When data is given in grouped form, the exact median value cannot be found. Instead, you must determine the group containing the median, also called the median class. This is the class interval in which the median lies.

 

 

Understanding the Median in Grouped Data

The median is the middle value when all data values are arranged in order.

 

For grouped data:
• individual data values are not known
• only frequencies within class intervals are given

 

Because of this, the median is located by position, not by calculating an exact value.

 

 

Using Total Frequency

The first step is to find the total frequency by adding all the class frequencies.

 

This tells you how many data values there are altogether.

 

The median position is halfway through the data set.

 

For grouped data, this is found by considering half of the total frequency.

 

The median is located by position, not by size of values

 

 

Using Cumulative Frequency

To find the group containing the median, cumulative frequency is used.

 

Cumulative frequency shows how many data values are included up to the end of each class interval.

 

To determine the median group:
• calculate the cumulative frequency for each class
• identify the point where the cumulative frequency first reaches or exceeds the median position

 

The class interval where this happens is the group containing the median.

 

This group is called the median class.

 

 

Important Points

The median class:
• contains the middle value of the data
• is identified using cumulative frequency
• is a class interval, not a single value

 

The class with the highest frequency is not necessarily the median class.

 

Common mistake: choosing the class with the highest frequency

 

 

Key Points to Remember

The median of grouped data cannot be found exactly.
Find the total frequency first.
Use cumulative frequency to locate the middle position.
The median class is where the cumulative frequency reaches the median position.
The median class is a group, not a single number.

 

Being able to determine the group containing the median is an essential step when analysing grouped data and prepares you for estimating the median accurately.