Williamson Elementary: math

The shaded band is this school'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.

2015 from sb_ca2015_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	60,832	2382.4	− 2436	−53.6	× 78 / 228	−18.3
4	60,834	2424.2	− 2485	−60.8	× 84 / 228	−22.4
5	60,836	2472.0	− 2528	−56	× 66 / 228	−16.2
Sum, rounded to a whole point						−57

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	56,441	2388.6	− 2436	−47.4	× 96 / 263	−17.3
4	56,443	2425.2	− 2485	−59.8	× 85 / 263	−19.3
5	56,445	2454.1	− 2528	−73.9	× 82 / 263	−23
Sum, rounded to a whole point						−60

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,086	2414.1	− 2436	−21.9	× 89 / 255	−7.6
4	58,089	2426.8	− 2485	−58.2	× 98 / 255	−22.4
5	58,091	2480.8	− 2528	−47.2	× 68 / 255	−12.6
Sum, rounded to a whole point						−43

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,221	2418.1	− 2436	−17.9	× 96 / 296	−5.8
4	58,224	2444.7	− 2485	−40.3	× 102 / 296	−13.9
5	58,225	2455.0	− 2528	−73	× 98 / 296	−24.2
Sum, rounded to a whole point						−44

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,468	2396.7	− 2436	−39.3	× 81 / 260	−12.2
4	58,469	2446.3	− 2485	−38.7	× 89 / 260	−13.2
5	58,470	2472.5	− 2528	−55.5	× 90 / 260	−19.2
Sum, rounded to a whole point						−45

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,539	2367.3	− 2436	−68.7	× 69 / 240	−19.8
4	58,540	2411.8	− 2485	−73.2	× 80 / 240	−24.4
5	58,541	2448.7	− 2528	−79.3	× 91 / 240	−30.1
Sum, rounded to a whole point						−74

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,499	2364.0	− 2436	−72	× 97 / 247	−28.3
4	58,500	2401.4	− 2485	−83.6	× 74 / 247	−25
5	58,501	2431.1	− 2528	−96.9	× 76 / 247	−29.8
Sum, rounded to a whole point						−83

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,410	2382.8	− 2436	−53.2	× 69 / 242	−15.2
4	58,411	2402.4	− 2485	−82.6	× 96 / 242	−32.8
5	58,412	2421.2	− 2528	−106.8	× 77 / 242	−34
Sum, rounded to a whole point						−82

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,169	2352.4	− 2436	−83.6	× 70 / 235	−24.9
4	58,170	2414.4	− 2485	−70.6	× 69 / 235	−20.7
5	58,171	2429.2	− 2528	−98.8	× 96 / 235	−40.4
Sum, rounded to a whole point						−86

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −57, −60, −43, −44, −45, −74, −83, −82, −86 → −63.8
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 3 · 2016→2017: 17 · 2017→2018: 1 · 2018→2019: 1 · 2019→2022: 29 · 2022→2023: 9 · 2023→2024: 1 · 2024→2025: 4 → average 8.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 8.1 × 2.66 = 21.5. Upper limit −42.3, lower limit −85.3.

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. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.