Abraham Lincoln: 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	36,073	2424.7	− 2436	−11.3	× 99 / 300	−3.7
4	36,076	2446.1	− 2485	−38.9	× 98 / 300	−12.7
5	36,077	2477.1	− 2528	−50.9	× 103 / 300	−17.5
Sum, rounded to a whole point						−34

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	33,698	2471.3	− 2436	35.3	× 96 / 301	11.3
4	33,701	2473.1	− 2485	−11.9	× 106 / 301	−4.2
5	33,702	2494.8	− 2528	−33.2	× 99 / 301	−10.9
Sum, rounded to a whole point						−4

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,288	2485.0	− 2436	49	× 92 / 293	15.4
4	34,290	2471.7	− 2485	−13.3	× 97 / 293	−4.4
5	34,292	2522.5	− 2528	−5.5	× 104 / 293	−2
Sum, rounded to a whole point						9

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,293	2475.4	− 2436	39.4	× 109 / 311	13.8
4	34,295	2486.7	− 2485	1.7	× 102 / 311	0.6
5	34,297	2516.1	− 2528	−11.9	× 100 / 311	−3.8
Sum, rounded to a whole point						11

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,459	2466.4	− 2436	30.4	× 102 / 317	9.8
4	34,460	2492.8	− 2485	7.8	× 116 / 317	2.9
5	34,461	2527.9	− 2528	−0.1	× 99 / 317	0
Sum, rounded to a whole point						13

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	33,670	2397.2	− 2436	−38.8	× 115 / 313	−14.3
4	33,671	2408.0	− 2485	−77	× 93 / 313	−22.9
5	33,672	2434.3	− 2528	−93.7	× 105 / 313	−31.4
Sum, rounded to a whole point						−69

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,390	2451.5	− 2436	15.5	× 85 / 314	4.2
4	34,391	2447.6	− 2485	−37.4	× 141 / 314	−16.8
5	34,392	2475.0	− 2528	−53	× 88 / 314	−14.9
Sum, rounded to a whole point						−27

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,449	2443.2	− 2436	7.2	× 87 / 300	2.1
4	34,450	2458.7	− 2485	−26.3	× 95 / 300	−8.3
5	34,451	2492.5	− 2528	−35.5	× 118 / 300	−14
Sum, rounded to a whole point						−20

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,301	2428.4	− 2436	−7.6	× 73 / 243	−2.3
4	34,302	2470.5	− 2485	−14.5	× 82 / 243	−4.9
5	34,303	2492.0	− 2528	−36	× 88 / 243	−13
Sum, rounded to a whole point						−20

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,148	2439.4	− 2436	3.4	× 73 / 230	1.1
4	34,149	2471.6	− 2485	−13.4	× 70 / 230	−4.1
5	34,150	2480.3	− 2528	−47.7	× 87 / 230	−18
Sum, rounded to a whole point						−21

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −34, −4, 9, 11, 13, −69, −27, −20, −20, −21 → −16.2
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 30 · 2016→2017: 13 · 2017→2018: 2 · 2018→2019: 2 · 2019→2021: 82 · 2021→2022: 42 · 2022→2023: 7 · 2023→2024: 0 · 2024→2025: 1 → average 19.9
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 19.9 × 2.66 = 52.9. Upper limit 36.7, lower limit −69.1.

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.