Centennial 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 6.

3rd The average 3rd grader scores just under the grade 3 bar. 2434 vs. 2436.
4th The average 4th grader meets the grade 4 bar. 2495 vs. 2485.
5th The average 5th grader scores 12 points under the grade 5 bar. 2516 vs. 2528.
6th The average 6th grader scores just under the grade 6 bar. 2547 vs. 2552.

2026 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	17,811	2434.5	− 2436	−1.5	× 72 / 313	−0.3
4	17,813	2490.5	− 2485	5.5	× 79 / 313	1.4
5	17,815	2492.0	− 2528	−36	× 79 / 313	−9.1
6	17,817	2521.6	− 2552	−30.4	× 83 / 313	−8.1
Sum, rounded to a whole point						−16

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	16,819	2428.1	− 2436	−7.9	× 67 / 312	−1.7
4	16,822	2490.1	− 2485	5.1	× 77 / 312	1.3
5	16,823	2522.7	− 2528	−5.3	× 87 / 312	−1.5
6	16,825	2530.4	− 2552	−21.6	× 81 / 312	−5.6
Sum, rounded to a whole point						−8

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,142	2446.8	− 2436	10.8	× 67 / 294	2.5
4	17,144	2497.9	− 2485	12.9	× 66 / 294	2.9
5	17,146	2523.8	− 2528	−4.2	× 75 / 294	−1.1
6	17,147	2563.6	− 2552	11.6	× 86 / 294	3.4
Sum, rounded to a whole point						8

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,164	2454.8	− 2436	18.8	× 73 / 292	4.7
4	17,167	2523.7	− 2485	38.7	× 64 / 292	8.5
5	17,168	2531.4	− 2528	3.4	× 73 / 292	0.9
6	17,171	2557.0	− 2552	5	× 82 / 292	1.4
Sum, rounded to a whole point						15

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,309	2438.0	− 2436	2	× 72 / 312	0.5
4	17,310	2519.1	− 2485	34.1	× 86 / 312	9.4
5	17,311	2567.3	− 2528	39.3	× 70 / 312	8.8
6	17,312	2556.8	− 2552	4.8	× 84 / 312	1.3
Sum, rounded to a whole point						20

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,361	2415.1	− 2436	−20.9	× 85 / 316	−5.6
4	17,362	2471.5	− 2485	−13.5	× 72 / 316	−3.1
5	17,363	2510.7	− 2528	−17.3	× 75 / 316	−4.1
6	17,364	2537.8	− 2552	−14.2	× 84 / 316	−3.8
Sum, rounded to a whole point						−17

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,299	2453.2	− 2436	17.2	× 75 / 324	4
4	17,300	2469.2	− 2485	−15.8	× 87 / 324	−4.2
5	17,301	2513.7	− 2528	−14.3	× 81 / 324	−3.6
6	17,302	2545.7	− 2552	−6.3	× 81 / 324	−1.6
Sum, rounded to a whole point						−5

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,254	2428.6	− 2436	−7.4	× 73 / 325	−1.7
4	17,255	2507.4	− 2485	22.4	× 72 / 325	5
5	17,256	2498.9	− 2528	−29.1	× 89 / 325	−8
6	17,257	2531.1	− 2552	−20.9	× 91 / 325	−5.9
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	17,251	2417.1	− 2436	−18.9	× 73 / 318	−4.3
4	17,252	2487.1	− 2485	2.1	× 82 / 318	0.5
5	17,253	2526.2	− 2528	−1.8	× 75 / 318	−0.4
6	17,254	2515.3	− 2552	−36.7	× 88 / 318	−10.2
Sum, rounded to a whole point						−14

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	17,256	2433.5	− 2436	−2.5	× 62 / 288	−0.5
4	17,257	2494.5	− 2485	9.5	× 68 / 288	2.2
5	17,258	2515.6	− 2528	−12.4	× 79 / 288	−3.4
6	17,259	2546.9	− 2552	−5.1	× 79 / 288	−1.4
Sum, rounded to a whole point						−3

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −16, −8, 8, 15, 20, −17, −5, −11, −14, −3 → −3.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 8 · 2016→2017: 16 · 2017→2018: 7 · 2018→2019: 5 · 2019→2022: 37 · 2022→2023: 12 · 2023→2024: 6 · 2024→2025: 3 · 2025→2026: 11 → average 11.7
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11.7 × 2.66 = 31.1. Upper limit 28, lower limit −34.2.

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.