Average correction after data error: The average age of 54 girls was initially computed as 14 years. One girl's actual age is 10.5 years, but it was taken as 13. Find the corrected average (approximate to the nearest whole year).

Introduction / Context:
When a recording error is found, adjust the total by removing the wrong entry and adding the correct one. The new average is the corrected total divided by the unchanged count. The prompt asks for an approximate whole-year answer.

Given Data / Assumptions:

• Count = 54 girls
• Old average = 14 years → old total = 54 * 14 = 756
• Wrong entry used = 13 years; correct value = 10.5 years

Concept / Approach:
Corrected total = old total - wrong value + correct value. Corrected average = corrected total / 54. Round to the nearest year as requested.

Step-by-Step Solution:

Verification / Alternative check:
Because the correction lowers the total by only 2.5 across 54 students, the average hardly changes and remains approximately 14 when rounded to the nearest year.

Why Other Options Are Wrong:

• 10.50, 12.50, 12: far from the computed 13.95.
• 13: this is closer than others but the prompt asks for rounding to a whole year; 13.95 rounds to 14.

Common Pitfalls:
Dividing by 53 after removing the incorrect entry; the headcount remains 54 because we replaced a value, not removed a student.

Final Answer:
14 yr