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.

Measured against the grade bars

The state's math test uses one scale for every grade, so a score means the same thing in grade 3 as in grade 5.

3rd The average 3rd grader scores 53 points under the grade 3 bar. 2383 vs. 2436.
4th The average 4th grader scores 24 points under the grade 4 bar. 2461 vs. 2485.
5th The average 5th grader scores 31 points under the grade 4 bar. 2454 vs. 2485. The 5th-grade bar is 2528.

2024 results. "Meets standard" is the state's mark for being on track for that grade.

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	21,115	2368.9	− 2436	−67.1	× 80 / 303	−17.7
4	21,117	2408.1	− 2485	−76.9	× 87 / 303	−22.1
5	21,118	2431.0	− 2528	−97	× 64 / 303	−20.5
6	21,121	2473.6	− 2552	−78.4	× 72 / 303	−18.6
Sum, rounded to a whole point						−79

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	20,020	2381.4	− 2436	−54.6	× 62 / 291	−11.6
4	20,022	2423.8	− 2485	−61.2	× 79 / 291	−16.6
5	20,025	2437.4	− 2528	−90.6	× 86 / 291	−26.8
6	20,027	2471.2	− 2552	−80.8	× 64 / 291	−17.8
Sum, rounded to a whole point						−73

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	20,332	2381.7	− 2436	−54.3	× 81 / 301	−14.6
4	20,335	2445.7	− 2485	−39.3	× 60 / 301	−7.8
5	20,337	2447.5	− 2528	−80.5	× 77 / 301	−20.6
6	20,339	2477.9	− 2552	−74.1	× 83 / 301	−20.4
Sum, rounded to a whole point						−63

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	20,323	2399.0	− 2436	−37	× 63 / 267	−8.7
4	20,325	2426.8	− 2485	−58.2	× 84 / 267	−18.3
5	20,327	2471.3	− 2528	−56.7	× 47 / 267	−10
6	20,329	2490.3	− 2552	−61.7	× 73 / 267	−16.9
Sum, rounded to a whole point						−54

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	20,506	2384.2	− 2436	−51.8	× 56 / 253	−11.5
4	20,507	2439.3	− 2485	−45.7	× 64 / 253	−11.6
5	20,508	2440.0	− 2528	−88	× 80 / 253	−27.8
6	20,509	2496.6	− 2552	−55.4	× 53 / 253	−11.6
Sum, rounded to a whole point						−62

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	19,991	2340.3	− 2436	−95.7	× 42 / 212	−19
4	19,992	2370.6	− 2485	−114.4	× 58 / 212	−31.3
5	19,993	2431.8	− 2528	−96.2	× 51 / 212	−23.1
6	19,994	2449.0	− 2552	−103	× 61 / 212	−29.6
Sum, rounded to a whole point						−103

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	20,530	2418.1	− 2436	−17.9	× 47 / 136	−6.2
4	20,531	2431.6	− 2485	−53.4	× 31 / 136	−12.2
5	20,532	2394.4	− 2528	−133.6	× 58 / 136	−57
Sum, rounded to a whole point						−75

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	20,495	2449.4	− 2436	13.4	× 34 / 129	3.5
4	20,496	2441.9	− 2485	−43.1	× 59 / 129	−19.7
5	20,497	2452.2	− 2528	−75.8	× 36 / 129	−21.2
Sum, rounded to a whole point						−37

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	20,377	2383.2	− 2436	−52.8	× 56 / 146	−20.3
4	20,378	2460.7	− 2485	−24.3	× 30 / 146	−5
5	20,379	2454.1	− 2528	−73.9	× 60 / 146	−30.4
Sum, rounded to a whole point						−56

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −79, −73, −63, −54, −62, −103, −75, −37, −56 → −66.9
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 6 · 2016→2017: 10 · 2017→2018: 9 · 2018→2019: 8 · 2019→2021: 41 · 2021→2022: 28 · 2022→2023: 38 · 2023→2024: 19 → 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 −14, lower limit −119.8.

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