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?
Aptitude
Average
Difficulty: Easy
Choose an option
Answer
Correct Answer: 5
Explanation
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:
Old total = 6 * 12 = 72New total = 7 * 11 = 77Seventh observation = 77 - 72 = 5Verification / 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:
5