**Median of Grouped Data:** With relation to a continuous group of data, a median is an important value that represents the middle value of a group of data. So it is one of the three measures of central tendencies, the other two being mean and mode. Since the median is an important concept of statistics and probability taught to students.

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**Median of Grouped Data**

We shall explain the concept of median here and provide you with solved examples of the median of grouped data. Understanding the concept of the median is extremely important to measure the results of data and calculate important properties of data such as standard deviation.

For finding the median of any finite list of numbers, the numbers must first be arranged from the smallest to the greatest. If there are an odd number of observations, then the middle value is picked.

### Median of Grouped Data Formula Examples

**Example 1:**

For example, consider the numbers 1,3,4,8,9,9,10

- In this case, the middle value is 8. Hence the median of the group is 8.
- If there are even a number of observations in a group, then there can not be a single middle value. Hence in such cases, the median is calculated by finding the mean of the two middle values.
- For example, consider the numbers 3,9,7,5,7,5
- The median, in this case, is found out by calculating the mean of the middle two numbers, i.e., (7+5)/2 = 6.

Any grouped data can be classified into odd-set or even-set of numbers. The formula for calculating the median for both cases is different. So here we are going to explain to you with examples of how you can find out the median for both odd numbers of numbers as well as even numbers of numbers.

**ODD NUMBER OF DATA**

- Let us take the example of the following data set :

102, 56, 34, 99, 89, 101, 10, 54

- First, we need to place the data in ascending order

10, 34, 54, 56, 86, 99, 101

- Then we need to find the middle numbers.

The middle number of the data is 56. Hence the median of the data is 56.

**EVEN NUMBER OF DATA**

- Now, let us take the example of the following set of numbers :

102, 56, 34, 99, 89, 101, 10, 54

- Since the data consists of an even number of numbers, we need to take out the mean of the middle two numbers
- Hence, the mean is (99+89)/2 = 94.
- Hence the median of the group is 94.