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?

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:

Verification / 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