The average of 10 observations is 40. Later it is found that one observation was wrongly read as 31 instead of 44. Find the correct average.

1. A

   41.3

2. B

   44.3

3. C

   40.3

4. D

   42.3

Appeared in: DSSSB 12 August 2024

Explanation

• First, calculate the initial sum of the observations by multiplying the average by the number of observations (40 × 10 = 400).
• Next, determine the net effect of the error. The value should have been 44 but was recorded as 31, so the sum is understated by 13 (44 - 31).
• Adjust the initial sum to get the correct sum by adding the difference: 400 + 13 = 413.
• Finally, calculate the correct average by dividing the correct sum by the number of observations: 413 / 10 = 41.3.

Why Other Options Were Wrong

• Option B: This value would result from a significant miscalculation and does not correspond to the corrected sum of 413.
• Option C: This result implies an error of only 3 was added to the sum (400 + 3 = 403), not the actual error of 13.
• Option D: This result implies an error of 23 was added to the sum (400 + 23 = 423), not the actual error of 13.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Average and Data Correction in Quantitative Aptitude as background academic context rather than a clinical decision trigger.
• Accuracy in data is fundamental in healthcare. A misrecorded lab value, vital sign, or medication dosage can have serious patient safety consequences.
• This principle is applied daily in nursing, for example, when calculating total fluid intake/output over a shift. If a 310 mL void was incorrectly charted as 130 mL, the patient's fluid balance would be inaccurately assessed.
• What if? If the observation was read as 44 instead of 31 (the reverse error), the initial sum would be overstated by 13. The correct sum would be 400 - 13 = 387, and the correct average would be 38.7.

How to Approach the Question

• Identify the key values given: number of observations (10), initial average (40), incorrect value (31), and correct value (44).
• Calculate the initial total sum by multiplying the average by the number of observations.
• Determine the difference between the correct and incorrect values. Note whether this makes the initial sum too high or too low.
• Adjust the initial sum by adding or subtracting the difference to find the correct sum.
• Divide the new, correct sum by the number of observations to find the correct average.
• Compare your calculated result with the given options to find the match.

Concept Tested & Keywords

• Concept Tested: Average and Data Correction in Quantitative Aptitude
• Stem keywords: average, observations, wrongly read, correct average
• Lead-in keywords: Find
• Negative lead-in flag: false

Question ID

QHoXpCVRr9PHpq9Ow3Wruw

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