which is an even number. The two middle numbers are 4 and 5. To find the average of 4 and 5, add them together and divide the sum by 2. That gives 9 divided by 2, which gives 4.5. So 4.5 is the median for this series of numbers. Notice that in the series of 12 numbers, exactly six numbers are less the median of 4.5 and exactly six numbers are greater than 4.5.