How we estimate percentiles

Plain-English 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 - the Colorado DOE CMAS results (CMAS: ELA & Math grades 3-8, Science grades 5 & 8). These files report, for each school / grade / year:

the number of students tested and their mean scale score, and
the counts of students in each performance level (5 for ELA/Math, 4 for Science) plus the mean scale score. Colorado masks small cells for privacy; those are reconstructed from the reported mean and standard deviation.

Important: the public data does not contain individual student scores - only these group summaries. So no tool can compute a true rank of one child against every other child. 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 Grade 3 Math, Level 5 “Exceeded Expectations” is 790-850). Given your child's score, we:

identify which performance level the score falls in;
count everyone in the lower levels as scoring below;
within the score's own level, use linear interpolation across that level's count - i.e. assume scores are spread evenly across the level's range.

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 real reported counts, anchored to the group's reported mean. It's there to visualize the shape of the group's scores. The headline percentile comes from the counts (step above), not from the curve.

Why estimates are still useful: the performance-level counts are real and complete for each group. The only assumption is how scores are distributed inside a level - a small, 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.

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.
Some school/grade cells are suppressed by the state (for privacy, small groups) and won't appear.
CMAS reports a scaled score from 650 to 850. ELA and Math have five levels (Did Not Yet Meet through Exceeded Expectations); Science has four. No statewide test was given in 2020 (COVID); 2021 had reduced participation.
Charter schools appear as their own districts in the state files and are included in the school, district and statewide comparisons.

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

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