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