Working Out a Test Score: Negative Marking, Weights and Grade Boundaries

Averaging percentages is not weighting them

Two tests, two ways of combining them, two different answers. By points: add all the earned marks, add all the available marks, divide. By percentage: convert each test to a percentage first, then average those. The two agree only when every test is out of the same total. The moment one test is worth ten marks and another is worth a hundred, averaging the percentages gives the ten-mark quiz the same voice as the hundred-mark exam, which is almost never what anyone intends.

Work the numbers once and you will never confuse the two again. Nine out of ten is 90 %; sixty out of a hundred is 60 %. Averaged, 75.00 %. By points, 69 out of 110, which is 62.73 %. The gap is 12.27 percentage points and it comes entirely from the quiz being eleven times smaller than the exam. On the site's default rows the same effect is mild — 85.71 % by points against 87.00 % averaged — because 50 and 20 are within a factor of three of each other. The rule of thumb: the further apart your totals, the further apart the two methods, and the more it matters which one your institution uses.

Neither method is the syllabus, and that is the third answer nobody expects. If the handbook says the exam is worth sixty per cent of the module, the correct calculation is 0.40 × 90 + 0.60 × 60 = 72.0 %, and it agrees with neither of the above. This tool cannot express that: it has no weight column, only earned and total. Two ways out. Rescale the marks so the points match the intent — enter the coursework as 36 out of 40 and the exam as 36 out of 60, which reproduces 72.0 % exactly — or use the weighted-grade calculator, which takes a weight per category and does the multiplication for you.

Negative marking and when guessing is worth it

A penalty for wrong answers exists to cancel the value of a blind guess, and it does that at exactly one setting: subtract one divided by the number of options minus one. On a five-option question with a quarter-mark deducted, a blind guess is worth 0.20 × 1 minus 0.80 × 0.25, which is precisely zero. Guess or leave blank, the expectation is identical. Change the penalty and the balance tips: a quarter-mark on a four-option question leaves a blind guess worth +0.0625 marks, so answering everything is correct; a half-mark on four options makes it −0.125, so leaving blanks is correct; a full mark deducted makes it −0.5, and a page of guesses becomes expensive.

The interesting move is not guessing but eliminating. Take the five-option question with the neutral quarter-mark penalty. Rule out one option and you are guessing among four, which is worth +0.0625 marks. Rule out two and you are among three, worth +0.1667. Down to two plausible answers, the guess is worth +0.375, six times more than the neutral point. This is why the standard advice under negative marking is not "never guess" but "never guess blind": the penalty is calibrated against total ignorance, and any partial knowledge at all puts you on the profitable side of it.

None of this lives in the calculator. It has no penalty field, no question count and no option count; the only thing you can do is compute the net yourself and enter it. Forty right and twenty wrong out of sixty questions, at a quarter-mark deducted, is 40 − 5 = 35, so type 35 and 60. The raw score would have been 66.7 %; the net is 58.3 %, which on the US standard scale is the difference between a D and an F. Two warnings if you do this. The tool accepts a negative earned score without complaint — enter −3 out of 50 and it reports −6.0 % and grades it F — and it accepts an earned score larger than the total, so 60 out of 50 returns 120 % and an A. Neither is flagged.

Grade boundaries differ by country, and none of them is the default

The scale menu offers ten conventions and defaults to the American A–F in every one of the six languages, which is worth changing before you read anything. The same overall score lands very differently across them. Take the tool's own default, 85.7 %: a B on the US scale, a First-class on the UK degree bands, 17.1 out of 20 with the mention Très bien in France, grade 2 in Germany, 8.6 out of 10 and Notable in Spain, Buono in Italy, Muito bom in Portugal. Now take 62 %: a D in the United States — which reads as barely passing — and an Upper second in the United Kingdom, which is the classification most graduate schemes ask for.

Two of the conversions are worth checking against the source, because they are not folklore. The German band edges the tool uses — 92, 81, 67, 50 and 30 — are exactly the IHK point-to-grade key used for vocational examinations, where 100 to 92 points is a 1, 91 to 81 a 2, 80 to 67 a 3, 66 to 50 a 4, 49 to 30 a 5 and 29 or below a 6. Note what the tool drops: the real key is a hundred-step scale that also yields a decimal grade from 1,0 to 6,0, so 85 points is a 2,0 and 82 points is a 2,3. The tool gives you the whole band and no decimal. The French mentions line up too — Assez bien from 12, Bien from 14, Très bien from 16 — which is what the Code de l'éducation sets for the baccalauréat, though the code has a fourth level at 18, Très bien with the jury's congratulations, that the tool does not offer.

