## 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?## Step-by-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.## 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

## 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.## You might also like...

statisticsfinding the mean from a grouped frequency tablefinding the mode group from a grouped frequency tableunderstanding cumulative grouped frequency tables

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## Worksheet

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