The average age of 24 students in a class is 12 years. It is later noticed that the age of one student was taken as 14 years instead of the correct value of 8 years. What is the correct average age, in years, of the class?

Introduction / Context:
This question is about correcting an average when one data value was recorded incorrectly. By understanding how a single correction alters the total sum, we can quickly recalculate the true average for the entire class.

Given Data / Assumptions:
- Number of students = 24. - Recorded average age = 12 years. - One student age was recorded as 14 years instead of the actual age of 8 years. - Only this single error is present in the data.

Concept / Approach:
Average equals total sum divided by number of students. From the recorded average, we know the incorrect total sum. We adjust this total by replacing the incorrect value with the correct one; that is, we subtract the wrong value and add the correct value. Dividing the corrected total by 24 gives the correct average age.

Step-by-Step Solution:
Step 1: Recorded total age = 24 * 12 = 288 years. Step 2: The age 14 was used but the actual age should be 8. Step 3: Correct total age = recorded total - wrong value + correct value. Step 4: So, correct total age = 288 - 14 + 8. Step 5: 288 - 14 = 274, and 274 + 8 = 282 years. Step 6: Correct average age = 282 / 24. Step 7: 282 / 24 = 11.75 years.

Verification / Alternative check:
Observe that the recorded age was 6 years higher than it should have been. Thus the recorded total is 6 years too high. If we subtract 6 from 288, we again get 282, which leads to the same correct average 11.75. This provides a quick mental check on the calculation.

Why Other Options Are Wrong:
- 11.25, 11.5 and 12.25 correspond to incorrect adjustments to the total sum. - 12 is the original incorrect average and ignores the correction.

Common Pitfalls:
Learners sometimes add the difference instead of subtracting it, or they divide the correction by the wrong number. A reliable method is to always start from total = average * number of items, then carefully adjust that total based on the direction and size of the error.

Final Answer:
The correct average age of the class is 11.75 years.