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 principle is that the total sum of a set of numbers is the average multiplied by the count of numbers.
First, calculate the total sum for the larger group: Sum of 8 numbers = 8 × 14 = 112.
Next, calculate the total sum for the known subgroup: Sum of 6 numbers = 6 × 16 = 96.
The sum of the remaining numbers is the difference between these two totals: 112 - 96 = 16.
Finally, find the average of these remaining numbers by dividing their sum by their count: 16 / 2 = 8.

Option A: Choosing 12 is incorrect. This would imply the sum of the remaining two numbers is 24 (12 × 2), but the calculated sum is 16.
Option B: Choosing 6 is incorrect. This would imply the sum of the remaining two numbers is 12 (6 × 2), which contradicts the calculated sum of 16.
Option D: Choosing 10 is incorrect. This would imply the sum of the remaining two numbers is 20 (10 × 2), whereas the actual sum is 16.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating averages from subsets of data as background academic context rather than a clinical decision trigger.
While not a clinical question, strong numeracy skills are essential for nurses for tasks like calculating drug dosages, monitoring fluid intake/output, and interpreting trends in vital signs or lab results.
This type of problem-solving demonstrates the ability to work with data sets, a skill applicable to analyzing patient charts and research.
What if the average of the 6 numbers was 15 instead of 16? The sum of the 6 numbers would be 6 × 15 = 90. The sum of the remaining two would be 112 - 90 = 22. The average of the remaining two would then be 22 / 2 = 11.

How to Approach the Question

First, identify the key information given: the average and count for a total group, and the average and count for a subgroup.
Recall the fundamental formula for averages: Average = (Sum of values) / (Number of values).
Rearrange the formula to find the total sum: Sum = Average × Number of values.
Calculate the total sum for the initial group (8 numbers).
Calculate the total sum for the subgroup (6 numbers).
Subtract the subgroup's sum from the total group's sum to find the sum of the remaining items.

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.