How to Calculate and Convert Average Marks of Periodic Tests to a Score Out of Ten According to CBSE
Understanding how to calculate the average marks of periodic tests and convert it into a score out of ten is crucial for students and educators, especially under the Central Board of Secondary Education (CBSE) marking scheme. In this guide, we will walk through the steps and provide examples to help you accurately calculate and convert your marks.
Step-by-Step Guide to Calculate the Average of Two Marks from Periodic Tests
To obtain the average of two marks from periodic tests, follow these simple steps:
Add the two marks together.
Divide the sum by 2.
The formula for the average is:
Average (Mark 1 Mark 2) / 2
Converting the Average to a Score Out of Ten
If the periodic tests are scored out of a maximum different from 10, such as 20 or 100, you need to scale the average to a score out of 10. The formula to convert the average mark to a score out of 10 is:
Score out of 10 (Average / Maximum Marks) × 10
Example Calculation 1
Example: Suppose Mark 1 18 and Mark 2 16.
Average (18 16) / 2 34 / 2 17
If these marks are out of 20, the conversion to a score out of 10 would be:
Score out of 10 (17 / 20) × 10 8.5
Example Calculation 2
Example: Suppose you have 27/30 in the first exam and 48/50 in the second one.
The least common multiple (LCM) of 30 and 50 is 150. So, adjust the marks as follows:
First mark (27/30) × (5/5) 135/150
Second mark (48/50) × (3/3) 144/150
Find the average:
135/150 144/150 279/150
Average 279/150 1.86
To convert this average to a score out of 10:
150 is the total marks, so 150 / 10 15. Now divide the average mark by 15:
1.86 / 15 0.124
Multiply by 10 to convert to a score out of 10:
0.124 × 10 1.24
Your mark is 1.24/10. Yay!
Summary
1. Calculate the average of the marks.
2. Convert the average to a score out of 10 based on the original maximum marks of the periodic tests.
3. If the maximum marks are different, adjust the conversion accordingly.
Additional Notes and Tips
1. If the total marks are the same (e.g., both exams are out of 50), simply add the marks and divide by 2.
2. If the total marks are not the same, find the least common multiple (LCM) to adjust the marks to a common denominator before calculating the average.
3. Always double-check your calculations to ensure accuracy.