Central Elementary: 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	18,639	2400.1	− 2436	−35.9	× 24 / 188	−4.6
4	18,640	2425.2	− 2485	−59.8	× 41 / 188	−13
5	18,643	2412.3	− 2528	−115.7	× 33 / 188	−20.3
6	18,644	2412.6	− 2552	−139.4	× 33 / 188	−24.5
7	18,647	2458.7	− 2567	−108.3	× 28 / 188	−16.1
8	18,648	2474.8	− 2586	−111.2	× 29 / 188	−17.2
Sum, rounded to a whole point						−96

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,638	2457.3	− 2436	21.3	× 34 / 191	3.8
4	17,640	2480.6	− 2485	−4.4	× 22 / 191	−0.5
5	17,641	2460.2	− 2528	−67.8	× 35 / 191	−12.4
6	17,644	2419.1	− 2552	−132.9	× 37 / 191	−25.7
7	17,646	2441.2	− 2567	−125.8	× 36 / 191	−23.7
8	17,647	2462.4	− 2586	−123.6	× 27 / 191	−17.5
Sum, rounded to a whole point						−76

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,977	2424.4	− 2436	−11.6	× 36 / 189	−2.2
4	17,980	2486.6	− 2485	1.6	× 30 / 189	0.3
5	17,981	2436.3	− 2528	−91.7	× 21 / 189	−10.2
6	17,983	2433.1	− 2552	−118.9	× 39 / 189	−24.5
7	17,985	2424.8	− 2567	−142.2	× 31 / 189	−23.3
8	17,988	2453.3	− 2586	−132.7	× 32 / 189	−22.5
Sum, rounded to a whole point						−82

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,990	2412.5	− 2436	−23.5	× 28 / 188	−3.5
4	17,993	2490.7	− 2485	5.7	× 35 / 188	1.1
5	17,994	2486.8	− 2528	−41.2	× 30 / 188	−6.6
6	17,997	2444.1	− 2552	−107.9	× 25 / 188	−14.3
7	17,998	2454.4	− 2567	−112.6	× 36 / 188	−21.6
8	18,001	2464.1	− 2586	−121.9	× 34 / 188	−22
Sum, rounded to a whole point						−67

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	18,139	2425.9	− 2436	−10.1	× 37 / 186	−2
4	18,140	2433.7	− 2485	−51.3	× 27 / 186	−7.4
5	18,141	2476.1	− 2528	−51.9	× 34 / 186	−9.5
6	18,142	2480.7	− 2552	−71.3	× 28 / 186	−10.7
7	18,143	2438.3	− 2567	−128.7	× 25 / 186	−17.3
8	18,144	2485.3	− 2586	−100.7	× 35 / 186	−18.9
Sum, rounded to a whole point						−66

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	18,183	2400.1	− 2436	−35.9	× 29 / 196	−5.3
4	18,184	2426.2	− 2485	−58.8	× 35 / 196	−10.5
5	18,185	2422.9	− 2528	−105.1	× 29 / 196	−15.6
6	18,186	2470.9	− 2552	−81.1	× 36 / 196	−14.9
7	18,187	2430.7	− 2567	−136.3	× 30 / 196	−20.9
8	18,188	2473.4	− 2586	−112.6	× 37 / 196	−21.3
Sum, rounded to a whole point						−88

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	18,122	2407.2	− 2436	−28.8	× 35 / 172	−5.9
4	18,123	2391.8	− 2485	−93.2	× 26 / 172	−14.1
5	18,124	2473.2	− 2528	−54.8	× 26 / 172	−8.3
6	18,125	2418.4	− 2552	−133.6	× 28 / 172	−21.7
7	18,126	2520.5	− 2567	−46.5	× 30 / 172	−8.1
8	18,127	2445.1	− 2586	−140.9	× 27 / 172	−22.1
Sum, rounded to a whole point						−80

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	18,081	2414.5	− 2436	−21.5	× 26 / 153	−3.7
4	18,082	2401.5	− 2485	−83.5	× 33 / 153	−18
5	18,083	2382.7	− 2528	−145.3	× 22 / 153	−20.9
6	18,084	2437.8	− 2552	−114.2	× 28 / 153	−20.9
7	18,085	2438.2	− 2567	−128.8	× 21 / 153	−17.7
8	18,086	2503.3	− 2586	−82.7	× 23 / 153	−12.4
Sum, rounded to a whole point						−94

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	18,077	2363.3	− 2436	−72.7	× 23 / 143	−11.7
4	18,078	2440.6	− 2485	−44.4	× 21 / 143	−6.5
5	18,079	2429.5	− 2528	−98.5	× 31 / 143	−21.4
6	18,080	2398.2	− 2552	−153.8	× 17 / 143	−18.3
7	18,081	2518.4	− 2567	−48.6	× 28 / 143	−9.5
8	18,082	2422.6	− 2586	−163.4	× 23 / 143	−26.3
Sum, rounded to a whole point						−94

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −96, −76, −82, −67, −66, −88, −80, −94, −94 → −82.6
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: 6 · 2017→2018: 15 · 2018→2019: 1 · 2019→2022: 22 · 2022→2023: 8 · 2023→2024: 14 · 2024→2025: 0 → average 10.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 10.8 × 2.66 = 28.7. Upper limit −53.9, lower limit −111.3.

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.