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Examoogle • User • info@examoogle.com • EE-2024-8821
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A student's marks were incorrectly entered as 25 instead of 37. Due to this, the average marks of the class got decreased by 34. What is the number of students in the class?
A) 1
B) 19
C) 3
D) 9
9
Calculate the difference in marks (37 - 25 = 12). Since the average decreased by 4/3, equate: 12/n = 4/3. Solving for n gives n = (12 * 3) / 4 = 9.
Incorrect marks entered = 25, Correct marks = 37, Change in average = 4/3, Number of students = n
Average=Number of observationsSum of observations
Calculate the difference in marks (37 - 25 = 12). Since the average decreased by 4/3, equate: 12/n = 4/3. Solving for n gives n = (12 * 3) / 4 = 9.
Confusing the increase/decrease in average with the sum. The total sum change is 12, so 12/n must equal the change in average.
Calculate the net change in total marks
The difference between the correct marks and the incorrect marks represents the total change in the sum of marks for the class. Change = 37−25=12.
ΔSum=37−25=12
Relate sum change to average change
The change in average is defined as the change in sum divided by the number of students n. Given the average decreased by 34, we set up the equation.
nΔSum=34
Solve for n
Substitute the change in sum into the equation: n12=34. Cross-multiplying gives 4n=36, so n=9.
n=412×3=9
D is correct because the total mark discrepancy of 12 spread across the class results in an average change of 4/3 only when the number of students is 9.
This concept is identical to finding the error in mean calculations in Statistics (CBTII); always equate Total Difference / Count = Average Difference.