The Lesson
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.Question
The grouped frequency table below shows the test scores for a class of students. What group of test scores is the median?StepbyStep:
1
Add another column onto the table, labelled Cumulative Frequency.
For each row of the table, add the entries in the Frequency column up to that row.
2
Find the entry in the bottom row of the Cumulative Frequency column. In this example, it is 9. (Check: You should get the same result if you add up the numbers in the Frequency column).
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}.
3
Find the first entry in the Cumulative Frequency column where this middle number (5) is first reached.
A cumulative frequency of 5 is first reached in the 2^{nd} row.
4
Find the group in the Score column of this row. This is the median group.
Answer:
The median group of the test scores is 6  10.Interactive Widget
Here is an interactive widget to help you learn about 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