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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
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.



Step 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 5th.

Step 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 2nd row.



Step 4
Find the group in the Score column of this row. This is the median group.

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
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Here'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 5th 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).

What's in a Name?

"Median" comes from the Latin "medianus", meaning "middle".