Introduction
When dealing with educational data, it's often necessary to integrate the performance of multiple classes to get a holistic view. This article will explore how to calculate the average marks percentage of two classes combined, using a practical example. We'll start by breaking down the formula and then walk through a detailed step-by-step solution.
Understanding the Problem
We are given the average marks percentage of two classes and need to find the combined average marks percentage. The first class has 20 students with an average of 66%, and the second class has 15 students with an average of 70%.
Formulating the Solution
Step 1: Calculate the Total Marks for Each Class
The total marks for a class can be found by multiplying the average marks percentage by the number of students, then converting the result to a base of 100 (in decimal form).
Class 1 (20 students, average 66%)
Total marks for Class 1:
( text{Total marks for Class 1} 20 times 0.66 times 100 1320 )
Class 2 (15 students, average 70%)
Total marks for Class 2:
( text{Total marks for Class 2} 15 times 0.70 times 100 1050 )
Step 2: Calculate the Combined Total Marks
To find the combined total marks, simply add the total marks of both classes:
Combined total marks 1320 1050 2370
Step 3: Determine the Total Number of Students
The total number of students in both classes is the sum of the number of students in each class:
Total students 20 15 35
Step 4: Calculate the Combined Average Marks Percentage
The combined average marks percentage can be found by dividing the combined total marks by the total number of students and then converting back to a percentage:
Average percentage (2370 / 35) * 100 ≈ 67.71%
Therefore, the average marks percentage of the two classes combined is approximately 67.71%.
Alternative Method: Using Weighted Averages
Step 1: Calculate the Total Number of Marks for Each Class
This step is the same as in the previous method:
Total marks for Class 1: 1320
Total marks for Class 2: 1050
Step 2: Calculate the Combined Total Marks
Add the total marks for both classes:
Combined total marks: 1320 1050 2370
Step 3: Calculate the Total Number of Students
Add the number of students in both classes:
Total students: 20 15 35
Step 4: Calculate the Combined Average Marks Percentage Using Weighted Average
The weighted average can be found using the formula:
Average percentage (1320 / 35) * (20 / 35) (1050 / 35) * (15 / 35)
Average percentage 67.71%
Conclusion
By following these steps, we can accurately calculate the average marks percentage of two classes combined. This method is especially useful when analyzing student performance across different classes or groups, and can be applied in educational research, school management, and other educational settings.