Winship-Robbins: 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	98,794	2422.7	− 2436	−13.3	× 23 / 130	−2.4
4	98,797	2475.2	− 2485	−9.8	× 20 / 130	−1.5
5	98,798	2466.6	− 2528	−61.4	× 21 / 130	−9.9
6	98,801	2512.4	− 2552	−39.6	× 21 / 130	−6.4
7	98,802	2474.2	− 2567	−92.8	× 22 / 130	−15.7
8	98,805	2466.0	− 2586	−120	× 23 / 130	−21.2
Sum, rounded to a whole point						−57

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	91,566	2435.6	− 2436	−0.4	× 21 / 123	−0.1
4	91,568	2452.9	− 2485	−32.1	× 21 / 123	−5.5
5	91,571	2494.6	− 2528	−33.4	× 17 / 123	−4.6
6	91,572	2502.3	− 2552	−49.7	× 21 / 123	−8.5
7	91,575	2571.4	− 2567	4.4	× 22 / 123	0.8
8	91,576	2531.3	− 2586	−54.7	× 21 / 123	−9.3
Sum, rounded to a whole point						−27

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	94,325	2410.6	− 2436	−25.4	× 14 / 101	−3.5
4	94,327	2483.1	− 2485	−1.9	× 16 / 101	−0.3
5	94,328	2491.4	− 2528	−36.6	× 17 / 101	−6.2
6	94,330	2533.1	− 2552	−18.9	× 14 / 101	−2.6
7	94,333	2555.6	− 2567	−11.4	× 20 / 101	−2.3
8	94,335	2620.7	− 2586	34.7	× 20 / 101	6.9
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	94,535	2401.5	− 2436	−34.5	× 12 / 89	−4.7
4	94,537	2443.8	− 2485	−41.2	× 13 / 89	−6
5	94,538	2479.2	− 2528	−48.8	× 17 / 89	−9.3
6	94,540	2552.6	− 2552	0.6	× 16 / 89	0.1
7	94,543	2590.1	− 2567	23.1	× 15 / 89	3.9
8	94,544	2603.8	− 2586	17.8	× 16 / 89	3.2
Sum, rounded to a whole point						−13

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	95,178	2447.4	− 2436	11.4	× 12 / 76	1.8
5	95,180	2509.4	− 2528	−18.6	× 14 / 76	−3.4
6	95,181	2535.7	− 2552	−16.3	× 14 / 76	−3
7	95,182	2564.4	− 2567	−2.6	× 22 / 76	−0.8
8	95,183	2629.0	− 2586	43	× 14 / 76	7.9
Sum, rounded to a whole point						3

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,127	2397.5	− 2436	−38.5	× 20 / 89	−8.7
4	93,128	2452.5	− 2485	−32.5	× 11 / 89	−4
5	93,129	2420.3	− 2528	−107.7	× 14 / 89	−16.9
6	93,130	2443.4	− 2552	−108.6	× 11 / 89	−13.4
7	93,131	2520.8	− 2567	−46.2	× 17 / 89	−8.8
8	93,132	2451.6	− 2586	−134.4	× 16 / 89	−24.2
Sum, rounded to a whole point						−76

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
4	95,393	2434.4	− 2485	−50.6	× 19 / 59	−16.3
6	95,395	2446.4	− 2552	−105.6	× 14 / 59	−25.1
7	95,396	2465.5	− 2567	−101.5	× 12 / 59	−20.6
8	95,397	2539.7	− 2586	−46.3	× 14 / 59	−11
Sum, rounded to a whole point						−73

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	95,290	2419.1	− 2436	−16.9	× 14 / 45	−5.3
5	95,292	2436.0	− 2528	−92	× 20 / 45	−40.9
7	95,294	2487.5	− 2567	−79.5	× 11 / 45	−19.4
Sum, rounded to a whole point						−66

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
4	95,156	2451.9	− 2485	−33.1	× 14 / 46	−10.1
6	95,158	2487.1	− 2552	−64.9	× 21 / 46	−29.6
8	95,160	2542.4	− 2586	−43.6	× 11 / 46	−10.4
Sum, rounded to a whole point						−50

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	94,887	2439.3	− 2436	3.3	× 12 / 51	0.8
5	94,889	2485.8	− 2528	−42.2	× 14 / 51	−11.6
7	94,891	2537.8	− 2567	−29.2	× 25 / 51	−14.3
Sum, rounded to a whole point						−25

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	94,493	2419.1	− 2436	−16.9	× 11 / 60	−3.1
4	94,494	2450.9	− 2485	−34.1	× 12 / 60	−6.8
6	94,496	2521.7	− 2552	−30.3	× 14 / 60	−7.1
8	94,498	2518.3	− 2586	−67.7	× 23 / 60	−26
Sum, rounded to a whole point						−43

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −57, −27, −8, −13, 3, −76, −73, −66, −50, −25, −43 → −39.5
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 30 · 2016→2017: 19 · 2017→2018: 5 · 2018→2019: 16 · 2019→2021: 79 · 2021→2022: 3 · 2022→2023: 7 · 2023→2024: 16 · 2024→2025: 25 · 2025→2026: 18 → average 21.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 21.8 × 2.66 = 58. Upper limit 18.5, lower limit −97.5.

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.

Winship-Robbins