George Lincoln Mosher: 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	79,229	2414.1	− 2436	−21.9	× 71 / 270	−5.8
4	79,230	2450.8	− 2485	−34.2	× 72 / 270	−9.1
5	79,233	2467.4	− 2528	−60.6	× 71 / 270	−15.9
6	79,234	2482.6	− 2552	−69.4	× 56 / 270	−14.4
Sum, rounded to a whole point						−45

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	73,416	2441.8	− 2436	5.8	× 71 / 283	1.5
4	73,418	2455.8	− 2485	−29.2	× 68 / 283	−7
5	73,421	2484.1	− 2528	−43.9	× 76 / 283	−11.8
6	73,422	2521.4	− 2552	−30.6	× 68 / 283	−7.4
Sum, rounded to a whole point						−25

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,373	2415.2	− 2436	−20.8	× 72 / 267	−5.6
4	75,376	2485.5	− 2485	0.5	× 59 / 267	0.1
5	75,377	2468.5	− 2528	−59.5	× 71 / 267	−15.8
6	75,379	2546.9	− 2552	−5.1	× 65 / 267	−1.2
Sum, rounded to a whole point						−23

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,568	2434.1	− 2436	−1.9	× 69 / 246	−0.5
4	75,570	2453.4	− 2485	−31.6	× 60 / 246	−7.7
5	75,572	2515.7	− 2528	−12.3	× 57 / 246	−2.9
6	75,574	2514.4	− 2552	−37.6	× 60 / 246	−9.2
Sum, rounded to a whole point						−20

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	76,095	2433.4	− 2436	−2.6	× 69 / 266	−0.7
4	76,096	2486.6	− 2485	1.6	× 68 / 266	0.4
5	76,097	2481.9	− 2528	−46.1	× 70 / 266	−12.1
6	76,098	2497.9	− 2552	−54.1	× 59 / 266	−12
Sum, rounded to a whole point						−24

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,654	2393.1	− 2436	−42.9	× 62 / 198	−13.4
4	74,655	2431.3	− 2485	−53.7	× 46 / 198	−12.5
5	74,656	2483.4	− 2528	−44.6	× 49 / 198	−11
6	74,657	2497.4	− 2552	−54.6	× 41 / 198	−11.3
Sum, rounded to a whole point						−48

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	76,241	2420.0	− 2436	−16	× 73 / 284	−4.1
4	76,242	2454.4	− 2485	−30.6	× 74 / 284	−8
5	76,243	2463.4	− 2528	−64.6	× 69 / 284	−15.7
6	76,244	2489.7	− 2552	−62.3	× 68 / 284	−14.9
Sum, rounded to a whole point						−43

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	76,223	2399.8	− 2436	−36.2	× 86 / 304	−10.2
4	76,224	2429.4	− 2485	−55.6	× 72 / 304	−13.2
5	76,225	2475.9	− 2528	−52.1	× 74 / 304	−12.7
6	76,226	2485.8	− 2552	−66.2	× 72 / 304	−15.7
Sum, rounded to a whole point						−52

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	76,218	2420.0	− 2436	−16	× 59 / 285	−3.3
4	76,219	2430.0	− 2485	−55	× 82 / 285	−15.8
5	76,220	2463.9	− 2528	−64.1	× 75 / 285	−16.9
6	76,221	2505.3	− 2552	−46.7	× 69 / 285	−11.3
Sum, rounded to a whole point						−47

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	75,891	2400.5	− 2436	−35.5	× 77 / 292	−9.4
4	75,892	2434.8	− 2485	−50.2	× 53 / 292	−9.1
5	75,893	2474.4	− 2528	−53.6	× 77 / 292	−14.1
6	75,894	2499.3	− 2552	−52.7	× 85 / 292	−15.3
Sum, rounded to a whole point						−48

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −45, −25, −23, −20, −24, −48, −43, −52, −47, −48 → −37.5
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 20 · 2016→2017: 2 · 2017→2018: 3 · 2018→2019: 4 · 2019→2021: 24 · 2021→2022: 5 · 2022→2023: 9 · 2023→2024: 5 · 2024→2025: 1 → 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 −16, lower limit −59.

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.