To compute the overall average of two groups with known averages and sizes, which method is correct?

• A. Compute the weighted average by multiplying each group average by its size, summing, and dividing by total size
• B. Use the smaller group's average only
• C. Take the simple average of the two group averages
• D. Use the larger group's average only

Answer: (B)

When you want the overall average of two groups that have different sizes, you must use a weighted average. Each group’s average should contribute in proportion to how many items are in that group. Multiply each group’s average by its size, add those products, and divide by the total number of items.

Mathematically: overall average = (n1 × m1 + n2 × m2) / (n1 + n2), where n1 and n2 are group sizes and m1 and m2 are their means.

For example, if one group has 40 items with an average of 75, and the other has 60 items with an average of 65, the combined average is (40×75 + 60×65) / (40+60) = (3000 + 3900) / 100 = 69. This result sits between the two means and is drawn toward the mean of the larger group, reflecting its bigger influence.

Using only one group's average or simply averaging the two means assumes equal group sizes, which isn’t given here, and would misrepresent the true overall average.