How to Solve Weighted Average Problems
Solve weighted average aptitude problems with the value times weight formula, a worked example, and practice questions with answers.
Expected Interview Answer
A weighted average multiplies each value by its own weight before summing, then divides by the total weight — Weighted Average = Σ(value × weight) / Σ(weight) — unlike a simple average which implicitly treats every weight as equal.
Averaging two groups of different sizes by simply averaging their two averages silently assumes both groups are equally weighted, which overstates or understates the true combined figure whenever the group sizes differ. The correct approach multiplies each group’s average by its own count, sums those products, and divides by the total count across all groups. This same logic extends beyond simple counts to any weight — probability, time, or proportion — and is the same mechanism used in alligation, where the ratio of quantities is derived by inverting the differences from the weighted mean. Weighted averages sit closer to the value with the larger weight, never exactly midway between two unequal-weight values.
- Prevents the classic error of averaging two averages directly
- Generalizes to any weight, not just group counts
- Directly connects to alligation for reverse ratio problems
AI Mentor Explanation
A batter’s career average is not the simple average of their average in ODIs and their average in Tests, it is the total runs across both formats divided by total dismissals across both, which weights each format by how many innings were actually played there. A player with 50 ODI innings averaging 40 and only 5 Test innings averaging 80 has a career average pulled strongly toward 40, not the naive midpoint of 60, because the weight (innings played) is wildly unequal. Weighted averages always favor the more heavily weighted value, exactly the mechanism a career-average calculation demonstrates.
Worked example
Class A
- 30 students, avg 70
- Total = 2100
Class B
- 10 students, avg 90
- Total = 900
Weighted average
- (2100+900)/40 = 75
Step-by-Step Explanation
Step 1
Identify each value and its weight
List every value alongside the count or proportion it represents.
Step 2
Multiply value by weight
Compute value × weight for every component, not just the raw values.
Step 3
Sum products and sum weights
Add all the value×weight products, and separately add all the weights.
Step 4
Divide to get the weighted average
Σ(value×weight) ÷ Σ(weight) gives the true combined average.
What Interviewer Expects
- Correct distinction between a simple average and a weighted average
- Recognizing when unequal group sizes make simple averaging wrong
- Ability to compute Σ(value×weight)/Σ(weight) accurately
- Connecting weighted average logic to alligation for reverse-ratio problems
Common Mistakes
- Averaging two averages directly without weighting by their respective counts
- Using the wrong quantity as the weight (e.g. using rate instead of count)
- Forgetting to divide by total weight rather than the number of groups
- Treating a weighted average as always the midpoint between the extreme values
Best Answer (HR Friendly)
“I never average two averages directly unless the groups are the same size — instead I multiply each value by its own weight, sum those products, and divide by the total weight. This pulls the result toward whichever component has more weight, which is exactly why a portfolio dominated by one stock, or a class with more students, skews the combined average toward itself rather than sitting at the naive midpoint.”
Follow-up Questions
- How does weighted average relate to the alligation method for finding a mixing ratio?
- How would you compute a weighted average when weights are given as percentages instead of counts?
- When is a simple average actually correct instead of a weighted one?
- How would you find a missing weight given the overall weighted average and all values?
MCQ Practice
1. A shop sells 20 units at 50 rupees and 30 units at 80 rupees. The average selling price per unit is?
(20×50 + 30×80)/50 = (1000+2400)/50 = 3400/50 = 68.
2. Group X (weight 3) has value 60. Group Y (weight 1) has value 100. The weighted average is?
(3×60 + 1×100)/4 = (180+100)/4 = 280/4 = 70.
3. Why can averaging two averages directly produce a wrong answer?
Simple averaging of two averages silently assumes both groups have identical weight, which is wrong whenever group sizes differ.
Flash Cards
Weighted average formula? — Σ(value × weight) ÷ Σ(weight).
Why not average two averages directly? — It assumes equal weights, which is wrong when group sizes or weights differ.
Which side does a weighted average lean toward? — Toward the value with the larger weight, never the simple midpoint.
How does weighted average relate to alligation? — Alligation is the reverse problem: given the weighted average, find the weight ratio.