American 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	17,784	2449.8	− 2436	13.8	× 111 / 427	3.6
4	17,786	2466.4	− 2485	−18.6	× 115 / 427	−5
5	17,788	2512.0	− 2528	−16	× 98 / 427	−3.7
6	17,790	2528.8	− 2552	−23.2	× 103 / 427	−5.6
Sum, rounded to a whole point						−11

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	16,792	2444.8	− 2436	8.8	× 92 / 446	1.8
4	16,793	2512.1	− 2485	27.1	× 120 / 446	7.3
5	16,796	2518.9	− 2528	−9.1	× 126 / 446	−2.6
6	16,798	2539.5	− 2552	−12.5	× 108 / 446	−3
Sum, rounded to a whole point						4

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,113	2458.5	− 2436	22.5	× 104 / 457	5.1
4	17,115	2494.6	− 2485	9.6	× 106 / 457	2.2
5	17,117	2544.1	− 2528	16.1	× 125 / 457	4.4
6	17,119	2555.6	− 2552	3.6	× 122 / 457	1
Sum, rounded to a whole point						13

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,132	2476.5	− 2436	40.5	× 98 / 448	8.9
4	17,134	2513.0	− 2485	28	× 111 / 448	6.9
5	17,136	2525.8	− 2528	−2.2	× 110 / 448	−0.5
6	17,138	2575.5	− 2552	23.5	× 129 / 448	6.8
Sum, rounded to a whole point						22

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,283	2484.3	− 2436	48.3	× 94 / 424	10.7
4	17,284	2531.4	− 2485	46.4	× 97 / 424	10.6
5	17,285	2542.6	− 2528	14.6	× 125 / 424	4.3
6	17,286	2562.1	− 2552	10.1	× 108 / 424	2.6
Sum, rounded to a whole point						28

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,333	2440.2	− 2436	4.2	× 99 / 431	1
4	17,334	2487.9	− 2485	2.9	× 112 / 431	0.8
5	17,335	2508.1	− 2528	−19.9	× 111 / 431	−5.1
6	17,336	2573.4	− 2552	21.4	× 109 / 431	5.4
Sum, rounded to a whole point						2

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,271	2433.3	− 2436	−2.7	× 107 / 443	−0.7
4	17,272	2514.9	− 2485	29.9	× 103 / 443	7
5	17,273	2501.0	− 2528	−27	× 120 / 443	−7.3
6	17,274	2546.1	− 2552	−5.9	× 113 / 443	−1.5
Sum, rounded to a whole point						−3

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,226	2433.0	− 2436	−3	× 98 / 441	−0.7
4	17,227	2498.0	− 2485	13	× 114 / 441	3.4
5	17,228	2517.9	− 2528	−10.1	× 110 / 441	−2.5
6	17,229	2541.5	− 2552	−10.5	× 119 / 441	−2.8
Sum, rounded to a whole point						−3

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,219	2427.0	− 2436	−9	× 105 / 440	−2.1
4	17,220	2493.8	− 2485	8.8	× 98 / 440	2
5	17,221	2487.3	− 2528	−40.7	× 124 / 440	−11.5
6	17,222	2556.2	− 2552	4.2	× 113 / 440	1.1
Sum, rounded to a whole point						−11

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −11, 4, 13, 22, 28, 2, −3, −3, −11 → 4.6
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 15 · 2016→2017: 9 · 2017→2018: 9 · 2018→2019: 6 · 2019→2022: 26 · 2022→2023: 5 · 2023→2024: 0 · 2024→2025: 8 → average 9.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 9.8 × 2.66 = 26.1. Upper limit 30.7, lower limit −21.5.

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.