How we estimate percentiles: South 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 state assessment results of the South Dakota Department of Education, downloaded from the South Dakota School Report Card, for grade 11: Smarter Balanced ELA and math in 2019 and 2021 to 2025, and the South Dakota Science Assessment (SDSA) in 2021 to 2025. For each school, school district and the state, and for each subject and year, these files give:

• the real number of students in each of the four performance levels, counting students enrolled for the full school year, and
• from those counts, an estimated average score: South Dakota does not publish an average, so the center of the curve is the one that best matches the share of students below each level’s cut score.

Hidden numbers. South Dakota hides a small school’s whole row, so a school is either shown in full or left out. The district and statewide rows still count every student. For 2019 South Dakota published school rows only, so that year’s district and statewide figures add up the schools it did not hide. In the years it published both, the shown schools held 86% to 97% of the state’s grade 11 test takers, and their combined level shares came within 0.6 of a point in ELA, 1 point in science and 3 points in math of the real statewide ones. Treat the 2019 district and statewide percentiles as a little less exact than the other years’.

Who is counted

South Dakota tests ELA, math and science in grade 11. A percentile compares a score with that year’s South Dakota public school students in grade 11 who were enrolled for the full school year, by the school where they tested, with the alternate assessment counted in: about 9,400 students in each subject in 2025. South Dakota also reports a small group of grade 12 students (about 100 to 300 a year in ELA and math, tested outside their grade). They are not part of these comparisons.

How the percentile is estimated

South Dakota publishes the exact score range for each performance level (e.g. for grade 11 Math, Level 3 is 2628-2717). 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.

When a group's students nearly all sit in one or two levels, as at some small schools, the counts can't say how spread out their scores are. About 1 in 200 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.

Cut scores

ELA and math have four levels, Level 1 to Level 4; Level 3 and above count as proficient. Science’s four levels are Does Not Meet, Approaching, Meets and Exceeds Standard.

• Grade 11 ELA: 2102-2492, 2493-2582, 2583-2681, 2682-3032
• Grade 11 Math: 2118-2542, 2543-2627, 2628-2717, 2718-3085
• Grade 11 Science: 1000-1072, 1073-1101, 1102-1133, 1134-1199

The ELA and math cut scores are South Dakota’s “State Assessment Cut Scores” table, the same as the Smarter Balanced consortium’s. The lowest and highest scores are the ones South Dakota’s Smarter Balanced technical reports print for every year from 2018-19 to 2024-25. The science ranges are from the SDSA score interpretation guide, the same in its 2021-22 to 2024-25 editions. 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.

• One line per subject. The grade 11 tests are taken by the whole class, so ELA, math and science continue the grades 3-8 lines in the same subject (science is tested in grades 5 and 8). Grade 11 ELA and math are on the same Smarter Balanced scale as grades 3-8; science has its own scale in each grade, but each point is a percentile among that year’s students in that grade, so the points compare.
• Earlier years are compared statewide only. You can add your child’s grades 3-8 scores. The tool doesn’t know which middle school or district they attended, so those years are compared with every student in the state in that grade, not with this high school or its district.
• The report opens on the statewide view, the one level with a result for every test.

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, and some are hidden.
• Not included: science in 2019 (the SDSA became the operational test in 2021, and its achievement levels were set that year), 2020 (no test, COVID), years before 2019, which the report card’s data download does not carry, and 2026, not yet in the download.
• South Dakota is compared at the school, district and state levels (its districts do not map to counties).

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