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How we estimate percentiles: Colorado 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 official public test-results files from the Colorado Department of Education, for the high-school tests Colorado gives every year: the PSAT 8/9 in grade 9, the PSAT 10 in grade 10 and the SAT in grade 11, each with a Reading and Writing section and a Math section (2021 to 2026), and the CMAS Science test in grade 11 (2018, 2019 and 2023 to 2026). These files report, for each school, district and the state, and for each test and year:

To protect student privacy, Colorado hides some of the level counts, always at least two at a time: in about half of the school PSAT and SAT results, and in most school science results (science’s top level holds only about 1 in 100 students, so it is usually hidden). We work them out from Colorado’s own numbers wherever they allow it. In most of those results the number who met or exceeded expectations is still shown, and it fixes how many of the hidden students are above and below that line. Each district’s counts are the sum of its schools’ counts (plus, in a few districts, students Colorado reports only at the district), the state’s are the sum of its districts’ (plus the small districts it hides), and from 2025 each school also reports an all-grades total, which is the sum of its grade 9, 10 and 11 results. Together these pin some hidden counts exactly and narrow most of the rest. Whatever is still open is split using the group’s reported average and standard deviation, and all the open counts in a district are chosen together, so its schools still add up to the district and state totals Colorado published. Every count Colorado printed is kept exactly as published.

We tested this on the school and district results where Colorado shows every count: we hid the counts the same way Colorado hides real ones and worked them back out. On the hidden levels the estimate was off by about 1.7 percentage points on average, against about 14 for simply splitting the hidden students evenly. Real hidden counts are often smaller groups than the ones we could test on, so treat a school with hidden counts as a little less certain.

Who is counted

Grade 9 is the PSAT 8/9, grade 10 the PSAT 10 and grade 11 the SAT: the tests Colorado gives public school students in those grades at school each spring. Each school’s numbers count its students in that grade who got a valid score, about 83 to 87 of every 100 students in the grade since 2022 and 73 to 80 in 2021. From 2024 the tests are digital and the reading section is called Reading and Writing (before 2024, Evidence-Based Reading and Writing). Science is the CMAS Science test in grade 11, which about half of grade 11 students took from 2023 (about 6 in 10 in 2018 and 2019).

So a PSAT or SAT percentile compares a score with Colorado public school students in the same grade who took that test at school that spring (about 55,000 to 56,000 students a grade in 2026). It is not the same as the national percentile on a College Board score report, which compares with test takers across the country. A science percentile compares a score with the grade 11 students who took CMAS Science that year (about 32,500 in 2026), who are not the whole grade.

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

Colorado publishes the exact scale-score range for each performance level (e.g. for SAT Math, “Approached Expectations” is 460-520, and for grade 11 science from 2023, “Met Expectations” is 750-786). 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 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 normal curve, cut off at the ends of the score scale, with the group’s own reported average and standard deviation: both are real figures Colorado publishes for every school, district and the state. 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.

Because the spread is a reported figure rather than a guess from the level counts, the curve stays sensible even for a group whose students all sit in one or two levels. Real scores are not perfectly bell-shaped, so the curve’s area in each level can differ a little from the real counts; the bars on the chart always show the real counts.

Why estimates are still useful: the number of students, the average score and the spread are real, reported figures for every group, and so are the level counts wherever Colorado shows them. The assumptions are how the hidden counts split (tested above) and how scores are distributed inside a level, a small and bounded range. Across a whole school, district, or the state, that averages out well, so the comparison ("above/below average here vs. statewide") is reliable even though the exact percentile is approximate.

Cut scores

The PSAT and SAT report each section in steps of 10: the PSAT 8/9 from 120 to 720, the PSAT 10 from 160 to 760 and the SAT from 200 to 800. Colorado sets its own four levels on each: Did Not Yet Meet, Approached, Met and Exceeded Expectations. On each test, Met Expectations starts at College Board’s own benchmark for that grade (on the SAT, Math 530 and Reading and Writing 480).

Colorado’s State Board of Education adopted these levels in March 2020, and Colorado first reported them for spring 2021. They come from the Colorado Department of Education’s “Approved Cut Scores and Colorado Achievement Levels for the SAT Suite of Assessments”. Colorado still links the same table as its cut scores since the tests went digital in 2024, and we found no separate table for the digital tests, so 2024 to 2026 use it too. Colorado says to compare 2024 and later results with earlier years with caution, especially in math.

CMAS Science has four levels: Partially Met, Approached, Met and Exceeded Expectations. Colorado moved science to a new 650-850 scale with new cut scores after new science standards, first tested in 2022: grade 11 is 650-724, 725-749, 750-786 and 787-850 from 2023. In 2018 and 2019 the high-school science test used the older 300-900 scale: 300-542, 543-672, 673-773 and 774-900. Scale scores from the two periods don’t line up; percentiles do. Both tables come from the Colorado Department of Education’s “CMAS Performance Levels and Policy Claims” (the 2019, 2023, 2025 and 2026 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.

Limitations to keep in mind

This site stores nothing you type. Scores are used only in your browser to draw your charts.

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