A. M. Thomas Middle: 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
6	17,402	2440.8	− 2552	−111.2	× 48 / 152	−35.1
7	17,403	2472.7	− 2567	−94.3	× 62 / 152	−38.5
8	17,406	2493.5	− 2586	−92.5	× 42 / 152	−25.6
Sum, rounded to a whole point						−99

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,419	2429.2	− 2552	−122.8	× 64 / 170	−46.2
7	16,420	2471.1	− 2567	−95.9	× 46 / 170	−25.9
8	16,422	2482.1	− 2586	−103.9	× 60 / 170	−36.7
Sum, rounded to a whole point						−109

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,727	2423.5	− 2552	−128.5	× 56 / 171	−42.1
7	16,730	2459.2	− 2567	−107.8	× 65 / 171	−41
8	16,732	2446.8	− 2586	−139.2	× 50 / 171	−40.7
Sum, rounded to a whole point						−124

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,747	2407.7	− 2552	−144.3	× 62 / 183	−48.9
7	16,749	2464.3	− 2567	−102.7	× 58 / 183	−32.5
8	16,751	2455.6	− 2586	−130.4	× 63 / 183	−44.9
Sum, rounded to a whole point						−126

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,880	2416.9	− 2552	−135.1	× 44 / 162	−36.7
7	16,881	2448.9	− 2567	−118.1	× 61 / 162	−44.5
8	16,882	2465.6	− 2586	−120.4	× 57 / 162	−42.4
Sum, rounded to a whole point						−124

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,472	2437.7	− 2552	−114.3	× 37 / 113	−37.4
7	16,473	2445.6	− 2567	−121.4	× 37 / 113	−39.8
8	16,474	2477.1	− 2586	−108.9	× 39 / 113	−37.6
Sum, rounded to a whole point						−115

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,924	2475.0	− 2552	−77	× 24 / 85	−21.7
7	16,925	2500.3	− 2567	−66.7	× 32 / 85	−25.1
8	16,926	2480.6	− 2586	−105.4	× 29 / 85	−36
Sum, rounded to a whole point						−83

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,858	2483.4	− 2552	−68.6	× 29 / 84	−23.7
7	16,859	2510.7	− 2567	−56.3	× 23 / 84	−15.4
8	16,860	2518.2	− 2586	−67.8	× 32 / 84	−25.8
Sum, rounded to a whole point						−65

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,815	2472.3	− 2552	−79.7	× 26 / 78	−26.6
7	16,816	2491.6	− 2567	−75.4	× 27 / 78	−26.1
8	16,817	2503.6	− 2586	−82.4	× 25 / 78	−26.4
Sum, rounded to a whole point						−79

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	16,800	2486.8	− 2552	−65.2	× 32 / 87	−24
7	16,801	2502.1	− 2567	−64.9	× 29 / 87	−21.6
8	16,802	2517.5	− 2586	−68.5	× 26 / 87	−20.5
Sum, rounded to a whole point						−66

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −99, −109, −124, −126, −124, −115, −83, −65, −79, −66 → −99
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 10 · 2016→2017: 15 · 2017→2018: 2 · 2018→2019: 2 · 2019→2021: 9 · 2021→2022: 32 · 2022→2023: 18 · 2023→2024: 14 · 2024→2025: 13 → average 12.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 12.8 × 2.66 = 34. Upper limit −65, lower limit −133.

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.