When finding the median of a set of data, first put the data in order and then find the number located right in the middle. The process is illustrated and summarized in the figure below.
As you can see from the figure above, the median is 18 when the dataset is {8, 11, 15, 18, 24, 30, 31}.
The figure also shows that the median is 21 when the dataset is {11, 15, 18, 24, 30, 31}.
When the number of values is even, it may not be obvious to see the middle value. In this case, you can find the median by taking the average of the two numbers in the middle.
The two values in the middle for the dataset {11, 15, 18, 24, 30, 31} are 18 and 24.
Since (18 + 24) / 2 = 42 / 2 = 21, the median is 21.
Example #1:
Find the median of the following set:
S_{1} = {15, 14, 11}
Put the numbers in the set in order
11, 14, 15
The median is 14 because it is in the middle.
Example #2:
Find the median of the following set:
S_{2} = {5, 3, 7, 2, 4}
Put the numbers in the set in order
2, 3, 4, 5, 7
In the example above, the median is 4 because 4 is in the middle.
When the number of numbers in the set is an odd number as in the two sets above, your median is right in the middle.
Example #3:
Find the median of the following set:
S_{3} = {15, 14, 11,16}
Put S_{3} in order
11, 14, 15, 16
The two values in the middle are 14 and 15
The average is (14+15) / 2 = 29 / 2 = 14.5
So, the median is 14.5
Example #4:
Find the median of the following set:
S_{4} = {6, 2, 8, 9, 1, 10, 4, 12}
Tips when finding the median
When a set contains many numbers, cross out numbers as you put them in order to keep yourself organized.
For example for S_{4}, put 1 in your new ordered list and then cross it out. Then, put 2 and cross it out...
Put S_{4} in order
1, 2, 4, 6, 8, 9, 10, 12
The two numbers in the middle are 6 and 8
(6 + 8) / 2 is 7, so the median is 7
When the number of numbers in the set is an even number, you will end up with two numbers in the middle. In this case, just take the average of the numbers.
You can also find the median quickly using the median formula below.
Median = value of the [(n+1)/2]th term in a ranked data set with n equal to the number of values.
The lesson about median of a set of data will show you how.