Grouped averages within a class: The average age of 30 students is 12 years. One group of 5 averages 10 years and another group of 5 averages 14 years. What is the average age of the remaining students?

Introduction / Context:
Partitioning a population into subgroups with known averages allows computing the remainder's average by subtracting subgroup totals from the grand total.

Given Data / Assumptions:

• Total students = 30; overall average = 12 ⇒ total age = 360.
• Group A (5 students) average = 10 ⇒ total = 50.
• Group B (5 students) average = 14 ⇒ total = 70.

Concept / Approach:
Remaining students = 30 − 10 = 20. Their total age = 360 − (50 + 70) = 240. Average = total / count.

Step-by-Step Solution:

Verification / Alternative check:
Weighted average check: (50 + 70 + 240)/30 = 360/30 = 12, matching the given overall average.

Why Other Options Are Wrong:

• 8 or 10 or 14 years: Do not balance to the grand total of 360 when combined with the two groups.

Common Pitfalls:
Dividing by 30 instead of 20 for the remainder or misadding subgroup totals.

Final Answer: