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.

For example, find the median for the following set:

S₁ = {15, 14, 11}

Put the numbers in order

11, 14, 15

The median is 14 because it is in the middle

Other examples:

S₂ = {5, 3, 7, 2, 4}

Put 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.

However, 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

Examples

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

S₄ = { 6, 2, 8, 9, 1, 10, 4, 12}

Put S₄ in order

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...

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