Replacement effect on class average age: In a class of 25 girls, the average age decreases by 6 months when a new girl replaces a 20-year-old. What is the age of the new girl?

Introduction / Context:This explores how replacing one member in a group changes the group average and what that implies about the new member's value.

Given Data / Assumptions:

• Class size = 25
• Average decreases by 6 months = 0.5 years
• Replaced girl had age = 20 years

Concept / Approach:Change in average * group size equals change in total. Here, the new total is lower by 25 * 0.5 = 12.5 years relative to before replacement. That drop equals (new age - old age).

Step-by-Step Solution:Change in total = 25 * (-0.5) = -12.5 yearsLet new age = xx - 20 = -12.5 → x = 7.5 years

Verification / Alternative check:New average reduction per student is 0.5 years; across 25 students this matches a 12.5-year reduction in total, consistent with replacing 20 by 7.5.

Why Other Options Are Wrong:8.5, 9, 6, 10 years don’t produce the exact 12.5-year reduction in total required.

Common Pitfalls:Using 24 instead of 25 for the multiplier or converting months to years incorrectly.

Final Answer:7.5 yr