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

Introduction / Context:
This question is about correcting an average when an individual value was misreported. You are given the average based on incorrect data and the nature of the mistake. The task is to adjust the total accordingly and compute the new corrected average. Such questions reflect real world data correction scenarios in classrooms or surveys.

Given Data / Assumptions:

• Number of students = 24.
• Original average age (with error) = 12 years.
• One student's age was recorded as 14 years instead of the correct 8 years.
• We assume all other ages were recorded correctly.

Concept / Approach:
We start by computing the total age based on the incorrect average. Then we adjust the total to correct the misrecorded age by subtracting the wrong value and adding the correct value. Finally, we divide the corrected total by the original number of students to obtain the corrected average.

Step-by-Step Solution:
Step 1: Incorrect total age based on original average = 24 * 12 = 288.Step 2: The wrong entry was 14, but it should have been 8.Step 3: Net correction needed = correct age − wrong age = 8 − 14 = −6.Step 4: Correct total age = 288 − 6 = 282.Step 5: Correct average age = 282 / 24.Step 6: 282 divided by 24 is 11.75 years.

Verification / Alternative check:
We can see that the incorrect total was 6 years too high because one student's age was overstated by 6 years. Reducing the total by 6 and dividing by 24 reduces the average by 6 / 24 = 0.25 years. Thus, the corrected average = 12 − 0.25 = 11.75 years, which matches our computation.

Why Other Options Are Wrong:
Option 11.25 would represent a decrease of 0.75 from 12, which is too much. Option 11.5 corresponds to a correction of 12 years in total, not 6. Option 12.25 increases the average, which contradicts the fact that the misrecorded age was higher than the true age. Option 12 is simply the uncorrected average.

Common Pitfalls:

• Adding the correction instead of subtracting when the wrong age is larger than the correct age.
• Forgetting to recalculate the total before dividing.
• Making arithmetic errors when dividing 282 by 24.

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