In a class of 25 students, the average marks were 64. Later, it was found that a student's marks were wrongly recorded as 45 instead of 75. What is the new average marks of the class after correcting the mistake?

1. A

   65

2. B

   64.8

3. C

   65.2

4. D

   66

Appeared in: NCL (Northern Coalfields Limited)-NO

Explanation

• The initial total marks for the 25 students were 25 * 64 = 1600.
• A student's marks were wrongly entered as 45 instead of 75, meaning the total score was undercounted by 75 - 45 = 30 marks.
• The correct total marks for the class should be 1600 + 30 = 1630.
• The new, correct average is the corrected total marks divided by the number of students: 1630 / 25 = 65.2.

Why Other Options Were Wrong

• Option A: This option is incorrect. It might be chosen due to a calculation error, possibly by incorrectly rounding the result or miscalculating the adjustment needed for the average.
• Option B: This option represents a decrease in the average, which is incorrect. The error involved under-reporting a score, so the corrected average must be higher than the original average of 64.
• Option D: This value is too high. To get an average of 66, the total marks would need to be 66 * 25 = 1650, which is an increase of 50 marks from the original total.

Related Visual

• Visual 1: Flowchart: A flowchart illustrating the 4-step process: 1. Calculate initial total. 2. Find the error difference. 3. Adjust the total. 4. Calculate the new average.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Average and Error Correction as background academic context rather than a clinical decision trigger.
• While not a clinical question, this type of problem tests basic numeracy and attention to detail, which are critical skills for nurses.
• Nurses frequently perform calculations for medication dosages, IV drip rates, and patient intake/output, where a simple arithmetic error can have serious consequences for patient safety.
• What if the error was reversed (recorded as 75 instead of 45)? In that case, the total marks would be over-reported by 30. The new total would be 1600 - 30 = 1570, and the new average would be 1570 / 25 = 62.8.

How to Approach the Question

• First, identify the given information: number of students (25), initial average (64), wrong value (45), and correct value (75).
• Calculate the initial sum of all marks by multiplying the number of students by the average: 25 × 64.
• Determine the effect of the error. The score was recorded as 45 but should have been 75, so the sum is lower than it should be. Find the difference: 75 - 45.
• Adjust the initial sum by adding this difference to correct the total.
• Finally, calculate the new average by dividing the new, corrected sum by the number of students.

Concept Tested & Keywords

• Concept Tested: Average and Error Correction
• Stem keywords: average marks, class of 25 students, wrongly recorded, 45 instead of 75
• Lead-in keywords: What is the new average

Question ID

QLIQunF3-jBvS0kqnlNH4y

Copy ID