Median – Definition and Explanation
The median is the middle value in a data set when the numbers are organized from smallest to largest.
Since the median is in the middle, it divides the data set into two groups.
The first group is the 50% of the data, excluding the median, that is less than the middle value.
The second group is the 50% of the data, excluding the median, that is greater than or equal to the middle value.
Exam questions on the median may simply give a list of values.
Other exam problems will provide practical problems with data sets.
How to Find the Median – Odd Number of Items
The median is easy to find when a data set has an odd number of items, such as 13 or 15 items.
When the group consists of an odd number of items, one item will be exactly in the middle.
Look at the example data set below.
15, 2, 14, 5, 9, 7, 6, 11, 12, 4, 10, 14, 8
We can see that there are 13 items in the above data set.
STEP 1:
To learn how to find the median on exam problem like this, you should first put the numbers in the group in ascending order.
So, first of all, reorder the numbers from lowest to highest.
2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 14, 15
STEP 2:
Since this set has 13 items, the median value is the 7th item in the reordered list.
In other words, six numbers are less than the middle value and six numbers are greater than the middle value.
2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 14, 15
So, the median is 9.
How to Find the Median – Even Number of Items
When the data set consists of an even number of items, like 10 or 12 items, the median is a little more difficult to find.
That is because in this case, there will be two items in the middle.
Look at the example data set that follows.
29, 35, 24, 31, 36, 39, 28, 22, 33, 37, 36, 25, 26, 30
We can see that the data set above contains 14 numbers.
STEP 1:
Remember to put the data set in ascending order first of all.
22, 24, 25, 26, 28, 29, 30, 31, 33, 35, 36, 36, 37, 39
STEP 2:
When the group has an even number of items, you will need to find the two values that are in the middle of the set.
Our data set in this problem has 14 items, so we need the 7th and 8th items in the set.
22, 24, 25, 26, 28, 29, 30, 31, 33, 35, 36, 36, 37, 39
We can check this by counting that there are 6 items in the list that are less than 30:
22, 24, 25, 26, 28, 29, 30, 31, 33, 35, 36, 36, 37, 39
There are also 6 items in the list that are greater than 31:
22, 24, 25, 26, 28, 29, 30, 31, 33, 35, 36, 36, 37, 39
STEP 3:
Add the two middle values together and then divide this result by 2.
30 + 31 = 61
61 ÷ 2 = 30.5
So, the median is 30.5.
You may also want to see our posts on range, mode, and mean.