Taft Union High: 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
11	18,081	2489.8	− 2628	−138.2	× 241 / 241	−138.2
Sum, rounded to a whole point						−138

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,088	2525.8	− 2628	−102.2	× 251 / 251	−102.2
Sum, rounded to a whole point						−102

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,408	2509.2	− 2628	−118.8	× 236 / 236	−118.8
Sum, rounded to a whole point						−119

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,431	2496.0	− 2628	−132	× 222 / 222	−132
Sum, rounded to a whole point						−132

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,570	2503.6	− 2628	−124.4	× 238 / 238	−124.4
Sum, rounded to a whole point						−124

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,168	2486.8	− 2628	−141.2	× 179 / 179	−141.2
Sum, rounded to a whole point						−141

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,624	2477.4	− 2628	−150.6	× 252 / 252	−150.6
Sum, rounded to a whole point						−151

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,566	2467.4	− 2628	−160.6	× 270 / 270	−160.6
Sum, rounded to a whole point						−161

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,516	2488.8	− 2628	−139.2	× 272 / 272	−139.2
Sum, rounded to a whole point						−139

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
11	17,510	2497.8	− 2628	−130.2	× 273 / 273	−130.2
Sum, rounded to a whole point						−130

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −138, −102, −119, −132, −124, −141, −151, −161, −139, −130 → −133.7
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 36 · 2016→2017: 17 · 2017→2018: 13 · 2018→2019: 8 · 2019→2021: 17 · 2021→2022: 10 · 2022→2023: 10 · 2023→2024: 22 · 2024→2025: 9 → average 15.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 15.8 × 2.66 = 42. Upper limit −91.7, lower limit −175.7.

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.