Understanding the Problem: Calculating the Average Marks of 28 Students
Introduction to the Problem
To find the average marks of 28 students in a group of 30, where two students scored 0, we can follow a step-by-step process that utilizes the concept of average and basic arithmetic. This problem may appear complex at first glance, but by breaking it down systematically, it becomes quite straightforward.
Step 1: Calculate the Total Marks of All 30 Students
The average marks of the entire group of 30 students is given as 42. To find the total marks of all 30 students, we use the formula for average:
[ text{Total marks} text{Average marks} times text{Number of students} 42 times 30 1260 ]
Step 2: Subtract the Marks of the Two Students Who Scored 0
Two members of the group scored 0 marks. Therefore, we subtract these marks from the total marks to find the sum of the marks of the remaining 28 students:
[ text{Marks of the two students} 0 0 0 ]
[ text{Total marks of the other 28 students} 1260 - 0 1260 ]
Step 3: Calculate the Average Marks of the Other 28 Students
The average of the remaining 28 students can be found by dividing the total sum of their marks by the number of those students:
[ text{Average marks of other students} frac{text{Total marks of other students}}{text{Number of other students}} frac{1260}{28} 45 ]
Therefore, the average marks of the other 28 students is 45.
Simplifying the Concept
This problem is an excellent example of how to apply the basic concept of average (which is the sum of numbers divided by the number of numbers) to more complex scenarios. By following these steps, one can see that such questions are not as daunting as they might initially seem. The key is to break the problem down into manageable parts and apply simple arithmetic principles.
Remember:
The formula for average is: [ text{Average} frac{text{Sum of numbers}}{text{Number of numbers}} ] In mathematical problems involving averages, it is crucial to identify the total quantity and then divide by the total count to find the average.Conclusion
In conclusion, by understanding the steps involved and using basic arithmetic, we can easily find the average marks of the remaining students. Such questions are crucial in mathematics and can be highly beneficial for students preparing for exams or simply brushing up on their problem-solving skills.
Throughout this process, it is important to maintain a clear and organized approach to solving such problems. By doing so, you can tackle any similar question with confidence and ease.