The average age of 19 students is 31 years. Later, it was found that the ages of 14, 24, and 31 were wrongly recorded as 41, 42, and 43 respectively. What is the correct average age?

1. A

   27

2. B

   30

3. C

   29

4. D

   28

Appeared in: KPSC Staff Nurse - 2017

Explanation

• The correct average is 28 years.
• The sum of the three wrongly recorded ages (41, 42, 43) is 126.
• The sum of the three correct ages (14, 24, 31) is 69.
• The total sum of ages was overestimated by 126 - 69 = 57.
• This overestimation of 57, when distributed across the 19 students, inflated the average by 57 / 19 = 3 years.
• Therefore, the correct average is the initial average minus the inflation: 31 - 3 = 28 years.

Why Other Options Were Wrong

• Option A: An average of 27 would imply a total decrease of 4 years from the initial average (31 - 27 = 4). This would mean the total error in the sum was 4 * 19 = 76, which is incorrect. The actual error is 57.
• Option B: An average of 30 would imply a total decrease of 1 year from the initial average (31 - 30 = 1). This would mean the total error in the sum was 1 * 19 = 19, which is incorrect.
• Option C: An average of 29 would imply a total decrease of 2 years from the initial average (31 - 29 = 2). This would mean the total error in the sum was 2 * 19 = 38, which is incorrect.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the correct average after rectifying data entry errors as background academic context rather than a clinical decision trigger.
• While this is a math problem, the underlying skill of ensuring data accuracy is critical in nursing. Errors in recording patient data, such as vital signs, lab values, or medication dosages, can have severe consequences.
• Attention to detail, double-checking calculations, and understanding the impact of errors are fundamental nursing competencies. For example, miscalculating an IV drip rate or a drug dosage can lead to patient harm.
• What if? If only one age was recorded incorrectly (e.g., 14 was recorded as 41), the error would be smaller (41 - 14 = 27). The change in average would be 27 / 19 ≈ 1.42, and the new average would be 31 - 1.42 ≈ 29.58. This shows how every piece of data impacts the overall picture.

How to Approach the Question

• First, identify the key information: the number of students (19) and the initial average age (31).
• Next, list the incorrect values (41, 42, 43) and the corresponding correct values (14, 24, 31).
• Calculate the sum of the incorrect values and the sum of the correct values.
• Find the difference between these two sums. This is the total error in the sum of ages.
• A faster method is to calculate the change in the average. Divide the total error by the number of students. This tells you by how much the average was off.
• Adjust the initial average by this calculated change. If the incorrect values were larger than the correct ones, the initial average was too high, so you must subtract the change.

Concept Tested & Keywords

• Concept Tested: Calculating the correct average after rectifying data entry errors.
• Stem keywords: average age, 19 students, wrongly recorded
• Lead-in keywords: What is the correct average age?

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QKy7YczTBKObMFhOMiuJmG

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