Exam path · Weighted Average
Weighted average questions combine groups of different sizes, or recover the value that moves an average to a target. Multiply each figure by its weight, add those products, and divide by the total weight. The unweighted mean of the two averages is the printed near miss, and it is wrong whenever the groups are different sizes.
Bank and SSC prelims ask this as a combined class average, a new member joining a group, or the missing value that pulls an average to a stated target. The arithmetic is one line once the weights are written down. Averaging the averages is the habit that loses the mark.
Try it against the clock. Weighted Average runs at 30s easy, 40s medium and 55s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
A class of 20 scoring 60 and a class of 30 scoring 80 are not two equal groups. The weights are 20 and 30. If a stem gives only the averages, the groups are the same size and the ordinary mean is enough — most stems do not.
20 × 60 = 1200 and 30 × 80 = 2400. The combined total is 3600. Skipping the multiply and adding 60 + 80 is the unweighted path.
Total weight is 20 + 30 = 50. Combined average = 3600 ÷ 50 = 72. That sits between the two averages, closer to the larger group.
If 5 numbers average 40 and four of them average 36, the full total is 200 and the known total is 144, so the missing number is 56. Do not subtract the averages.
| What the paper asks | The move |
|---|---|
| Two groups, different sizes, combined average | Sum of (size × average) ÷ total size |
| One member joins and the average changes | New total minus old total is the new member |
| One member leaves | Old total minus the leaver, then divide by one fewer |
| All but one number given via a smaller average | Full total minus the known total |
Generated by the same engine that mints the ComputePrep daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
The average of 8 numbers is 63. Seven of them average 67.
What is the missing number?
The average of 6 numbers is 30. Five of them average 34.
What is the missing number?
A group of 8 members has an average of 84. One new member joins, and the new average is 78.
What is the value of the new member?
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
The mean of 60 and 80 is 70. The weighted answer is 72 when the second group is larger. 70 is printed on purpose.
Two groups do not mean divide by 2. The divisor is the headcount, 50 in the example above, not the count of averages you were given.
Averages are not the numbers. Convert both averages back to totals, then subtract. The gap between 40 and 36 is not the missing number.
The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here.
70 is the unweighted mean of 60 and 80. The second class is larger, so it pulls harder: (20×60 + 30×80) ÷ 50 = 3600 ÷ 50 = 72.
4 is the gap between the averages, not a number in the list. The five total 200 and the four total 144, so the missing number is 200 − 144 = 56.
You cannot subtract a member's value from the average. The old total is 300. Remove 80 to leave 220, then divide by the 5 who remain: 44.
It is an average where each value is multiplied by how many times it occurs, or by the size of its group, before you divide. Equal groups collapse to the ordinary mean. Unequal groups do not.
Yes. Prelims papers ask them as combined class averages, a new student joining, or a wrong entry that has to be replaced. They are usually one mark and they sit next to ordinary averages.
About 30 to 55 seconds in prelims. This drill enforces that on the server: 30 seconds on easy, 40 on medium and 55 on hard.
Yes, free with no account. Every question is generated fresh, so the numbers are never the same twice.
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