How to Find the Median

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Introduction

The median, which means the middle, is the value in the center of a sorted list of numbers. The median gives information about how the numbers are distributed.

Terms

Median - The median is the middle value in a list when values are sorted.

Lesson

To find the median of a set of numbers, first arrange the numbers in ascending order, the median is then the number in the center of the list. If the number of items in the set is odd, there will always be a well-defined median. If however the number of items in the set is even, the median is defined as the mean of the two items in the center of the list.

For example, the median of the set , which contains 7 items, is the 4th item in the list, 5.

To find the median of the even set , take the average of the two center terms, 2 and 4.

$ext{Median}=dfrac{a+b}{2}$

$ext{Median}=dfrac{2+4}{2}$

$ext{Median}=dfrac{6}{2}$

$ext{Median}=3$

Examples

Find the Median (Example #1)

7, 8, 5, 2, 1

Right now the numbers are out of order, so it is difficult to tell which number will be in the middle of the list. So first put the numbers in order:

1, 2, 5, 7\text{ and }8

We can see that 5 is in the middle of the list. There are two numbers less than 5, and two numbers greater than 5.

The median of this set is 5

Find The Median (Example #2)

Each day Allison went for a walk. On Monday she walked 4 miles, on Tuesday 4 miles, on Wednesday 2 miles, on Thursday 3 miles, and on Friday 3 miles. What was the median number of miles that Allison walked?

Right now the numbers are out of order, so it is difficult to tell which number will be in the middle of the list. So first put the numbers in order:

2, 3, 3, 4\text{ and }4

We can see that 3 is in the middle of the list. There are two numbers less than 3, and two numbers greater than 3.

The median of this set is 3

Find the Median (Example #3)

22, 14, 13, 12, 19, 10

Right now the numbers are out of order, so it is difficult to tell which number will be in the middle of the list. So first put the numbers in order:

10, 12, 13, 14, 19\text{ and }22

To find the median in this situation, take the average (mean) of 13 and 14

\dfrac{\text{13 + 14}}{\text{2}} = 13.5

The median of the set is 13.5