How to Find the Median from a Grouped Frequency Table (Mathematics Lesson)
Finding the Median Group from a Grouped Frequency TableWe can find which group in a grouped frequency table is the median.
How to Find the Median Group from a Grouped Frequency TableFinding the median group from a grouped frequency table is easy.
An Example QuestionThe grouped frequency table below shows the test scores for a class of students.
What group of test scores is the median?
For each row of the table, add the entries in the Frequency column up to that row.
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.
A cumulative frequency of 5 is first reached in the 2nd row.
The median group of the test scores is 6 - 10.
A Real Example of How to Find the Median Group from a Grouped Frequency TableThe 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 TableWe 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
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.
A Formula to Find the Middle NumberThe 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
Grouped Frequency Tables Are for Continuous DataA 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.
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).