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 9 Prelims-2025

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 and 70) is 123.
The new sum of the remaining numbers is the initial sum minus the sum of the discarded numbers: 960 - 123 = 837.
The number of remaining items is 20 - 2 = 18.
The new average is the new sum divided by the new count: 837 ÷ 18 = 46.5.

Option A: This value may result from a calculation error, such as incorrectly dividing the new sum or rounding down.
Option B: This is an incorrect calculation. It might arise from a mistake in subtraction or division.
Option D: This value is incorrect and likely stems from a calculation error, possibly in the division step or by only subtracting one of the numbers.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of arithmetic mean after removing data points from a set as background academic context rather than a clinical decision trigger.
While this is a mathematics question, the underlying skill of calculating and interpreting averages is crucial in healthcare.
Nurses use averages to analyze trends in patient vital signs (e.g., average heart rate over 24 hours), interpret lab results, and understand population health data.
This skill is fundamental for evidence-based practice, allowing nurses to critically appraise research studies that report statistical data.

How to Approach the Question

First, understand the core concept: Average = Total Sum / Number of Items.
Identify the initial information given: Number of items = 20, Average = 48.
Calculate the initial total sum using the formula: Total Sum = Average × Number of Items.
Account for the change in the dataset: two numbers (53 and 70) are removed.
Calculate the new total sum by subtracting the removed numbers from the initial sum.
Calculate the new number of items by subtracting the count of removed items.

Concept Tested & Keywords

Concept Tested: Calculation of arithmetic mean after removing data points from a set.
Stem keywords: average, 20 numbers, 48, discarded, 53, 70
Lead-in keywords: what is the average
Negative lead-in flag: false

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