What is the overall average for 10 students with an average of 78 and 5 students with an average of 88?

• A. 81.33
• B. 79.00
• C. 82.67
• D. 84.00

Answer: (C)

To find the overall average when groups have different sizes, multiply each group’s average by the number in that group, add those totals, and divide by the total number of students. Here, the first group contributes 10 × 78 = 780 points, and the second group contributes 5 × 88 = 440 points. The combined total is 780 + 440 = 1220 points among 15 students. 1220 ÷ 15 = 81.333..., so the overall average is 81.33. The correct value is 81.33; the other numbers don’t match the actual total when properly weighted. Note that averaging the two group averages without weighting by group size would give (78 + 88)/2 = 83, which is higher than the true weighted average because the larger group has the lower average.