How to Solve Average Marks of a Class Problems
Solve average marks of a class aptitude problems by combining subgroup totals and counts, with a worked example and practice questions.
Expected Interview Answer
Average marks of a class problems are solved by converting each subgroup’s average marks into a total (Total = Average × number of students), combining subgroup totals and subgroup counts separately, and only dividing once at the very end to get the combined average.
When a class splits into subgroups — boys and girls, pass and fail, or sections A and B — each subgroup’s total marks is its own average times its own count; these totals simply add together, and the counts simply add together, giving a combined average of (Total₁ + Total₂) ÷ (Count₁ + Count₂). This weighted-average approach is essential whenever subgroup sizes differ, because a naive average of the two subgroup averages ignores that a larger subgroup should pull the combined average closer to its own value. The same total-and-count method extends to three or more subgroups without any change in logic.
- Weighted averaging correctly accounts for unequal subgroup sizes
- Totals-then-divide-once avoids compounding rounding errors
- Scales cleanly from two subgroups to any number of subgroups
AI Mentor Explanation
A squad’s combined batting average across top-order and lower-order batters is not the simple average of the two group averages, because the top order usually faces far more innings. Instead, add the top order’s total runs to the lower order’s total runs, add their innings counts, then divide once — the same weighted-average method needed whenever a class’s average marks come from combining a large group with a small one.
Worked example (combining two sections)
Section A
- 30 students, avg 70
- Total = 2100
Section B
- 20 students, avg 80
- Total = 1600
Combined average
- 3700 / 50 = 74
Step-by-Step Explanation
Step 1
Convert each subgroup to a total
Total = Average marks × number of students, for each subgroup separately.
Step 2
Sum the totals
Add all subgroup totals together to get the combined total marks.
Step 3
Sum the counts
Add all subgroup student counts together to get the combined count.
Step 4
Divide once
Combined average = Combined total ÷ Combined count.
What Interviewer Expects
- Correct conversion of each subgroup average into a total before combining
- Recognizing why simple averaging of two averages is wrong for unequal group sizes
- Correct final division using the combined count, not the number of subgroups
- Extending the method cleanly to three or more subgroups
Common Mistakes
- Averaging the two subgroup averages directly, ignoring different sizes
- Forgetting to also sum the counts, not just the totals
- Dividing by the number of subgroups instead of the combined student count
- Mixing up which subgroup total belongs to which count
Best Answer (HR Friendly)
“I always convert each group’s average marks into a total by multiplying by its student count, add up all the totals, add up all the counts, and divide only once at the very end. Averaging the two averages directly is a common trap because it silently assumes the groups are the same size, which is rarely true in these problems.”
Follow-up Questions
- How would you extend this to combine three class sections instead of two?
- What changes if you are given the combined average and asked to find one subgroup’s average?
- How does this weighted-average method relate to a general averages problem?
- When would the simple average of two averages happen to be correct?
MCQ Practice
1. Class A has 25 students averaging 60 marks. Class B has 15 students averaging 80 marks. The combined average is?
Total = 25×60 + 15×80 = 1500+1200 = 2700. Combined average = 2700/40 = 67.5.
2. A class of 40 students has an average score of 55. If 10 students with average score 75 are added, the new class average is?
Total = 40×55 + 10×75 = 2200+750 = 2950. New count = 50. Average = 2950/50 = 59.
3. Two sections have equal average marks. What must be true of their combined average?
If both subgroup averages are equal, the weighted combination always equals that same average, independent of group sizes.
Flash Cards
How to combine two class sections’ average marks? — Sum both totals (avg × count), sum both counts, divide once.
Why not average the two section averages directly? — It ignores unequal section sizes, which skews the true combined average.
Formula for combined average? — (Total₁ + Total₂) / (Count₁ + Count₂).
Does this method extend to 3+ sections? — Yes — sum all totals and all counts, then divide once, regardless of the number of groups.