The average of 10 observations is 40. It was realized that an observation was misread as 30 in place of 50. Find the correct average.

Appeared in: DSSSB October 2024

Explanation

The initial sum of 10 observations with an average of 40 is calculated as 10 × 40 = 400.
An observation was misread as 30 instead of the correct value of 50, introducing an error.
The difference between the correct and incorrect value is 50 - 30 = 20. This is the amount by which the total sum was underestimated.
The correct sum is found by adding this difference to the initial sum: 400 + 20 = 420.
The correct average is the correct sum divided by the number of observations: 420 / 10 = 42.

Option A: This value would arise from a calculation error, such as miscalculating the final division or the initial sum.
Option B: This value is incorrect and does not result from the proper adjustment of the total sum based on the identified error.
Option D: This value is too close to the original average and implies a much smaller correction was made to the total sum.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating a corrected average after identifying an error in an observation as background academic context rather than a clinical decision trigger.
Accuracy in data handling is a fundamental skill in many fields, including healthcare, where misreading a value (like a lab result, medication dose, or vital sign) can have significant patient safety consequences.
This problem demonstrates a quick method to correct statistical summaries without re-analyzing an entire dataset, a useful skill for quality control and data verification in research or clinical audits.
What if? If the observation was misread as 50 in place of 30 (the reverse error), the difference would be 30 - 50 = -20. The correct sum would be 400 - 20 = 380, and the correct average would be 38.

How to Approach the Question

First, identify the key values given in the problem: number of observations (10), initial average (40), the incorrect value (30), and the correct value (50).
Calculate the initial total sum by multiplying the average by the number of observations (40 × 10 = 400).
Determine the size and direction of the error by subtracting the incorrect value from the correct value (50 - 30 = +20).
Adjust the initial sum to find the correct sum. Since the correct value is larger, add the difference to the sum (400 + 20 = 420).
Calculate the new, correct average by dividing the adjusted sum by the original number of observations (420 / 10 = 42).
Finally, match your calculated result to the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Calculating a corrected average after identifying an error in an observation.
Stem keywords: average, observations, misread
Lead-in keywords: Find the correct average

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Practise the full DSSSB October 2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.