A student’s marks were incorrectly entered as 32 instead of 96. Due to this, the average marks of the class got decreased by \(\frac{4}{3}\). What is the number of students in the class?
Solving for Number of Students with Marks Error Impact
This problem involves calculating the total number of students in a class based on a discrepancy in marks entry and its effect on the class average.
Step-by-Step Calculation
- Calculate the difference between the correct marks and the incorrectly entered marks. Difference = Correct Marks - Incorrect Marks Difference = \(96 - 32 = 64\)
- Identify the decrease in the class average. Average Decrease = \(\frac{4}{3}\)
- Understand that the total difference in marks (64) caused the average decrease when distributed among all students. Let '\(n\)' be the number of students. The total decrease in the sum of marks is \(n \times \text{Average Decrease}\). Total Decrease = \(n \times \frac{4}{3}\)
- Equate the total difference in marks to the total decrease caused by the error. \(n \times \frac{4}{3} = 64\)
- Solve for '\(n\)', the number of students. \(n = 64 \div \frac{4}{3}\) \(n = 64 \times \frac{3}{4}\) \(n = \frac{64}{4} \times 3\) \(n = 16 \times 3\) \(n = 48\)
Therefore, the number of students in the class is 48.
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