Weighted average of ages after new admissions: The average age of 45 students in a class is 13 years. Then 15 new students with an average age of 18 years join the class. What is the average age of all 60 students now?
Correct Answer: 14.25 yr
Introduction / Context:This is a weighted average across two groups with different sizes and averages.
Given Data / Assumptions:
- Group 1: 45 students, average 13 yr
- Group 2: 15 students, average 18 yr
- Total after joining = 60 students
Concept / Approach:Weighted average = (sum1 + sum2) / total count, where sum is average * count for each group.
Step-by-Step Solution:Sum1 = 45 * 13 = 585Sum2 = 15 * 18 = 270Combined sum = 585 + 270 = 855Average = 855 / 60 = 14.25 yr
Verification / Alternative check:Note that the final average must lie between 13 and 18 and closer to 13 because the larger group is at 13; 14.25 is reasonable.
Why Other Options Are Wrong:13.15 and 12.28 are too low; 16.42 is too high; 15.00 does not match the weighted calculation.
Common Pitfalls:Taking the average of 13 and 18 directly (15.5) without weighting by group sizes.
Final Answer:14.25 yr