Williams Unified: science

The shaded band is this district's normal range. If nothing about how it works changes, nearly every future year should land inside it. Zero means the typical student just meets the state standard. The small numbers under the years are how many students were tested.

Step 1 · Each year's result

For each grade tested, take the average (mean) scale score from the California Department of Education's results file, and subtract the lowest score that counts as "Standard Met" for that grade. That is the grade's distance from standard. Weight each grade by its share of the students tested, then add the grades up. Grades where the state hides the average because ten or fewer students tested are left out entirely.

2019 from cast_ca2019_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	1,537	188.4	− 214	−25.6	× 106 / 368	−7.4
8	1,538	379.5	− 415	−35.5	× 101 / 368	−9.7
10	1,539	588.0	− 615	−27	× 91 / 368	−6.7
12	1,540	584.9	− 615	−30.1	× 70 / 368	−5.7
Sum, rounded to a whole point						−30

2022 from cast_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	1,913	194.8	− 214	−19.2	× 94 / 372	−4.9
8	1,914	383.4	− 415	−31.6	× 114 / 372	−9.7
11	1,915	583.7	− 615	−31.3	× 93 / 372	−7.8
12	1,916	588.6	− 615	−26.4	× 71 / 372	−5
Sum, rounded to a whole point						−27

2023 from cast_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	1,923	189.4	− 214	−24.6	× 83 / 289	−7.1
8	1,924	385.7	− 415	−29.3	× 108 / 289	−10.9
11	1,925	593.5	− 615	−21.5	× 98 / 289	−7.3
Sum, rounded to a whole point						−25

2024 from cast_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	1,944	191.7	− 214	−22.3	× 92 / 281	−7.3
8	1,945	386.9	− 415	−28.1	× 100 / 281	−10
11	1,946	593.4	− 615	−21.6	× 89 / 281	−6.8
Sum, rounded to a whole point						−24

2025 from cast_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	1,918	191.4	− 214	−22.6	× 89 / 240	−8.4
8	1,919	393.1	− 415	−21.9	× 85 / 240	−7.8
11	1,920	588.6	− 615	−26.4	× 66 / 240	−7.3
Sum, rounded to a whole point						−23

2026 from cast_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	1,922	192.4	− 214	−21.6	× 91 / 303	−6.5
8	1,923	389.0	− 415	−26	× 82 / 303	−7
11	1,924	590.8	− 615	−24.2	× 96 / 303	−7.7
12	1,925	578.9	− 615	−36.1	× 34 / 303	−4.1
Sum, rounded to a whole point						−25

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −30, −27, −25, −24, −23, −25 → −25.7
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2019→2022: 3 · 2022→2023: 2 · 2023→2024: 1 · 2024→2025: 1 · 2025→2026: 2 → average 1.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 1.8 × 2.66 = 4.8. Upper limit −20.9, lower limit −30.5.

Why 2.66? It is the standard factor from quality control, the work of Walter Shewhart and W. Edwards Deming. It turns "how much the result typically changes in a year" into "how far it can wander by chance alone".

Years with no result (no state tests were given in spring 2020) are skipped: the year-to-year change runs from the last year with a result to the next one.

Step 3 · Free or reduced-price meals

The share of enrolled students eligible for free or reduced-price meals — for a district, the total across its schools. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.

Williams Unified