How we estimate percentiles

A clear explanation of the data and the method, so you can judge how much weight to give the numbers.

What the data is

Every number here comes from official public test-results files: the North Dakota Department of Public Instruction assessment data (NDSA through 2024 and ND A+ from 2025, ELA & Math in grades 3-8, and Science in grades 4 and 8). These files report, for each school / grade / year:

the percentage of students in each performance level, for every school, district, and the state. For privacy, North Dakota prints most school and district percentages as ranges (such as 15-19%), so we use a value inside each range that makes the levels add up to 100%. North Dakota doesn’t publish the number tested, so a group’s size comes from its enrollment in that grade (scaled to the state’s published number tested where its technical report gives one). Every group’s student counts are whole numbers that land back inside North Dakota’s own ranges. When no whole-number split of the enrollment figure can do that, the group size is moved to the nearest one that can (about 3% of groups, usually by one or two students), and
from those figures, an estimated average score: the center of the bell curve that best matches the share of students below each level’s cut score.

Important: the public data does not contain individual student scores, only these group summaries. So no tool can compute a true rank of one child against every other child. What we provide is a well-grounded estimate.

How the percentile is estimated

North Dakota publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Proficient” is 428-462). Given your child's score, we:

identify which performance level the score falls in;
count everyone in the lower levels as scoring below;
within the score's own level, spread that level's students along the group's fitted curve (below) rather than evenly across the level's range. Students bunch up toward the middle of the scale, so an even spread would put too many of them out at the far ends of the lowest and highest levels. Checked against published statewide score distributions, this lands within about one percentile point of the true value for a typical score.

That gives the percentile: the estimated share of students in the group who scored at or below the entered score.

About the smooth curve

The bell-like curve on each chart is a truncated-normal distribution fitted so that its area within each performance level matches the level counts, centered on that estimated average score. It's there to visualize the shape of the group's scores. The level counts set the headline percentile (steps above); the curve only decides where inside the student's own level the line falls.

When a group's students all sit in one or two levels, the counts can't say how spread out their scores are, and the fitted curve can come out far too narrow. Those curves are drawn no narrower than one fifth of the statewide spread, which is about the size of the test's own measurement error, and inside the student's level the percentile spreads that level's students evenly instead.

Why estimates are still useful: the performance-level percentages are North Dakota’s own for each group, though often printed as ranges. The average score shown is estimated from how students split across the levels, and, as with every state, the only other assumption is how scores are distributed inside a level, a small and bounded range. Across a whole school, district, or the state, that assumption averages out well, so the comparison ("above/below average here vs. statewide") is reliable even though the exact percentile is approximate.

Limitations to keep in mind

Percentiles are estimates, not official rankings. Treat a "62nd percentile" as "roughly the top 40%," not an exact standing.
Small schools have small counts, so their estimates are noisier.
Some school/grade cells are suppressed by the state (for privacy, small groups) and won't appear.
North Dakota used two different tests over this window, so we key every year to that year's own test. Through 2024 the state gave the North Dakota State Assessment (NDSA), which reports a scale score with its own range for each grade and subject (English Language Arts runs 420-750 at Grade 3 up to 480-870 at Grade 8, and Mathematics 300-550 at Grade 3 up to 350-830 at Grade 8), across four performance levels: Novice, Partially Proficient, Proficient, and Advanced, with Proficient marking the state proficiency line. Starting in 2025 the state replaced the NDSA with a brand-new assessment, ND A+, from a different testing company on new academic standards. ND A+ uses its own 850-1150 scale and its own cut scores for every grade and subject, and it renames the second level "Approaching Proficient" (Novice, Approaching Proficient, Proficient, Advanced). Because ND A+ is a different test on a different scale, a 2025 scale score is not comparable to an NDSA scale score from 2024 or earlier; we apply each year's own official score ranges so the level shown always matches that year's test. Percentiles still compare across years, because a percentile places your child against the other students who took the same test that year, whichever test it was. North Dakota publishes, for every school, district, and the state, the percentage of students at each level (exact for larger groups, rounded to a narrow band for small ones); it does not publish an average scale score or a subject-level number tested, so counts are estimated from each group's grade enrollment and the curve's center is estimated by fitting a normal distribution to the reported percentages across the official score ranges. Results cover 2018 through 2025; no test was given in 2020 (COVID). North Dakota is compared at the school, district, and state levels (it has no county tier).

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