Exam path · Averages
Average questions are solved through the total, not the mean. Multiply the average by the count to recover the sum, do the addition or subtraction the question actually asks about, then divide once at the end. Almost every average question in a bank paper — a missing number, a changed average, a replaced member — is that same three-step move with different words around it.
Averages carry one to two marks directly and sit underneath data interpretation, where a sloppy mean costs a whole set. Search interest in this topic is up 175% year on year, which tracks how often it now appears. It is also the fastest topic on the paper once the total-first habit is in place: the drill below gives you 30 seconds on medium, and that is generous when you stop trying to average the averages.
Try it against the clock. Averages runs at 20s easy, 30s medium and 40s 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.
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 7 numbers is 52. The other 6 of them add up to 314. What is the remaining number?
Averages — total and mean, no paper.
The average of 5 numbers is 46. The other 4 of them add up to 190. What is the remaining number?
Averages — total and mean, no paper.
The average of 6 numbers is 21. The other 5 of them add up to 107. What is the remaining number?
Averages — total and mean, no paper.
Average × count = total. Eight numbers averaging 43 sum to 344. Nothing else in the question can be done safely until that number is on the table.
A missing value is total minus the part you were given (344 − 313 = 31). A new member added is total plus that member, over count plus one. Every variant is an addition or a subtraction, on the total.
Dividing early creates decimals that then have to be carried through the rest of the question. One division at the end is both faster and where the arithmetic errors stop happening.
If adding one member changes the mean by d across n+1 members, that member is the old average plus d × (n+1). Worth knowing, because the setter times these expecting you to do it the long way.
| What the paper asks | The move |
|---|---|
| Find the missing number | Total minus the sum of the rest |
| A new member joins and the average rises by d | New member = old average + d × (new count) |
| One member is replaced | Change in total = change in average × count |
| Average of the first n and the last n overlap | Add both totals, subtract the whole, and the overlap is left |
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 two groups is not the mean of their means unless the groups are the same size. The unweighted answer is always an option, and it is right often enough by coincidence to feel safe.
Divide early and you carry a decimal through three more steps. Keep everything as a total until the final line.
Adding one member changes both the total and the denominator. Forgetting the second half is the classic near-miss, and it produces an answer that is close enough to look plausible.
Convert the average into a total immediately by multiplying by the count, do the addition or subtraction on that total, and divide only once at the end. It removes decimals from the middle of the working, which is where the errors happen.
They are among the quickest arithmetic questions on the paper. This drill allows 20 seconds on easy, 30 on medium and 40 on hard, enforced on the server.
Only if both groups have the same number of members. Otherwise you must weight each average by its count, which in practice means going back to totals and adding those.
Constantly. A table or caselet set will typically include at least one average across a row or a column, so speed here pays twice: once in arithmetic and once in DI.
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