Average adjustment after removing outliers: The average of 50 numbers is 38. If two numbers, 45 and 55, are discarded, what is the new average of the remaining 48 numbers?
Aptitude
Average
Difficulty: Easy
Choose an option
Answer
Correct Answer: 37.5
Explanation
Introduction / Context:When elements are removed from a dataset, recompute the total and divide by the new count to get the updated average. This problem reinforces careful sum tracking.
Given Data / Assumptions:
- Initial average = 38, count = 50
- Removed numbers = 45 and 55
Concept / Approach:Total = average * count. Subtract removed values from the total, then divide by the new count.
Step-by-Step Solution:
Initial total = 50 * 38 = 1900Remove 45 and 55: new total = 1900 - 100 = 1800New count = 48New average = 1800 / 48 = 37.5Verification / Alternative check:The two removed values have mean 50 which is above 38. Removing higher values should lower the average, consistent with 37.5.
Why Other Options Are Wrong:
- 36.5, 37.0, 37.52, 38.5: do not match the exact recomputation.
Common Pitfalls:Forgetting to adjust the count or mis-adding the removed values, which skews the final mean.
Final Answer:37.5