Williams Unified: math

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.

2015 from sb_ca2015_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,696	2371.7	− 2436	−64.3	× 112 / 653	−11
4	5,697	2401.7	− 2485	−83.3	× 109 / 653	−13.9
5	5,700	2449.9	− 2528	−78.1	× 94 / 653	−11.2
6	5,701	2466.9	− 2552	−85.1	× 90 / 653	−11.7
7	5,704	2525.3	− 2567	−41.7	× 83 / 653	−5.3
8	5,705	2485.4	− 2586	−100.6	× 81 / 653	−12.5
11	5,708	2499.7	− 2628	−128.3	× 84 / 653	−16.5
Sum, rounded to a whole point						−82

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,160	2387.4	− 2436	−48.6	× 106 / 680	−7.6
4	5,162	2408.9	− 2485	−76.1	× 109 / 680	−12.2
5	5,165	2431.6	− 2528	−96.4	× 106 / 680	−15
6	5,166	2454.6	− 2552	−97.4	× 93 / 680	−13.3
7	5,168	2478.8	− 2567	−88.2	× 88 / 680	−11.4
8	5,170	2534.7	− 2586	−51.3	× 88 / 680	−6.6
11	5,173	2543.4	− 2628	−84.6	× 90 / 680	−11.2
Sum, rounded to a whole point						−77

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,266	2390.9	− 2436	−45.1	× 110 / 685	−7.2
4	5,269	2437.5	− 2485	−47.5	× 106 / 685	−7.4
5	5,270	2450.5	− 2528	−77.5	× 107 / 685	−12.1
6	5,272	2471.8	− 2552	−80.2	× 108 / 685	−12.6
7	5,274	2471.9	− 2567	−95.1	× 78 / 685	−10.8
8	5,276	2482.1	− 2586	−103.9	× 88 / 685	−13.3
11	5,279	2530.4	− 2628	−97.6	× 88 / 685	−12.5
Sum, rounded to a whole point						−76

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,271	2397.3	− 2436	−38.7	× 114 / 701	−6.3
4	5,272	2437.7	− 2485	−47.3	× 109 / 701	−7.4
5	5,274	2447.3	− 2528	−80.7	× 101 / 701	−11.6
6	5,276	2482.2	− 2552	−69.8	× 104 / 701	−10.4
7	5,279	2481.6	− 2567	−85.4	× 106 / 701	−12.9
8	5,280	2455.3	− 2586	−130.7	× 89 / 701	−16.6
11	5,282	2489.1	− 2628	−138.9	× 78 / 701	−15.5
Sum, rounded to a whole point						−81

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,318	2382.6	− 2436	−53.4	× 95 / 710	−7.1
4	5,319	2403.1	− 2485	−81.9	× 106 / 710	−12.2
5	5,320	2426.6	− 2528	−101.4	× 106 / 710	−15.1
6	5,321	2455.7	− 2552	−96.3	× 104 / 710	−14.1
7	5,322	2478.4	− 2567	−88.6	× 102 / 710	−12.7
8	5,323	2469.6	− 2586	−116.4	× 107 / 710	−17.5
11	5,324	2534.3	− 2628	−93.7	× 90 / 710	−11.9
Sum, rounded to a whole point						−91

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,155	2359.9	− 2436	−76.1	× 97 / 700	−10.5
4	5,156	2394.2	− 2485	−90.8	× 87 / 700	−11.3
5	5,157	2417.4	− 2528	−110.6	× 94 / 700	−14.9
6	5,158	2450.3	− 2552	−101.7	× 103 / 700	−15
7	5,159	2438.3	− 2567	−128.7	× 103 / 700	−18.9
8	5,160	2425.8	− 2586	−160.2	× 115 / 700	−26.3
11	5,161	2446.1	− 2628	−181.9	× 101 / 700	−26.2
Sum, rounded to a whole point						−123

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,157	2367.4	− 2436	−68.6	× 95 / 665	−9.8
4	5,158	2398.6	− 2485	−86.4	× 94 / 665	−12.2
5	5,159	2421.2	− 2528	−106.8	× 84 / 665	−13.5
6	5,160	2463.9	− 2552	−88.1	× 89 / 665	−11.8
7	5,161	2442.1	− 2567	−124.9	× 100 / 665	−18.8
8	5,162	2420.0	− 2586	−166	× 106 / 665	−26.5
11	5,163	2498.9	− 2628	−129.1	× 97 / 665	−18.8
Sum, rounded to a whole point						−111

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,092	2387.8	− 2436	−48.2	× 90 / 647	−6.7
4	5,093	2395.6	− 2485	−89.4	× 98 / 647	−13.5
5	5,094	2418.6	− 2528	−109.4	× 93 / 647	−15.7
6	5,095	2460.4	− 2552	−91.6	× 85 / 647	−12
7	5,096	2441.1	− 2567	−125.9	× 91 / 647	−17.7
8	5,097	2444.2	− 2586	−141.8	× 100 / 647	−21.9
11	5,098	2468.7	− 2628	−159.3	× 90 / 647	−22.2
Sum, rounded to a whole point						−110

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,056	2389.3	− 2436	−46.7	× 92 / 624	−6.9
4	5,057	2422.2	− 2485	−62.8	× 88 / 624	−8.9
5	5,058	2403.3	− 2528	−124.7	× 89 / 624	−17.8
6	5,059	2442.3	− 2552	−109.7	× 99 / 624	−17.4
7	5,060	2459.9	− 2567	−107.1	× 83 / 624	−14.2
8	5,061	2469.1	− 2586	−116.9	× 85 / 624	−15.9
11	5,062	2468.6	− 2628	−159.4	× 88 / 624	−22.5
Sum, rounded to a whole point						−104

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,052	2391.1	− 2436	−44.9	× 94 / 637	−6.6
4	5,053	2427.0	− 2485	−58	× 89 / 637	−8.1
5	5,054	2416.6	− 2528	−111.4	× 92 / 637	−16.1
6	5,055	2434.1	− 2552	−117.9	× 89 / 637	−16.5
7	5,056	2441.7	− 2567	−125.3	× 95 / 637	−18.7
8	5,057	2429.8	− 2586	−156.2	× 82 / 637	−20.1
11	5,058	2451.3	− 2628	−176.7	× 96 / 637	−26.6
Sum, rounded to a whole point						−113

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −82, −77, −76, −81, −91, −123, −111, −110, −104, −113 → −96.8
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 5 · 2016→2017: 1 · 2017→2018: 5 · 2018→2019: 10 · 2019→2022: 32 · 2022→2023: 12 · 2023→2024: 1 · 2024→2025: 6 · 2025→2026: 9 → average 9
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 9 × 2.66 = 23.9. Upper limit −72.9, lower limit −120.7.

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.

Schools in Williams Unified

Elementary schools

Middle and high schools

Williams Junior/Senior High