Adjusting an average after removing two values: The average of 50 numbers is 38. If two values, 45 and 55, are excluded, what is the average of the remaining 48 numbers?

Introduction / Context:Average adjustments are often easiest by working with totals. Removing some values reduces both the total and the count; recompute the mean from the new total and count.

Given Data / Assumptions:

• Initial count = 50; average = 38
• Removing values 45 and 55

Concept / Approach:Compute original total, subtract the removed numbers, then divide by the new count (48).

Step-by-Step Solution:Original total = 50 * 38 = 1900New total = 1900 - (45 + 55) = 1900 - 100 = 1800New average = 1800 / 48 = 37.5

Verification / Alternative check:Because 45 and 55 average to 50 (above 38), removing them should decrease the mean, which aligns with 37.5.

Why Other Options Are Wrong:36.5 and 37 are too low; 37.52 is a rounding-like distractor; 38 ignores the removal of above-average values.

Common Pitfalls:Dividing by 50 after removal or forgetting to subtract both removed values from the total.

Final Answer:37.5