The average of 20 numbers is 48. If two numbers, namely, 53 and 70 are discarded, what is the average of the remaining numbers?

Appeared in: NORCET 3 - 2022 (Shift-2)

Explanation

The initial sum of the 20 numbers is calculated by multiplying the average by the count (20 × 48 = 960).
The sum of the two discarded numbers (53 + 70 = 123) is subtracted from the initial sum to get the new sum (960 - 123 = 837).
The new average is found by dividing the new sum by the new count of numbers (20 - 2 = 18), resulting in 837 ÷ 18 = 46.5.

Why Other Options Were Wrong

Option A: This result is incorrect. It may arise from a calculation error, such as incorrectly summing the discarded numbers as 150 (instead of 123). This would lead to a new sum of 810, and 810 ÷ 18 = 45.
Option B: This is an incorrect value, likely resulting from a minor miscalculation during the final division step (837 ÷ 18).
Option D: This incorrect answer might be obtained if the sum of the discarded numbers was wrongly calculated as 105 (instead of 123). This would give a new sum of 855, and 855 ÷ 18 = 47.5.

Related Visual

$step flowchart showing: 1. Start with Average \= 48, Count \= 20. 2. Calculate Total Sum \= 48 20 \= 960. 3. Identify Discarded Sum \= 53 + 70 \= 123. 4. Calculate New Sum \= 96...$

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of average (mean) and its adjustment upon removal of data points as background academic context rather than a clinical decision trigger.
While not a clinical question, the ability to calculate and interpret averages is a fundamental quantitative skill required in many fields, including healthcare.
Nurses use average calculations for tasks like determining average fluid intake/output over a shift or analyzing trends in vital signs.
What if? If only one number (53) was discarded, the new sum would be 960 - 53 = 907, the new count would be 19, and the new average would be 907 ÷ 19 ≈ 47.74.

How to Approach the Question

First, understand the definition of average (mean): Sum of values divided by the count of values.
Use the given average and count to find the initial total sum: Total Sum = Average × Count.
Calculate the sum of the values that are being removed from the dataset.
Subtract the sum of the removed values from the initial total sum to find the new sum.
Adjust the count of numbers by subtracting the number of discarded values.
Finally, divide the new sum by the new count to find the new average.

Concept Tested & Keywords

Concept Tested: Calculation of average (mean) and its adjustment upon removal of data points.
Stem keywords: average, 20 numbers, discarded, 53, 70
Lead-in keywords: what is the average
Negative lead-in flag: false

Question ID

QbrxEQlKknfKEl6KzA1An4

Reference Book

E6 NursingResearch Sukhpal Kaur p. 441-443

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