Finding the median

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.

The figure above shows that the median is 21 when the set is {11, 15, 18, 24, 30, 31}.

You can find the median by taking the average of 18 and 24 since (18 + 24) / 2 = 42 / 2 = 21.

Finding the median when the number of values is odd

Example #1:

Find the median of the following set:

S₁ = {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:

S₂ = {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.

Finding the median when the number of values is even

Example #3:

Find the median of the following set:

S₃ = {15, 14, 11,16}

Put S₃ 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:

S₄ = {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 S₄, put 1 in your new ordered list and then cross it out. Then, put 2 and cross it out...

Put S4 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.

Measures of central tendency

Finding the mode