The average of 8 numbers is 14 and the average of 6 of these numbers is 16. What is the average of the remaining 2 numbers?

Appeared in: NORCET 1 - 2020

Explanation

The core concept is that Average = (Sum of Values) / (Number of Values).
First, calculate the total sum for the larger group: Sum of 8 numbers = 8 × 14 = 112.
Next, calculate the total sum for the smaller, known group: Sum of 6 numbers = 6 × 16 = 96.
The sum of the remaining 2 numbers is the difference between the two totals: 112 - 96 = 16.
Finally, find the average of these remaining 2 numbers: 16 / 2 = 8.

Option A: This is an incorrect calculation. If the average of the two numbers were 12, their sum would be 24 (12 × 2). The actual sum is 16.
Option B: This is an incorrect calculation. If the average of the two numbers were 6, their sum would be 12 (6 × 2). The actual sum is 16.
Option D: This is an incorrect calculation. If the average of the two numbers were 10, their sum would be 20 (10 × 2). The actual sum is 16.

Visual 1: Infographic: A visual breakdown showing the formula for average (Sum of items / Number of items) and how to rearrange it to find the total sum (Average × Number of items).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Averages (Mean) as background academic context rather than a clinical decision trigger.
While this is a math question, the ability to calculate and interpret averages is crucial in nursing for tasks like determining average fluid intake/output over a shift, calculating the mean arterial pressure (MAP), or understanding trends in a patient's vital signs or lab results over time.
What if? If the average of the 6 numbers was 15 instead of 16, the calculation would change. The sum of the 6 numbers would be 6 × 15 = 90. The sum of the remaining two would be 112 - 90 = 22, and their average would be 22 / 2 = 11.

How to Approach the Question

Identify the core task: The question asks for the average of a subset of numbers.
Recognize the key formula: Average = Sum / Count. This can be rearranged to Sum = Average × Count.
Step 1: Calculate the total sum of the initial group (8 numbers).
Step 2: Calculate the total sum of the known subgroup (6 numbers).
Step 3: Find the sum of the remaining numbers by subtracting the subgroup's sum from the total sum.
Step 4: Calculate the average of the remaining numbers using their sum and count (2).

Concept Tested & Keywords

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Practise the full NORCET 1 - 2020

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