How to Find the Median from a Grouped Frequency Table (Mathematics Lesson)
Finding the Median Group from a Grouped Frequency Table
We can find which group in a grouped frequency table is the median.How to Find the Median Group from a Grouped Frequency Table
Finding the median group from a grouped frequency table is easy.An Example Question
The grouped frequency table below shows the test scores for a class of students.What group of test scores is the median?
Step 1
For each row of the table, add the entries in the Frequency column up to that row.
Step 2
Find the middle number of this number. (See Finding the Middle Number in the Top Tip).
In this example, there are 9 numbers, so the middle number is the 5^{th}.
Step 3
A cumulative frequency of 5 is first reached in the 2^{nd} row.
Step 4
The median group of the test scores is 6  10.
A Real Example of How to Find the Median Group from a Grouped Frequency Table
The slider below gives another example of how to find the median group from a grouped frequency table.How to Find Other Averages from a Grouped Frequency Table
We can use a grouped frequency table to find the other types of average: the mean and the mode.Read more about finding the mean from a grouped frequency table
Read more about finding the mode group from a grouped frequency table
Interactive Test
showHere's a second test on finding the median group from a grouped frequency table.
Here's a third test on finding the median group from a grouped frequency table.
Top Tip
A Formula to Find the Middle Number
The median is the middle number in an ordered set. If you know how many numbers there are in a set, which is the middle number?The formula for finding the middle number is:
In this formula, n is how many numbers there are in the set.
In the example on this page, we asserted that the 5^{th} number is the middle of 9.
We can now use the formula to show this:

n = 9
(n + 1) ÷ 2 = (9 + 1) ÷ 2 = 5
Top Tip
Grouped Frequency Tables Are for Continuous Data
A grouped frequency table is for continuous data.Continuous data can take any value (within a range). For example, it may take any value from 1  10: 1.5, 2.31, 3.05.
This is unlike discrete data, which can only take certain values. For example: 1, 2, 3. It can't take values in between these values: it can't take 1.5.
Note
What Is a Grouped Frequency Table?
A grouped frequency table is a frequency table where the numbers are grouped together.It shows you how often numbers within each group appear in a list of numbers.
What Is the Median?
The median is an average of a set of numbers.The median is the middle number in a set of numbers that has been arranged in order. (If there are an even number of numbers in a set, the median is the mean of the middle two numbers).