Class Mark

The class mark is the midpoint of a class interval. It is also known as the class midpoint. The class interval is calculated by summing the upper limit and lower limit of the class interval in a grouped data and then dividing the result by two. We use class marks in various places to calculate the mean, and to draw the line graph etc. 
 

The class mark can be also calculated by calculating difference between the average upper limit and the average lower limit of the class interval.

But we use a formula to calculate the class mark. The formula is as follows:
     
   Class Mark = Lower Limit + Upper Limit / 2

Here, 

The Upper Limit, refers to the highest value of the class interval.

Lower Limit, refers to the lowest value of the class interval

Class Interval, refers to the size of each group in a grouped frequency distribution.
 

To calculate the class mark, follow these steps:


Step 1: First, we have to identify the upper and lower limits of the class interval.


Step 2: Then, we have to add the upper limit and the lower limit together.


Step 3: Finally, divide the sum of both the limits by two to find the average of the class mark.
 

A class mark in a frequency distribution denotes the average value or midway of each class interval. It is computed by summing up the interval’s upper and lower bounds, then dividing it by two. In the frequency distribution given below, it shows the class mark also:

 

There are many types of class mark, but the most important types of class mark is mentioned below:
 

• Simple Class Marks
• Exclusive Class Marks
• Inclusive Class Marks

Let us now see more about these types of class marks:


Simple Class Marks:

Simple class marks represent the midpoint of each class interval and are calculated by taking the average of the lower and upper class limits. For example, if a class interval is from 40-50, the simple class marks would be (40 + 50)/2 = 45.


Exclusive Class Marks:

Exclusive class marks are used when the class intervals do not include both endpoints. In this case, exclusive class marks are calculated in the same way as simple class marks, but with the consideration that there is exclusion of one or both endpoints.


Inclusive Class Marks:

We use inclusive class marks when the class intervals are both the endpoints. These class marks represent the midpoint of the inclusive range. For example, if a class interval is from 10-20 and both includes both 10 and 20, the inclusive class mark would be
(10 + 20)/2 = 15.
 

There are a lot of real-life applications of class marks. Let us now see the applications and uses of class mark in our day-to-day applications:

Market Research and Consumer Analysis:

In market research, businesses analyze consumer age groups, income ranges and expenditure brackets to identify purchasing trends. Class marks help estimate the average consumer characteristics for better decision-making.


Education and Student Performance Analysis:


Educational institutions use class marks to analyze student performance based on their mark's distribution in exams. The class mark provides a representative score for each interval, making statistical analysis easier for performance evaluation.


Demographic and Census Studies:


Government agencies conducting census surveys frequently categorize their population into age groups, income brackets or other demographic divisions. Class marks help in estimating average income, median age or literacy rates, which are important for policymaking and resource allocation.