One conversion is visibly wrong at the edge, and it is worth knowing about because it lands on the pass mark. On the French scale the tool picks the band first and formats the mark second, and the mark is rounded to one decimal. At 49.9 % it therefore prints "10.0/20 · Insuffisant": a passing mark of ten out of twenty next to a verdict of fail. The verdict is the correct one — 49.9 % is below the 50 % threshold the tool uses for a pass — and the 10.0 is a rounding artefact of 9.98. If you are anywhere near the line, read the percentage rather than the converted mark.

Small things the tool does silently

A row whose total is zero, blank or unparseable simply disappears from the calculation. It stays on screen with an em dash where its percentage would be, and it contributes nothing to the overall — no warning, no strike-through. That is usually what you want when you have added an empty row, and exactly not what you want when you have typed a letter into a number field and not noticed.

The per-test badges are rounded to whole percentages while the overall carries one decimal, so 42 out of 50 shows as 84 % and 18 out of 20 as 90 %, but the total is 85.7 %. Do not try to reconstruct the total from the badges; they have already lost the fractions. And when a numeric national scale is selected, the badge under the total switches from showing your raw points to showing the converted mark — on the French scale you get "17.1/20 · Très bien" instead of "B · 60/70". If you wanted to see the points, keep a non-numeric scale selected.

Finally, know which tool you are on. This one takes several tests and combines them by points. Its single-test sibling, the grade calculator, takes one pair of numbers and returns a percentage and an American letter, with no country scales at all. The weighted-grade calculator is the one with a weight column, and the easy grader turns a number of questions and a number of wrong answers into a whole grading chart. Four calculators, four different questions, and only one of them can honour the weights in your handbook.

Frequently asked questions

Why is my overall score lower than the average of my test percentages?

Because the tool adds all the earned points and all the available points, then divides once. That gives a big test more say than a small one, which is usually right and is definitely different from averaging. If your best result was on a short quiz and your worst on a long exam, the points method will pull you down; if it was the other way round, it will pull you up. The gap is small when your tests are of similar size and large when they are not — 9/10 and 60/100 come out at 62.73 % by points and 75.00 % averaged.

How do I enter an exam with negative marking?

Compute the net yourself and enter it as the earned points, leaving the total as the maximum available. Forty correct and twenty wrong out of sixty questions at a quarter-mark deducted per wrong answer is 40 minus 5, so enter 35 and 60. Do not enter 40 and then try to subtract afterwards — the tool has no penalty field and will not do it for you. Watch two things: a negative net is accepted without warning and reported as a negative percentage, and there is no cap at 100 %, so a mistyped total will happily give you 120 % and an A.

Should I guess when there is a penalty for wrong answers?

It depends on the size of the penalty against the number of options, and on how much you know. A penalty of one divided by the number of options minus one makes a blind guess worth exactly zero — a quarter-mark on five options, a third of a mark on four. Below that threshold, blind guessing gains slightly; above it, blind guessing loses. But almost nobody is truly blind. Eliminate one plausible answer out of five under a quarter-mark penalty and the guess is worth +0.0625 marks; get down to two and it is worth +0.375. Under any of the usual penalties, answering a question you have partly narrowed is the right call, and leaving it blank is the mistake.

Which grading scale should I pick?

The one your institution uses, and note that the menu opens on the American A–F in every language, so it is almost certainly not already right. The choice changes nothing about the arithmetic — the percentage is the same on all ten — it changes only the label attached to it and, on the numeric national scales, the converted mark. Two things worth knowing before you rely on the label. The German bands match the IHK point key used for vocational exams, but the tool gives you only the whole grade where the real key also yields a decimal from 1,0 to 6,0. And the French pass threshold sits at half marks, so anything at or above 50 % converts to ten out of twenty or better.

One of my rows shows a dash instead of a percentage. Why?

Its total is zero, empty, or something the parser could not read as a number. Rows in that state are dropped from the overall as well as from the badge, silently and without a warning, so the total you are looking at was computed from fewer tests than you can see. Check the total column of every row that shows a dash. A leftover blank row is harmless; a row where you typed a letter or a stray space into the total is not, because it removes a real result from the calculation without telling you.