Combined average of two datasets: The average of 30 results is 20, and the average of another 20 results is 30. Find the average of all 50 results combined.

Introduction / Context:
Combining datasets requires weighted averaging. Multiply each subgroup average by its count to get totals, then divide the sum by the combined count.

Given Data / Assumptions:

• Group 1: 30 results, average 20
• Group 2: 20 results, average 30

Concept / Approach:
Overall average = (sum of group totals) / total number of results.

Step-by-Step Solution:

Verification / Alternative check:
The two groups contribute equally to the total. With equal totals but different counts, the overall mean lies between 20 and 30, specifically 24 given the 30 to 20 split.

Why Other Options Are Wrong:

• 25, 27: incorrect weighting.
• 48, 50: misread as totals, not averages.

Common Pitfalls:
Doing an unweighted mean of 20 and 30 (which would be 25) without considering different counts.

Final Answer:
24