Average decreases after adding an observation: The average of six observations is 12. When a seventh observation is added, the average decreases by 1. What is the seventh observation?

Introduction / Context:
This mirrors a standard totals method: a new value below the current average pulls the mean down. Compute it via totals.

Given Data / Assumptions:

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

Concept / Approach:
Totals from averages yield the exact seventh value.

Step-by-Step Solution:

Verification / Alternative check:
Rechecking averages confirms correctness.

Why Other Options Are Wrong:

• 1, 3, 6: Do not produce the required new total of 77.

Common Pitfalls:
Assuming the seventh equals the new average without computing totals.

Final Answer: