Arthur C. Butler Elementary: english

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	60,371	2410.7	− 2432	−21.3	× 127 / 521	−5.2
4	60,372	2468.4	− 2473	−4.6	× 132 / 521	−1.2
5	60,375	2490.3	− 2502	−11.7	× 130 / 521	−2.9
6	60,376	2523.8	− 2531	−7.2	× 132 / 521	−1.8
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	56,068	2414.9	− 2432	−17.1	× 145 / 562	−4.4
4	56,070	2448.5	− 2473	−24.5	× 143 / 562	−6.2
5	56,071	2501.8	− 2502	−0.2	× 135 / 562	0
6	56,074	2523.4	− 2531	−7.6	× 139 / 562	−1.9
Sum, rounded to a whole point						−13

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	57,700	2435.9	− 2432	3.9	× 116 / 559	0.8
4	57,703	2474.3	− 2473	1.3	× 154 / 559	0.4
5	57,705	2518.5	− 2502	16.5	× 146 / 559	4.3
6	57,707	2537.6	− 2531	6.6	× 143 / 559	1.7
Sum, rounded to a whole point						7

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	57,836	2453.9	− 2432	21.9	× 117 / 530	4.8
4	57,837	2489.1	− 2473	16.1	× 119 / 530	3.6
5	57,840	2510.2	− 2502	8.2	× 154 / 530	2.4
6	57,841	2542.2	− 2531	11.2	× 140 / 530	3
Sum, rounded to a whole point						14

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,086	2438.9	− 2432	6.9	× 104 / 529	1.4
4	58,087	2490.5	− 2473	17.5	× 128 / 529	4.2
5	58,088	2524.6	− 2502	22.6	× 134 / 529	5.7
6	58,089	2539.6	− 2531	8.6	× 163 / 529	2.6
Sum, rounded to a whole point						14

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	56,773	2394.4	− 2432	−37.6	× 116 / 442	−9.9
4	56,774	2435.3	− 2473	−37.7	× 120 / 442	−10.2
5	56,775	2484.5	− 2502	−17.5	× 97 / 442	−3.8
6	56,776	2536.6	− 2531	5.6	× 109 / 442	1.4
Sum, rounded to a whole point						−23

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,127	2452.1	− 2432	20.1	× 131 / 474	5.6
4	58,128	2442.6	− 2473	−30.4	× 122 / 474	−7.8
5	58,129	2516.7	− 2502	14.7	× 123 / 474	3.8
6	58,130	2550.9	− 2531	19.9	× 98 / 474	4.1
Sum, rounded to a whole point						6

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	58,101	2432.9	− 2432	0.9	× 123 / 501	0.2
4	58,102	2466.3	− 2473	−6.7	× 135 / 501	−1.8
5	58,103	2486.8	− 2502	−15.2	× 119 / 501	−3.6
6	58,104	2530.2	− 2531	−0.8	× 124 / 501	−0.2
Sum, rounded to a whole point						−5

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	57,998	2410.4	− 2432	−21.6	× 123 / 513	−5.2
4	57,999	2450.4	− 2473	−22.6	× 134 / 513	−5.9
5	58,000	2503.2	− 2502	1.2	× 133 / 513	0.3
6	58,001	2532.3	− 2531	1.3	× 123 / 513	0.3
Sum, rounded to a whole point						−10

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	57,757	2430.5	− 2432	−1.5	× 134 / 531	−0.4
4	57,758	2459.8	− 2473	−13.2	× 125 / 531	−3.1
5	57,759	2505.6	− 2502	3.6	× 127 / 531	0.9
6	57,760	2563.9	− 2531	32.9	× 145 / 531	9
Sum, rounded to a whole point						6

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −11, −13, 7, 14, 14, −23, 6, −5, −10, 6 → −1.5
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: 20 · 2017→2018: 7 · 2018→2019: 0 · 2019→2021: 37 · 2021→2022: 29 · 2022→2023: 11 · 2023→2024: 5 · 2024→2025: 16 → average 14.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 14.1 × 2.66 = 37.5. Upper limit 36, lower limit −39.

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.