Hubert Howe Bancroft Middle: 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
6	32,804	2451.6	− 2552	−100.4	× 179 / 807	−22.3
7	32,806	2464.0	− 2567	−103	× 307 / 807	−39.2
8	32,808	2494.3	− 2586	−91.7	× 321 / 807	−36.5
Sum, rounded to a whole point						−98

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	31,016	2470.1	− 2552	−81.9	× 187 / 761	−20.1
7	31,018	2482.7	− 2567	−84.3	× 280 / 761	−31
8	31,019	2476.4	− 2586	−109.6	× 294 / 761	−42.3
Sum, rounded to a whole point						−93

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	31,579	2445.7	− 2552	−106.3	× 212 / 764	−29.5
7	31,581	2476.4	− 2567	−90.6	× 283 / 764	−33.6
8	31,582	2483.0	− 2586	−103	× 269 / 764	−36.3
Sum, rounded to a whole point						−99

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	31,623	2441.6	− 2552	−110.4	× 191 / 749	−28.2
7	31,626	2464.5	− 2567	−102.5	× 287 / 749	−39.3
8	31,627	2493.1	− 2586	−92.9	× 271 / 749	−33.6
Sum, rounded to a whole point						−101

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	31,801	2448.2	− 2552	−103.8	× 155 / 728	−22.1
7	31,802	2471.2	− 2567	−95.8	× 269 / 728	−35.4
8	31,803	2480.1	− 2586	−105.9	× 304 / 728	−44.2
Sum, rounded to a whole point						−102

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	31,828	2435.4	− 2552	−116.6	× 121 / 484	−29.2
7	31,829	2466.3	− 2567	−100.7	× 152 / 484	−31.6
8	31,830	2476.1	− 2586	−109.9	× 211 / 484	−47.9
Sum, rounded to a whole point						−109

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	31,885	2426.3	− 2552	−125.7	× 108 / 427	−31.8
7	31,886	2466.0	− 2567	−101	× 160 / 427	−37.8
8	31,887	2459.5	− 2586	−126.5	× 159 / 427	−47.1
Sum, rounded to a whole point						−117

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	31,751	2440.0	− 2552	−112	× 141 / 494	−32
7	31,752	2456.5	− 2567	−110.5	× 164 / 494	−36.7
8	31,753	2470.3	− 2586	−115.7	× 189 / 494	−44.3
Sum, rounded to a whole point						−113

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	31,610	2466.2	− 2552	−85.8	× 107 / 437	−21
7	31,611	2501.6	− 2567	−65.4	× 164 / 437	−24.5
8	31,612	2491.4	− 2586	−94.6	× 166 / 437	−35.9
Sum, rounded to a whole point						−81

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −98, −93, −99, −101, −102, −109, −117, −113, −81 → −101.4
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: 6 · 2017→2018: 2 · 2018→2019: 1 · 2019→2022: 7 · 2022→2023: 8 · 2023→2024: 4 · 2024→2025: 32 → average 8.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 8.1 × 2.66 = 21.5. Upper limit −79.9, lower limit −122.9.

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.