Class Average Calculator — Mean, Median & Standard Deviation
Paste a list of test scores below — one per line, or separated by commas or spaces — and get the class average (mean), median, standard deviation, range, and a full grade distribution instantly. Perfect for teachers checking a curve and students seeing how they compare.
Grade distribution
Standard deviation shown is the population standard deviation. Grade distribution uses the standard 90/80/70/60 cutoffs.
How class statistics are calculated
Every number this calculator shows comes from a standard statistics formula. Here are all three, with exactly how they work:
Mean (the class average)
Add up every score and divide by the number of scores. Every score counts equally, which is why one or two extreme scores can pull the mean away from the middle of the class.
Median (the middle score)
Sort all scores from lowest to highest and pick the middle one. With an even number of scores, the median is the average of the two middle scores. The median ignores outliers — a 12% and a 100% have the same effect on it as an 81% and an 82%.
Population standard deviation (the spread)
Subtract the mean from each score, square the differences, average them, and take the square root. A small standard deviation means the class bunched up near the average; a large one means scores were all over the place.
Worked example: every step by hand
Take three scores: 90, 80, and 70.
| Step | Math | Result |
|---|---|---|
| 1. Mean | (90 + 80 + 70) ÷ 3 | 80 |
| 2. Median | sorted: 70, 80, 90 → middle value | 80 |
| 3. Differences from mean | 90−80 = 10; 80−80 = 0; 70−80 = −10 | 10, 0, −10 |
| 4. Square the differences | 10² = 100; 0² = 0; (−10)² = 100 | 100, 0, 100 |
| 5. Average the squares | (100 + 0 + 100) ÷ 3 = 66.67 | 66.67 |
| 6. Square root | √66.67 | ≈ 8.165 |
The calculator above returns the same three numbers — mean 80, median 80, standard deviation ≈ 8.165 — plus a lowest of 70, a highest of 90, a count of 3, and a distribution of one A, one B, one C.
What the numbers mean for a teacher
Mean vs. median gap. If the mean is well below the median, a few very low scores are skewing the average — the bulk of the class did better than the average suggests. If the mean is above the median, a few high flyers are pulling it up.
Standard deviation as a curve check. On a 100-point test, an SD around 10–15 is typical. An SD under 5 means almost everyone scored alike (easy or very uniform class); an SD over 20 means wildly uneven performance — the classic case where curving by the median or by a fixed number of points helps. A common curve adds points so the median lands on the desired grade, which is fairer than shifting the mean when outliers exist.
The distribution chart. The A/B/C/D/F bars use the standard 90/80/70/60 cutoffs. A healthy test usually shows a bell-ish spread; a huge F bar plus a big A bar (a "two-hump" shape) can signal the class split into two groups — often a sign some students missed a key concept the others grasped.
Want to combine these into a course grade?
Open the Weighted Grade Calculator →Frequently Asked Questions
What is the difference between the class mean and the class median?
The mean is the arithmetic average — every score added together, divided by the number of scores. The median is the middle score when all scores are sorted. If a few very low or very high scores pull the mean away from the middle, the median is the fairer picture of a typical score.
What does the standard deviation of test scores tell me?
Standard deviation measures how spread out the scores are. A small value means most scores cluster near the average; a large value means scores vary widely. Teachers sometimes use it to curve grades fairly.
How should I paste my scores?
Put each score on its own line, or separate them with commas or spaces. The calculator ignores blank lines and non-numeric labels, so you can paste a column straight from a spreadsheet.
How is the grade distribution calculated?
Every score is placed in a letter-grade bucket using the standard cutoffs: A for 90 and above, B for 80–89.99, C for 70–79.99, D for 60–69.99, and F below 60. The distribution chart counts how many scores fall in each bucket.
Why is the mean lower than the median on my test?
That means the distribution is skewed left: a few very low scores are dragging the average down while most of the class scored above the mean. The median ignores the extremes, so it stays higher.
What is a normal standard deviation for a test?
For a 100-point test, a standard deviation of about 10–15 points is typical. Under 5 means scores are tightly bunched; over 20 means they are very spread out, which is when teachers most often consider a curve.
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