How we estimate percentiles: Tennessee 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 Tennessee Department of Education’s public assessment files for the TCAP end-of-course tests (called TNReady through 2021). The tests are English I, English II, Algebra I, Geometry, Algebra II, Integrated Math I and II, and U.S. History (2018, 2019 and 2021 to 2026), Integrated Math III (2018, 2019 and 2021 to 2023), Biology (2018 and 2021 to 2026; Tennessee published no Biology results for 2019), and English III and Chemistry (2018 only). For each school, school district and the state, and for each test and year, these files report:

• the number of valid tests and the number of students in each of the four performance levels. To protect students’ privacy, Tennessee hides all four level counts of a school when any one level holds less than 5% or more than 95% of its students (less than 1% or more than 99% for a district). That happens to about two in three of the school results here, most often in math and English I. The number tested is still printed, and so, for most of them, is the share of students who met or exceeded expectations. So only two things are unknown: how the students under that line split between Below and Approaching, and how the students over it split between the top two levels;
• how we fill those two splits in. When a district’s own result leaves only one of its schools unknown, the school’s counts follow exactly from the district’s, and we use them (1,808 school results). Otherwise we estimate the split with a bell curve whose spread we fitted on district results that Tennessee does print and that look like the hidden ones, and we choose all of a year’s estimated results together, so that a district’s schools still add up to the district and the districts add up to the state. Every estimated result still matches every number Tennessee printed for it. We measured how close the estimate comes: on printed district results treated as hidden, it misses the Below share by 3.6 percentage points on average and the top level by 1.2; on the 1,808 hidden school results whose true counts the district results give away, estimated as if the district had not, by 4.6 and 1.7 points, which moves the percentile the tool shows by about 1.7 points on average (under 5 points for nine scores in ten); and
• no average score. Tennessee publishes no averages for these tests, so the average is estimated from how the students split across the levels: the center of the bell curve that best matches the share of students below each level’s cut score.

Who is counted

Each course test is taken by the students in that course that year, whatever their grade. Tennessee says its results include the fall end-of-course tests, taken by students in fall block-schedule courses, as well as the spring ones (its 2023-24 results release says so). Middle-school students who take a high-school course early, almost always Algebra I, take its end-of-course test and are counted here at their middle school: about one Algebra I tester in nine (11% in 2026), mostly 8th graders. Schools with fewer than 10 testers are not shown; the district and state results still count every student.

A course test is taken by whoever is in the course that year, so each test has its own group: about 66,600 students took Algebra I in 2026, and about 38,500 took U.S. History. A percentile compares a score with that year’s takers of the same test, not with every student of the same age, and an Algebra I percentile says nothing about Biology.

In 2021 only 84% to 92% of the students enrolled in these courses took the tests, according to the Tennessee Department of Education, against 94% or more in 2019 and in 2022 to 2026, so 2021 compares a somewhat smaller group. The tool shows a note on those results.

How the percentile is estimated

Tennessee publishes the exact scale-score range for each performance level (for Algebra I since 2024, Met Expectations is 330 to 351). 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, which are very wide on these tests (Algebra I’s highest level runs from 352 to 450).

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 centered on the group’s estimated average score, with its spread fitted so that its area within each level matches the level counts. 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 nearly all of a group’s students sit in one or two levels, the counts can’t say how spread out their scores are. For an estimated school result that happens often, and there the curve is the one we used to estimate the school’s split.

Cut scores

Every test here is reported on a scale from 200 to 450 with four performance levels, except Biology and Chemistry in 2018, which still used Tennessee’s older 500 to 900 scale. The levels are named Below, Approaching, On Track and Mastered through 2021, and Below, Approaching, Met Expectations and Exceeded Expectations from 2022 (the same levels under new names). Biology and Chemistry in 2018 used Below Basic, Basic, Proficient and Advanced.

The English and math cut scores were set in 2016 and kept until math was reset in 2024. Algebra I, for example, started Approaching at 307, On Track at 326 and Mastered at 345 through 2023; from 2024 those cuts are 300, 330 and 352, and the other math courses moved too. Biology and U.S. History got new standards and new cut scores in 2021 (Biology 300, 330 and 375; U.S. History 300, 330 and 360), and Biology’s top cut moved to 367 in 2026. So scale scores and level shares do not line up across those changes. Percentiles compare students within one test and year, so they are not affected.

The ranges come from the Tennessee State Board of Education’s cut-score approvals (October 2016, July 2021, August 2024 and July 2026), the Tennessee Department of Education’s end-of-course assessment overviews, and, for Biology and Chemistry in 2018, its 2017-18 science fact sheet and spring 2015 scale-score ranges. 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.

• Each course exam is its own point. Every Tennessee high-school test here is a course exam (such as Algebra I or Biology), taken by the students in that course that year, a different group for each course, so the report does not join them with a line.
• Earlier years are compared statewide only. You can add your child’s grades 3-8 scores in the same subjects. 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. Schools with fewer than 10 testers on a test are left out; the district and state results still count every student.
• For the school results Tennessee hides, the split between the two lower levels and between the two upper levels is our estimate (see above), so a percentile against those schools is less exact than against a school with all four counts. The statewide result is always Tennessee’s own.
• Not included: 2020 (no test, COVID); Biology in 2019 (Tennessee published no results); English III and Chemistry after 2018 (no longer given); and Integrated Math III from 2024, because the only published table of its new cut scores labels that row as Integrated Math II, so we can't confirm which numbers belong to Math III.
• Tennessee is compared at the school, school district and state levels.

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