Daniel Webster: 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	36,412	2417.0	− 2436	−19	× 76 / 235	−6.1
4	36,414	2444.3	− 2485	−40.7	× 77 / 235	−13.3
5	36,416	2476.9	− 2528	−51.1	× 82 / 235	−17.8
Sum, rounded to a whole point						−37

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,001	2434.8	− 2436	−1.2	× 78 / 221	−0.4
4	34,002	2465.0	− 2485	−20	× 72 / 221	−6.5
5	34,005	2484.1	− 2528	−43.9	× 71 / 221	−14.1
Sum, rounded to a whole point						−21

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,597	2436.7	− 2436	0.7	× 70 / 222	0.2
4	34,599	2468.1	− 2485	−16.9	× 82 / 222	−6.2
5	34,601	2496.5	− 2528	−31.5	× 70 / 222	−9.9
Sum, rounded to a whole point						−16

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,600	2455.6	− 2436	19.6	× 50 / 188	5.2
4	34,601	2483.5	− 2485	−1.5	× 68 / 188	−0.5
5	34,604	2492.3	− 2528	−35.7	× 70 / 188	−13.3
Sum, rounded to a whole point						−9

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,771	2445.5	− 2436	9.5	× 68 / 182	3.5
4	34,772	2498.0	− 2485	13	× 52 / 182	3.7
5	34,773	2475.4	− 2528	−52.6	× 62 / 182	−17.9
Sum, rounded to a whole point						−11

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,680	2427.9	− 2436	−8.1	× 43 / 146	−2.4
4	34,681	2449.3	− 2485	−35.7	× 55 / 146	−13.4
5	34,682	2438.8	− 2528	−89.2	× 48 / 146	−29.3
Sum, rounded to a whole point						−45

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,743	2421.1	− 2436	−14.9	× 44 / 152	−4.3
4	34,744	2467.3	− 2485	−17.7	× 48 / 152	−5.6
5	34,745	2474.5	− 2528	−53.5	× 60 / 152	−21.1
Sum, rounded to a whole point						−31

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,597	2418.7	− 2436	−17.3	× 42 / 141	−5.2
4	34,598	2446.1	− 2485	−38.9	× 49 / 141	−13.5
5	34,599	2506.6	− 2528	−21.4	× 50 / 141	−7.6
Sum, rounded to a whole point						−26

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,444	2420.7	− 2436	−15.3	× 42 / 130	−4.9
4	34,445	2453.6	− 2485	−31.4	× 39 / 130	−9.4
5	34,446	2470.2	− 2528	−57.8	× 49 / 130	−21.8
Sum, rounded to a whole point						−36

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −37, −21, −16, −9, −11, −45, −31, −26, −36 → −25.8
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 16 · 2016→2017: 5 · 2017→2018: 7 · 2018→2019: 2 · 2019→2022: 34 · 2022→2023: 14 · 2023→2024: 5 · 2024→2025: 10 → average 11.6
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11.6 × 2.66 = 30.9. Upper limit 5.1, lower limit −56.7.

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. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.