Average adjustment after adding one value: The average of 6 observations is 12. After including a 7th observation, the new average decreases by 1. Find the value of the 7th observation.

Introduction / Context:
This problem highlights how adding one item can decrease an average if the item is below the current average. We compute the exact value via totals.

Given Data / Assumptions:

• Average of 6 = 12
• Average of 7 after adding one = 11

Concept / Approach:
Total = average * count. The new observation equals the difference between the new and old totals.

Step-by-Step Solution:

Verification / Alternative check:
New average check: (72 + 5)/7 = 77/7 = 11. Correct.

Why Other Options Are Wrong:

• 1, 3, 6: These would produce totals 73, 75, or 78, which do not give an average of 11.

Common Pitfalls:
Assuming the new value equals the new average instead of using totals.

Final Answer: