Grade Distribution
Class average, spread, pass rate, and the letter-grade breakdown from a list of scores.
Median 80%, standard deviation 10.5, range 58–95. Mean and median are close, so the distribution is fairly symmetric.
19 of 20 students at or above 60%.
| Grade | Range | Students | Share |
|---|---|---|---|
| A | 90+ | 4 | 20% |
| B | 80–89 | 6 | 30% |
| C | 70–79 | 6 | 30% |
| D | 60–69 | 3 | 15% |
| F | 0–59 | 1 | 5% |
Letter bands here are the common 90/80/70/60 cut-offs. If your scheme differs, read the distribution from the scores rather than the letters — the mean, spread, and shape are what tell you whether an assessment worked.
A distribution shows what an average hides. For a class of 20 with a mean of 79.3% and a median of 80%, the spread is a standard deviation of 10.5 across a range of 58 to 95 — with 4 A grades, 6 Bs, 6 Cs, 3 Ds, and one fail.
The average is the least interesting number
Two classes can both average 75% while telling completely different stories. In one, almost everyone scored between 70 and 80 — the teaching landed consistently. In the other, half the class scored above 90 and half below 60 — which usually means something went wrong for a specific group, and the average conceals it entirely.
The standard deviation is what separates those cases. A small SD means scores cluster tightly around the mean; a large one means they are spread out. For a classroom test an SD somewhere around 10 to 15 percentage points is typical, and a very small SD can indicate a test that was too easy to separate anyone.
Mean against median
Comparing the two reveals the shape. When they are close, the distribution is roughly symmetric. When the mean sits below the median, a few very low scores are dragging the average down — often a handful of students who did not attempt the paper properly, and the median describes the typical student better. When the mean sits above, a few very high scores are pulling it up.
This matters practically: if three students scored zero for reasons unrelated to the teaching, the mean will suggest the class did worse than it did, and the median is the fairer summary to act on.
This uses the sample standard deviation, dividing by n − 1, which is the usual convention when a class is treated as a sample of possible performance.
Reading a distribution
Work through the numbers in order, because each one qualifies the last:
- 1 Start with the mean. 79.3% for the example class — a reasonable overall result on its own.
- 2 Compare it against the median. The median is 80%, almost identical, so the distribution is fairly symmetric with no extreme outliers distorting it.
- 3 Look at the spread. A standard deviation of 10.5 across a 58–95 range is a healthy spread — the test separated students without anyone bottoming out.
- 4 Check the shape. The letter breakdown is 4 A, 6 B, 6 C, 3 D, 1 F — a single peak in the middle, which is what a well-pitched assessment usually produces.
- 5 Read the pass rate. 19 of 20 at or above 60% is a 95% pass rate.
- 6 Ask what the shape suggests. A cluster at the top means the test was too easy to discriminate; two separate humps often mean part of the class missed a prerequisite.
What different shapes tend to indicate
Shape is a prompt for investigation, not a diagnosis. The explanation always sits in the teaching and the paper, not in the statistics.
| Pattern | What it often means |
|---|---|
| Single peak near the middle | A well-pitched assessment that separates students |
| Bunched at the top, small SD | Too easy — it cannot distinguish the strongest students |
| Bunched at the bottom | Too hard, or content that was not adequately covered |
| Two separate humps | Part of the class missed a prerequisite or a key lesson |
| Wide flat spread | Very mixed prior attainment, or inconsistent marking |
| Mean well below median | A few non-attempts dragging the average — use the median |
Distribution is not a curve
Describing how a class performed is a separate act from changing those results. This tool only describes. If a paper turns out to have been unfairly hard and you decide to adjust the marks, that is curving, and it needs its own method and its own justification — the grade curve calculator handles that side.
Two cautions on reading too much into a single set of scores. A class of twenty is a small sample, so a distribution that looks alarming may simply be noise; the same test given to the same cohort a week later would look somewhat different. And the letter bands used here are the common 90/80/70/60 cut-offs, which many institutions do not use — if yours differ, read the underlying scores rather than the letters, since the mean, spread, and shape do not depend on where the boundaries fall.