Cardiff Elementary: 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	70,445	2486.7	− 2436	50.7	× 105 / 412	12.9
4	70,446	2516.6	− 2485	31.6	× 108 / 412	8.3
5	70,449	2527.3	− 2528	−0.7	× 86 / 412	−0.1
6	70,450	2602.8	− 2552	50.8	× 113 / 412	13.9
Sum, rounded to a whole point						35

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	65,274	2480.9	− 2436	44.9	× 109 / 406	12.1
4	65,276	2516.2	− 2485	31.2	× 108 / 406	8.3
5	65,278	2566.9	− 2528	38.9	× 111 / 406	10.6
6	65,280	2585.0	− 2552	33	× 78 / 406	6.3
Sum, rounded to a whole point						37

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,086	2495.4	− 2436	59.4	× 80 / 405	11.7
4	67,088	2510.0	− 2485	25	× 110 / 405	6.8
5	67,089	2567.6	− 2528	39.6	× 109 / 405	10.7
6	67,091	2610.2	− 2552	58.2	× 106 / 405	15.2
Sum, rounded to a whole point						44

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,181	2490.1	− 2436	54.1	× 84 / 386	11.8
4	67,183	2527.1	− 2485	42.1	× 83 / 386	9.1
5	67,185	2550.3	− 2528	22.3	× 114 / 386	6.6
6	67,187	2607.1	− 2552	55.1	× 105 / 386	15
Sum, rounded to a whole point						42

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,679	2500.9	− 2436	64.9	× 100 / 386	16.8
4	67,680	2535.7	− 2485	50.7	× 84 / 386	11
5	67,681	2550.2	− 2528	22.2	× 83 / 386	4.8
6	67,682	2585.3	− 2552	33.3	× 119 / 386	10.3
Sum, rounded to a whole point						43

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,825	2479.4	− 2436	43.4	× 89 / 367	10.5
4	67,826	2523.0	− 2485	38	× 101 / 367	10.5
5	67,827	2545.6	− 2528	17.6	× 85 / 367	4.1
6	67,828	2607.4	− 2552	55.4	× 92 / 367	13.9
Sum, rounded to a whole point						39

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,835	2463.5	− 2436	27.5	× 80 / 353	6.2
4	67,836	2527.6	− 2485	42.6	× 93 / 353	11.2
5	67,837	2556.6	− 2528	28.6	× 99 / 353	8
6	67,838	2597.8	− 2552	45.8	× 81 / 353	10.5
Sum, rounded to a whole point						36

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,829	2475.0	− 2436	39	× 109 / 374	11.4
4	67,830	2502.3	− 2485	17.3	× 82 / 374	3.8
5	67,831	2562.7	− 2528	34.7	× 90 / 374	8.4
6	67,832	2600.1	− 2552	48.1	× 93 / 374	12
Sum, rounded to a whole point						35

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,587	2482.8	− 2436	46.8	× 87 / 378	10.8
4	67,588	2520.1	− 2485	35.1	× 112 / 378	10.4
5	67,589	2541.1	− 2528	13.1	× 85 / 378	2.9
6	67,590	2617.7	− 2552	65.7	× 94 / 378	16.3
Sum, rounded to a whole point						40

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,632	2472.7	− 2436	36.7	× 92 / 371	9.1
4	67,633	2514.2	− 2485	29.2	× 88 / 371	6.9
5	67,634	2544.4	− 2528	16.4	× 109 / 371	4.8
6	67,635	2595.9	− 2552	43.9	× 82 / 371	9.7
Sum, rounded to a whole point						31

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 35, 37, 44, 42, 43, 39, 36, 35, 40, 31 → 38.2
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 2 · 2016→2017: 7 · 2017→2018: 2 · 2018→2019: 1 · 2019→2022: 4 · 2022→2023: 3 · 2023→2024: 1 · 2024→2025: 5 · 2025→2026: 9 → average 3.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 3.8 × 2.66 = 10.1. Upper limit 48.3, lower limit 28.1.

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.

Cardiff Elementary