How we estimate percentiles

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: the DC Office of the State Superintendent of Education assessment data (DC CAPE, ELA & Math, grades 3-8). These files report, for each school / grade / year:

the percentage of students in each performance level (school rows) or the real count (district/state rows), plus the number tested, and
from those figures, a mean we estimate from the count-weighted midpoint of each performance level’s scale range, which we then fit a curve around.

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

District of Columbia publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 4 “Met Expectations” is 750-789). 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, assuming 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 level counts, anchored to a mean estimated from the count-weighted midpoint of each level. 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 mean figure shown is approximated from where students fall within each level, and, as with every state, the only other assumption is how scores are distributed inside a level, a small and bounded range. Across a whole school, district, county, 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.
DC CAPE is the District's continuation of PARCC and uses the same 650-850 scale with five performance levels, stable across years (the lower cuts sit at 700, 725, and 750 for every grade, and only the top “Exceeded” cut moves by grade). OSSE publishes the percentage of students at each performance level for every school and grade; those percentages are real, and because student counts are not released the shares are shown out of 100. Where a small level is suppressed, it is filled from the levels that are reported. No test was given in 2020 (COVID). The District is compared at the school, LEA (the local education agency, DC's district-equivalent), and District-of-Columbia levels.
Charter schools appear as their own districts in the state files and are included in the school, district, county and statewide comparisons.

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