Williams Junior/Senior High: 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
7	5,724	2525.3	− 2567	−41.7	× 83 / 243	−14.2
8	5,725	2485.4	− 2586	−100.6	× 81 / 243	−33.5
11	5,728	2504.7	− 2628	−123.3	× 79 / 243	−40.1
Sum, rounded to a whole point						−88

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	5,188	2478.8	− 2567	−88.2	× 88 / 260	−29.9
8	5,190	2534.7	− 2586	−51.3	× 88 / 260	−17.4
11	5,193	2552.7	− 2628	−75.3	× 84 / 260	−24.3
Sum, rounded to a whole point						−72

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	5,294	2471.9	− 2567	−95.1	× 78 / 254	−29.2
8	5,296	2482.1	− 2586	−103.9	× 88 / 254	−36
11	5,298	2530.4	− 2628	−97.6	× 88 / 254	−33.8
Sum, rounded to a whole point						−99

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	5,299	2481.6	− 2567	−85.4	× 106 / 271	−33.4
8	5,300	2455.3	− 2586	−130.7	× 89 / 271	−42.9
11	5,303	2489.5	− 2628	−138.5	× 76 / 271	−38.8
Sum, rounded to a whole point						−115

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	5,342	2478.4	− 2567	−88.6	× 102 / 290	−31.2
8	5,343	2469.6	− 2586	−116.4	× 107 / 290	−42.9
11	5,344	2549.4	− 2628	−78.6	× 81 / 290	−22
Sum, rounded to a whole point						−96

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	5,179	2438.3	− 2567	−128.7	× 103 / 311	−42.6
8	5,180	2425.8	− 2586	−160.2	× 115 / 311	−59.2
11	5,181	2452.6	− 2628	−175.4	× 93 / 311	−52.5
Sum, rounded to a whole point						−154

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	5,181	2442.1	− 2567	−124.9	× 100 / 295	−42.3
8	5,182	2420.0	− 2586	−166	× 106 / 295	−59.6
11	5,183	2511.8	− 2628	−116.2	× 89 / 295	−35.1
Sum, rounded to a whole point						−137

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	5,116	2441.1	− 2567	−125.9	× 91 / 272	−42.1
8	5,117	2444.2	− 2586	−141.8	× 100 / 272	−52.1
11	5,118	2478.6	− 2628	−149.4	× 81 / 272	−44.5
Sum, rounded to a whole point						−139

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	5,080	2459.9	− 2567	−107.1	× 83 / 256	−34.7
8	5,081	2469.1	− 2586	−116.9	× 85 / 256	−38.8
11	5,082	2468.6	− 2628	−159.4	× 88 / 256	−54.8
Sum, rounded to a whole point						−128

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −88, −72, −99, −115, −96, −154, −137, −139, −128 → −114.2
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 16 · 2016→2017: 27 · 2017→2018: 16 · 2018→2019: 19 · 2019→2022: 58 · 2022→2023: 17 · 2023→2024: 2 · 2024→2025: 11 → average 20.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 20.8 × 2.66 = 55.3. Upper limit −58.9, lower limit −169.5.

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