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How we estimate percentiles: North Dakota high school

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 the assessment files of the North Dakota Department of Public Instruction (ND Insights), for the grade 10 state test: ELA and math in 2018, 2019 and 2021 to 2025, and science in 2021 to 2025. The test was the North Dakota State Assessment (NDSA) through 2024 and ND A+ from 2025. For each school, school district and the state, and for each subject and year, these files give:

The number of students. North Dakota doesn’t publish how many students each school tested, so it is estimated from the school’s grade 10 enrollment. Where its technical reports print the statewide number tested (2021 to 2023), every count is scaled so the state matches it exactly. The level counts we use always land inside every range North Dakota printed.

Who is counted

A percentile compares a score with that year’s North Dakota public school students in grade 10 who took the state test, by the school where they tested. Through 2024, a district could give the ACT in grade 11 instead of the grade 10 ELA and math test, so for those years ELA and math compare a score only with the districts that gave the grade 10 test: about 2,400 to 3,800 students a year, roughly a third of the class. From 2025 every grade 10 student takes ND A+, about 8,600 students. Science was given in grade 10 nearly everywhere from 2021.

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

How the percentile is estimated

North Dakota publishes the exact score range for each performance level (e.g. for grade 10 NDSA Math, Proficient is 650-692). Given a score, we:

  1. identify which performance level the score falls in;
  2. count everyone in the lower levels as scoring below;
  3. 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.

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.

We checked the statewide curve against the average and spread North Dakota published for grade 10 ELA and math in 2021 and 2022. The real grade 10 scores are more spread out than a bell curve: the curve’s average sits about 5 points high and its spread about 14 points narrow, on scales about 400 (ELA) and 600 (math) points wide. So inside the lowest and highest levels a percentile can be a few points off.

When a group's students nearly all sit in one or two levels, the counts can't say how spread out their scores are. About 4 in 100 high-school groups are like this. Their curves are drawn no narrower than one fifth of the statewide spread, and inside the student's level the percentile spreads that level's students evenly instead.

Why estimates are still useful: the performance-level shares are North Dakota’s own published numbers for each group. The average score shown is estimated from how students split across the levels, and 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.

Cut scores

Each test has four levels: Novice, Partially Proficient (Approaching Proficient on ND A+), Proficient and Advanced. Proficient and above count as proficient.

The NDSA ranges are from its annual technical reports (the 2020-21 to 2022-23 editions print the same grade 10 rows), and the ND A+ ranges from Pearson’s ND A+ score interpretation guide for 2024-25. The two tests are on different scales, so a scale score from one doesn’t compare with the other, but a percentile does: each year places the student among that year’s grade 10 students. The score range for each level, by year, is on the score guides.

The high-school progress report

The paid progress report puts every high-school test your child took in one table, with the percentile at each level from the school to the state, and charts each subject across the years.

Limitations to keep in mind

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