Banning Independent Study: 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
8	55,430	2434.7	− 2586	−151.3	× 15 / 43	−52.8
11	55,433	2474.2	− 2628	−153.8	× 28 / 43	−100.1
Sum, rounded to a whole point						−153

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	51,483	2403.2	− 2567	−163.8	× 11 / 78	−23.1
8	51,485	2388.8	− 2586	−197.2	× 19 / 78	−48
11	51,487	2452.0	− 2628	−176	× 48 / 78	−108.3
Sum, rounded to a whole point						−179

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	52,962	2430.6	− 2567	−136.4	× 11 / 95	−15.8
8	52,965	2377.5	− 2586	−208.5	× 16 / 95	−35.1
11	52,967	2445.4	− 2628	−182.6	× 68 / 95	−130.7
Sum, rounded to a whole point						−182

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	53,052	2387.1	− 2567	−179.9	× 16 / 114	−25.2
8	53,053	2401.6	− 2586	−184.4	× 23 / 114	−37.2
11	53,056	2435.9	− 2628	−192.1	× 75 / 114	−126.4
Sum, rounded to a whole point						−189

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	53,284	2383.9	− 2567	−183.1	× 16 / 89	−32.9
8	53,285	2379.3	− 2586	−206.7	× 16 / 89	−37.2
11	53,286	2416.3	− 2628	−211.7	× 57 / 89	−135.6
Sum, rounded to a whole point						−206

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	53,284	2376.2	− 2628	−251.8	× 13 / 13	−251.8
Sum, rounded to a whole point						−252

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	53,242	2415.4	− 2552	−136.6	× 13 / 58	−30.6
7	53,243	2419.2	− 2567	−147.8	× 15 / 58	−38.2
8	53,244	2436.8	− 2586	−149.2	× 12 / 58	−30.9
11	53,245	2457.7	− 2628	−170.3	× 18 / 58	−52.9
Sum, rounded to a whole point						−153

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	53,095	2388.8	− 2567	−178.2	× 12 / 40	−53.5
8	53,096	2416.3	− 2586	−169.7	× 11 / 40	−46.7
11	53,097	2442.6	− 2628	−185.4	× 17 / 40	−78.8
Sum, rounded to a whole point						−179

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
8	52,838	2428.4	− 2586	−157.6	× 11 / 34	−51
11	52,839	2443.8	− 2628	−184.2	× 23 / 34	−124.6
Sum, rounded to a whole point						−176

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −153, −179, −182, −189, −206, −252, −153, −179, −176 → −185.4
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 26 · 2016→2017: 3 · 2017→2018: 7 · 2018→2019: 17 · 2019→2022: 46 · 2022→2023: 99 · 2023→2024: 26 · 2024→2025: 3 → average 28.4
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 28.4 × 2.66 = 75.5. Upper limit −109.9, lower limit −260.9.

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.