Madison 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	80,854	2329.6	− 2436	−106.4	× 89 / 417	−22.7
4	80,855	2424.7	− 2485	−60.3	× 83 / 417	−12
5	80,858	2423.8	− 2528	−104.2	× 57 / 417	−14.2
6	80,859	2418.0	− 2552	−134	× 57 / 417	−18.3
7	80,862	2438.7	− 2567	−128.3	× 77 / 417	−23.7
8	80,863	2470.7	− 2586	−115.3	× 54 / 417	−14.9
Sum, rounded to a whole point						−106

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,954	2328.6	− 2436	−107.4	× 98 / 459	−22.9
4	74,956	2413.4	− 2485	−71.6	× 78 / 459	−12.2
5	74,959	2451.1	− 2528	−76.9	× 82 / 459	−13.7
6	74,960	2436.9	− 2552	−115.1	× 59 / 459	−14.8
7	74,963	2443.0	− 2567	−124	× 58 / 459	−15.7
8	74,964	2477.1	− 2586	−108.9	× 84 / 459	−19.9
Sum, rounded to a whole point						−99

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	76,964	2352.3	− 2436	−83.7	× 91 / 433	−17.6
4	76,966	2386.7	− 2485	−98.3	× 93 / 433	−21.1
5	76,968	2395.8	− 2528	−132.2	× 70 / 433	−21.4
6	76,970	2446.0	− 2552	−106	× 70 / 433	−17.1
7	76,971	2445.5	− 2567	−121.5	× 54 / 433	−15.2
8	76,973	2442.3	− 2586	−143.7	× 55 / 433	−18.3
Sum, rounded to a whole point						−111

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	77,153	2360.6	− 2436	−75.4	× 90 / 457	−14.8
4	77,154	2419.0	− 2485	−66	× 76 / 457	−11
5	77,157	2417.6	− 2528	−110.4	× 84 / 457	−20.3
6	77,158	2408.4	− 2552	−143.6	× 64 / 457	−20.1
7	77,161	2473.0	− 2567	−94	× 82 / 457	−16.9
8	77,162	2458.2	− 2586	−127.8	× 61 / 457	−17.1
Sum, rounded to a whole point						−100

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	77,675	2386.7	− 2436	−49.3	× 96 / 467	−10.1
4	77,676	2409.6	− 2485	−75.4	× 67 / 467	−10.8
5	77,677	2471.4	− 2528	−56.6	× 67 / 467	−8.1
6	77,678	2447.9	− 2552	−104.1	× 90 / 467	−20.1
7	77,679	2479.4	− 2567	−87.6	× 66 / 467	−12.4
8	77,680	2476.3	− 2586	−109.7	× 81 / 467	−19
Sum, rounded to a whole point						−81

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	77,825	2359.9	− 2436	−76.1	× 89 / 441	−15.4
4	77,826	2369.5	− 2485	−115.5	× 71 / 441	−18.6
5	77,827	2413.4	− 2528	−114.6	× 70 / 441	−18.2
6	77,828	2407.5	− 2552	−144.5	× 91 / 441	−29.8
7	77,829	2447.5	− 2567	−119.5	× 63 / 441	−17.1
8	77,830	2461.8	− 2586	−124.2	× 57 / 441	−16.1
Sum, rounded to a whole point						−115

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	77,817	2354.3	− 2436	−81.7	× 92 / 419	−17.9
4	77,818	2387.4	− 2485	−97.6	× 66 / 419	−15.4
5	77,819	2431.0	− 2528	−97	× 65 / 419	−15
6	77,820	2419.0	− 2552	−133	× 60 / 419	−19
7	77,821	2437.4	− 2567	−129.6	× 81 / 419	−25.1
8	77,822	2452.1	− 2586	−133.9	× 55 / 419	−17.6
Sum, rounded to a whole point						−110

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	77,835	2350.1	− 2436	−85.9	× 76 / 441	−14.8
4	77,836	2392.6	− 2485	−92.4	× 88 / 441	−18.4
5	77,837	2421.0	− 2528	−107	× 68 / 441	−16.5
6	77,838	2414.5	− 2552	−137.5	× 67 / 441	−20.9
7	77,839	2454.9	− 2567	−112.1	× 62 / 441	−15.8
8	77,840	2441.9	− 2586	−144.1	× 80 / 441	−26.1
Sum, rounded to a whole point						−113

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	77,497	2332.5	− 2436	−103.5	× 70 / 405	−17.9
4	77,498	2403.5	− 2485	−81.5	× 70 / 405	−14.1
5	77,499	2422.0	− 2528	−106	× 85 / 405	−22.2
6	77,500	2438.9	− 2552	−113.1	× 63 / 405	−17.6
7	77,501	2453.3	− 2567	−113.7	× 59 / 405	−16.6
8	77,502	2431.2	− 2586	−154.8	× 58 / 405	−22.2
Sum, rounded to a whole point						−111

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −106, −99, −111, −100, −81, −115, −110, −113, −111 → −105.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 7 · 2016→2017: 12 · 2017→2018: 11 · 2018→2019: 19 · 2019→2022: 34 · 2022→2023: 5 · 2023→2024: 3 · 2024→2025: 2 → average 11.6
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11.6 × 2.66 = 30.9. Upper limit −74.2, lower limit −136.

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.