Gratton Charter: 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	96,742	2475.2	− 2436	39.2	× 11 / 70	6.2
4	96,745	2503.9	− 2485	18.9	× 14 / 70	3.8
5	96,746	2526.5	− 2528	−1.5	× 11 / 70	−0.2
6	96,749	2537.2	− 2552	−14.8	× 12 / 70	−2.5
7	96,750	2567.5	− 2567	0.5	× 11 / 70	0.1
8	96,753	2569.8	− 2586	−16.2	× 11 / 70	−2.5
Sum, rounded to a whole point						5

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	89,704	2471.4	− 2436	35.4	× 11 / 74	5.3
4	89,706	2500.8	− 2485	15.8	× 12 / 74	2.6
5	89,709	2526.4	− 2528	−1.6	× 15 / 74	−0.3
6	89,710	2549.3	− 2552	−2.7	× 12 / 74	−0.4
7	89,713	2561.2	− 2567	−5.8	× 12 / 74	−0.9
8	89,714	2610.8	− 2586	24.8	× 12 / 74	4
Sum, rounded to a whole point						10

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	92,329	2454.5	− 2436	18.5	× 15 / 76	3.7
4	92,330	2499.4	− 2485	14.4	× 12 / 76	2.3
5	92,332	2541.3	− 2528	13.3	× 12 / 76	2.1
6	92,335	2546.3	− 2552	−5.7	× 14 / 76	−1.1
7	92,336	2524.9	− 2567	−42.1	× 11 / 76	−6.1
8	92,338	2563.9	− 2586	−22.1	× 12 / 76	−3.5
Sum, rounded to a whole point						−3

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	92,526	2503.0	− 2436	67	× 11 / 65	11.3
4	92,527	2508.1	− 2485	23.1	× 15 / 65	5.3
5	92,530	2528.1	− 2528	0.1	× 14 / 65	0
6	92,531	2551.1	− 2552	−0.9	× 12 / 65	−0.2
7	92,534	2538.0	− 2567	−29	× 13 / 65	−5.8
Sum, rounded to a whole point						11

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,159	2470.7	− 2436	34.7	× 18 / 84	7.4
4	93,160	2552.3	− 2485	67.3	× 12 / 84	9.6
5	93,161	2555.4	− 2528	27.4	× 13 / 84	4.2
6	93,162	2564.1	− 2552	12.1	× 14 / 84	2
7	93,163	2546.2	− 2567	−20.8	× 13 / 84	−3.2
8	93,164	2613.4	− 2586	27.4	× 14 / 84	4.6
Sum, rounded to a whole point						25

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	91,184	2426.3	− 2436	−9.7	× 12 / 85	−1.4
4	91,185	2498.1	− 2485	13.1	× 16 / 85	2.5
5	91,186	2554.6	− 2528	26.6	× 18 / 85	5.6
6	91,187	2580.7	− 2552	28.7	× 12 / 85	4.1
7	91,188	2543.3	− 2567	−23.7	× 15 / 85	−4.2
8	91,189	2630.2	− 2586	44.2	× 12 / 85	6.2
Sum, rounded to a whole point						13

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,394	2437.9	− 2436	1.9	× 15 / 87	0.3
4	93,395	2503.5	− 2485	18.5	× 13 / 87	2.8
5	93,396	2566.5	− 2528	38.5	× 15 / 87	6.6
6	93,397	2499.3	− 2552	−52.7	× 18 / 87	−10.9
7	93,398	2574.3	− 2567	7.3	× 11 / 87	0.9
8	93,399	2632.9	− 2586	46.9	× 15 / 87	8.1
Sum, rounded to a whole point						8

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,288	2442.5	− 2436	6.5	× 12 / 81	1
4	93,289	2514.0	− 2485	29	× 15 / 81	5.4
5	93,290	2581.3	− 2528	53.3	× 13 / 81	8.6
6	93,291	2562.0	− 2552	10	× 14 / 81	1.7
7	93,292	2549.5	− 2567	−17.5	× 16 / 81	−3.5
8	93,293	2619.9	− 2586	33.9	× 11 / 81	4.6
Sum, rounded to a whole point						18

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,183	2414.0	− 2436	−22	× 14 / 76	−4.1
4	93,184	2500.5	− 2485	15.5	× 12 / 76	2.4
5	93,185	2569.1	− 2528	41.1	× 15 / 76	8.1
6	93,186	2543.8	− 2552	−8.2	× 12 / 76	−1.3
7	93,187	2573.7	− 2567	6.7	× 11 / 76	1
8	93,188	2599.3	− 2586	13.3	× 12 / 76	2.1
Sum, rounded to a whole point						8

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	92,909	2485.3	− 2436	49.3	× 12 / 75	7.9
4	92,910	2475.0	− 2485	−10	× 13 / 75	−1.7
5	92,911	2588.7	− 2528	60.7	× 12 / 75	9.7
6	92,912	2572.4	− 2552	20.4	× 14 / 75	3.8
7	92,913	2616.0	− 2567	49	× 12 / 75	7.8
8	92,914	2581.9	− 2586	−4.1	× 12 / 75	−0.7
Sum, rounded to a whole point						27

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 5, 10, −3, 11, 25, 13, 8, 18, 8, 27 → 12.2
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 5 · 2016→2017: 13 · 2017→2018: 14 · 2018→2019: 14 · 2019→2021: 12 · 2021→2022: 5 · 2022→2023: 10 · 2023→2024: 10 · 2024→2025: 19 → average 11.3
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11.3 × 2.66 = 30.1. Upper limit 42.3, lower limit −17.9.

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.