How we estimate percentiles: Wyoming 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 school assessment reports of the Wyoming Department of Education, for WY-TOPP ELA and math in grades 9 and 10, 2018, 2019 and 2021 to 2026. For each school, and for each subject, grade and year, the report gives:

• the share of students in each of the four performance levels, to two decimal places, and a range for the number tested (for example “220 - 229”). The exact number is the one in that range that reproduces every printed percentage, and
• from those counts, an estimated average score: the report has no average, so the center of the curve is the one that best matches the share of students below each level’s cut score.

Districts, counties and the state. Wyoming publishes school results only, so the district, county and statewide figures add up the schools shown. Schools with fewer than about 10 students are hidden. Wyoming’s districts are named for their county (for example “Natrona #1”), which is how each school gets its county.

Who is counted

Wyoming gives WY-TOPP ELA and math in grades 9 and 10 (and the ACT in grade 11, which Wyoming reports as averages only). A percentile compares a score with that year’s Wyoming public school students in that grade who took the test, by the school where they tested: about 6,500 to 7,000 students per grade and subject.

How the percentile is estimated

Wyoming publishes the exact score cut for each performance level (e.g. for grade 10 Math in 2026, Proficient is 649-716). 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.

The lowest and highest possible scores are estimated. Wyoming prints the bottom and top levels as open ranges (“≤572”, “≥672”) and publishes no lowest or highest score. We use the statewide average plus or minus four standard deviations from 2018, the year the scale was set, which reproduces the real ends published for grade 4. These ends only affect where a score falls inside the bottom or top level, by a few percentile points at most; every level cut is Wyoming’s own.

We also check each year against the statewide average and spread Wyoming publishes. ELA agrees closely. In math, the real grade 9 and 10 scores sit more in the middle than a bell curve would put them, by about 5 to 7 percentage points per level, so inside a level a math percentile can be a few points off.

Cut scores

Each test has four levels: Below Basic, Basic, Proficient and Advanced. Proficient and above count as proficient.

• Grade 9 ELA: 629 Basic, 656 Proficient, 709 Advanced (estimated range 440-850)
• Grade 10 ELA: 631 Basic, 667 Proficient, 713 Advanced (estimated range 450-880)
• Grade 9 Math: 573 Basic, 617 Proficient, 668 Advanced through 2025, 672 from 2026 (estimated range 340-860)
• Grade 10 Math: 603 Basic, 653 Proficient and 714 Advanced through 2025; 649 Proficient and 717 Advanced from 2026 (estimated range 270-990)

The cut scores are from Wyoming’s “WY-TOPP Score Proficiency-Level Ranges” (the 2024 and 2026 editions) and its 2022 cut-score FAQ. An educator committee adjusted the grade 9 and 10 math cuts in 2026. 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. Grades 9 and 10 continue the grades 3-8 ELA and math lines on the same WY-TOPP scale. 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 the smallest are hidden.
• Not included: grade 10 science (Wyoming publishes no lowest or highest score for it), the grade 11 ACT (averages only), and 2020 (no test, COVID).

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