William Saroyan 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	12,474	2426.3	− 2436	−9.7	× 89 / 391	−2.2
4	12,476	2463.0	− 2485	−22	× 100 / 391	−5.6
5	12,478	2485.3	− 2528	−42.7	× 104 / 391	−11.4
6	12,480	2527.3	− 2552	−24.7	× 98 / 391	−6.2
Sum, rounded to a whole point						−25

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,500	2454.9	− 2436	18.9	× 100 / 395	4.8
4	11,503	2484.5	− 2485	−0.5	× 93 / 395	−0.1
5	11,505	2488.5	− 2528	−39.5	× 98 / 395	−9.8
6	11,506	2528.0	− 2552	−24	× 104 / 395	−6.3
Sum, rounded to a whole point						−11

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,833	2460.0	− 2436	24	× 102 / 385	6.4
4	11,835	2500.5	− 2485	15.5	× 92 / 385	3.7
5	11,837	2506.8	− 2528	−21.2	× 96 / 385	−5.3
6	11,839	2529.9	− 2552	−22.1	× 95 / 385	−5.5
Sum, rounded to a whole point						−1

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,869	2463.9	− 2436	27.9	× 111 / 401	7.7
4	11,870	2497.5	− 2485	12.5	× 90 / 401	2.8
5	11,873	2508.5	− 2528	−19.5	× 97 / 401	−4.7
6	11,874	2533.4	− 2552	−18.6	× 103 / 401	−4.8
Sum, rounded to a whole point						1

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,961	2443.8	− 2436	7.8	× 103 / 383	2.1
4	11,962	2475.3	− 2485	−9.7	× 110 / 383	−2.8
5	11,963	2515.1	− 2528	−12.9	× 76 / 383	−2.6
6	11,964	2537.6	− 2552	−14.4	× 94 / 383	−3.5
Sum, rounded to a whole point						−7

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,952	2429.7	− 2436	−6.3	× 98 / 393	−1.6
4	11,953	2426.9	− 2485	−58.1	× 90 / 393	−13.3
5	11,954	2481.4	− 2528	−46.6	× 101 / 393	−12
6	11,955	2505.7	− 2552	−46.3	× 104 / 393	−12.3
Sum, rounded to a whole point						−39

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,935	2420.5	− 2436	−15.5	× 102 / 389	−4.1
4	11,936	2453.6	− 2485	−31.4	× 88 / 389	−7.1
5	11,937	2472.6	− 2528	−55.4	× 96 / 389	−13.7
6	11,938	2505.1	− 2552	−46.9	× 103 / 389	−12.4
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	11,898	2445.8	− 2436	9.8	× 98 / 387	2.5
4	11,899	2439.7	− 2485	−45.3	× 100 / 387	−11.7
5	11,900	2470.2	− 2528	−57.8	× 86 / 387	−12.8
6	11,901	2481.9	− 2552	−70.1	× 103 / 387	−18.7
Sum, rounded to a whole point						−41

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,841	2451.6	− 2436	15.6	× 74 / 343	3.4
4	11,842	2451.8	− 2485	−33.2	× 93 / 343	−9
5	11,843	2451.4	− 2528	−76.6	× 91 / 343	−20.3
6	11,844	2496.2	− 2552	−55.8	× 85 / 343	−13.8
Sum, rounded to a whole point						−40

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −25, −11, −1, 1, −7, −39, −37, −41, −40 → −22.2
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 14 · 2016→2017: 10 · 2017→2018: 2 · 2018→2019: 8 · 2019→2022: 32 · 2022→2023: 2 · 2023→2024: 4 · 2024→2025: 1 → average 9.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 9.1 × 2.66 = 24.2. Upper limit 2, lower limit −46.4.

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.