Centralia Elementary: 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
3	48,968	2443.1	− 2436	7.1	× 637 / 2559	1.8
4	48,971	2465.6	− 2485	−19.4	× 655 / 2559	−5
5	48,972	2503.9	− 2528	−24.1	× 638 / 2559	−6
6	48,975	2531.3	− 2552	−20.7	× 629 / 2559	−5.1
Sum, rounded to a whole point						−14

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	45,518	2456.0	− 2436	20	× 619 / 2550	4.9
4	45,519	2491.5	− 2485	6.5	× 632 / 2550	1.6
5	45,521	2514.0	− 2528	−14	× 651 / 2550	−3.6
6	45,523	2547.6	− 2552	−4.4	× 648 / 2550	−1.1
Sum, rounded to a whole point						2

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	46,726	2455.1	− 2436	19.1	× 610 / 2545	4.6
4	46,727	2498.2	− 2485	13.2	× 632 / 2545	3.3
5	46,729	2519.9	− 2528	−8.1	× 643 / 2545	−2
6	46,731	2542.3	− 2552	−9.7	× 660 / 2545	−2.5
Sum, rounded to a whole point						3

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	46,736	2462.4	− 2436	26.4	× 584 / 2453	6.3
4	46,737	2502.3	− 2485	17.3	× 605 / 2453	4.3
5	46,740	2522.1	− 2528	−5.9	× 632 / 2453	−1.5
6	46,741	2563.5	− 2552	11.5	× 632 / 2453	3
Sum, rounded to a whole point						12

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	46,915	2465.2	− 2436	29.2	× 545 / 2361	6.7
4	46,916	2505.5	− 2485	20.5	× 575 / 2361	5
5	46,917	2536.6	− 2528	8.6	× 609 / 2361	2.2
6	46,918	2563.8	− 2552	11.8	× 632 / 2361	3.2
Sum, rounded to a whole point						17

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	46,751	2452.1	− 2436	16.1	× 567 / 2278	4
4	46,752	2496.8	− 2485	11.8	× 555 / 2278	2.9
5	46,753	2507.0	− 2528	−21	× 617 / 2278	−5.7
6	46,754	2553.2	− 2552	1.2	× 539 / 2278	0.3
Sum, rounded to a whole point						1

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	46,741	2458.4	− 2436	22.4	× 530 / 2240	5.3
4	46,742	2494.0	− 2485	9	× 560 / 2240	2.3
5	46,743	2524.3	− 2528	−3.7	× 554 / 2240	−0.9
6	46,744	2542.8	− 2552	−9.2	× 596 / 2240	−2.4
Sum, rounded to a whole point						4

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	46,594	2458.8	− 2436	22.8	× 529 / 2194	5.5
4	46,595	2504.7	− 2485	19.7	× 542 / 2194	4.9
5	46,596	2521.0	− 2528	−7	× 562 / 2194	−1.8
6	46,597	2559.6	− 2552	7.6	× 561 / 2194	1.9
Sum, rounded to a whole point						11

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	46,352	2450.2	− 2436	14.2	× 559 / 2181	3.6
4	46,353	2499.1	− 2485	14.1	× 511 / 2181	3.3
5	46,354	2531.2	− 2528	3.2	× 541 / 2181	0.8
6	46,355	2549.8	− 2552	−2.2	× 570 / 2181	−0.6
Sum, rounded to a whole point						7

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	46,224	2450.3	− 2436	14.3	× 485 / 2102	3.3
4	46,225	2502.4	− 2485	17.4	× 552 / 2102	4.6
5	46,226	2528.3	− 2528	0.3	× 512 / 2102	0.1
6	46,227	2564.5	− 2552	12.5	× 553 / 2102	3.3
Sum, rounded to a whole point						11

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −14, 2, 3, 12, 17, 1, 4, 11, 7, 11 → 5.4
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: 1 · 2017→2018: 9 · 2018→2019: 5 · 2019→2022: 16 · 2022→2023: 3 · 2023→2024: 7 · 2024→2025: 4 · 2025→2026: 4 → average 7.2
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 7.2 × 2.66 = 19.2. Upper limit 24.6, lower limit −13.8.

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.

Centralia Elementary