Reading a class in five numbers
A column of scores answers "how did each student do." It takes five summary numbers to answer the teacher's question — "how did the assessment do" — and each of the five catches something the others miss. This guide works all five on one honest 12-student roster, the same one the calculator loads as its example, so every number here can be checked against the tool.
The roster
Twelve scores: 55, 62, 68, 71, 74, 77, 79, 83, 85, 88, 91, 95. Paste them into the calculator (they are pre-loaded) and follow along.
Mean 77.3: the center of gravity
The scores sum to 928; divided by 12 that is 77.33, shown as 77.3. On the common plus-minus scale the class average is a C+. The mean is the number everyone reports and the one every point of curve moves directly — but it is also the number a single outlier drags hardest, which is why it never travels alone.
Median 78: the middle student
Sorted, the 6th and 7th scores are 77 and 79; their average, 78, is the median. Here the median sits seven tenths above the mean (78 − 77.33 = 0.67) — near-agreement, which says the roster is roughly symmetric. When the mean falls well below the median, a few very low scores are pulling it down and the "class average" understates the typical student; that gap, not either number alone, is the first thing worth reading.
Range 40: the spread's crude first cut
Low 55, high 95, range 40. Two students, one number — useful mostly as a sanity check that both ends of the roster were real scores and not typos. The range says nothing about the ten students between them, which is the standard deviation's job.
Standard deviation 11.5: the honest spread
The population standard deviation of this roster is 11.5 points. Rule-of-thumb reading: the typical student sits about 11.5 points from the mean, so most of the class lands between roughly 66 and 89 — and glancing back at the sorted list, eight of twelve do, with two stragglers on each side. A tight SD (5–7 on a 100-point test) says the assessment sorted the class into a narrow band; a wide one (15+) says the test split the room, and any single "class average" hides that split.
One honest technicality the tool documents rather than buries: it divides by n (population), treating the roster as the whole class rather than a sample of some larger one. The sample version divides by n−1 and reads slightly larger — 12.0 here instead of 11.5. Neither is wrong; they answer different questions, and for "how spread out was my class," population is the question actually being asked.
The distribution: where the letters landed
Against the common default scale the twelve scores fall: one A (95), one A− (91), one B+ (88), two B (83, 85), no B−, two C+ (77, 79), one C (74), one C− (71), one D+ (68), no D, one D− (62), one F (55). That empty B− row and the lone F are exactly the kind of detail the mean erases: a 77.3 average sounds uneventful, but a twelfth of this class is failing while a quarter holds a B+ or better. The distribution is also where a scale edit shows its teeth — drop the A minimum from 93 to 90 and the roster's letter mix changes without a single score moving.
What this page deliberately does not do
It does not store, transmit, or analyze anything you paste — there is no server behind it, which is the only honest way to handle a roster. And it does not recommend a curve: it measures. When the five numbers convince you the assessment ran hot or cold, the curve applier is the next page — it takes the same pasted roster and shows what each standard curve would actually do to it, student by student, before anyone commits.