San Francisco: math

The shaded band is this county'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	77,544	2439.5	− 2436	3.5	× 4507 / 28209	0.6
4	77,547	2475.3	− 2485	−9.7	× 4394 / 28209	−1.5
5	77,548	2508.2	− 2528	−19.8	× 4372 / 28209	−3.1
6	77,551	2523.0	− 2552	−29	× 3782 / 28209	−3.9
7	77,552	2546.6	− 2567	−20.4	× 3743 / 28209	−2.7
8	77,555	2562.2	− 2586	−23.8	× 3727 / 28209	−3.1
11	77,556	2605.9	− 2628	−22.1	× 3684 / 28209	−2.9
Sum, rounded to a whole point						−17

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	71,830	2441.4	− 2436	5.4	× 4517 / 28561	0.9
4	71,833	2477.6	− 2485	−7.4	× 4432 / 28561	−1.1
5	71,835	2505.3	− 2528	−22.7	× 4286 / 28561	−3.4
6	71,836	2523.5	− 2552	−28.5	× 4013 / 28561	−4
7	71,838	2554.7	− 2567	−12.3	× 3823 / 28561	−1.6
8	71,840	2570.0	− 2586	−16	× 3744 / 28561	−2.1
11	71,843	2613.3	− 2628	−14.7	× 3746 / 28561	−1.9
Sum, rounded to a whole point						−13

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	73,778	2451.7	− 2436	15.7	× 4270 / 28575	2.3
4	73,779	2480.3	− 2485	−4.7	× 4362 / 28575	−0.7
5	73,781	2504.9	− 2528	−23.1	× 4363 / 28575	−3.5
6	73,784	2518.2	− 2552	−33.8	× 3973 / 28575	−4.7
7	73,786	2555.5	− 2567	−11.5	× 3993 / 28575	−1.6
8	73,787	2575.6	− 2586	−10.4	× 3805 / 28575	−1.4
11	73,790	2618.0	− 2628	−10	× 3809 / 28575	−1.3
Sum, rounded to a whole point						−11

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	73,941	2446.5	− 2436	10.5	× 4240 / 28509	1.6
4	73,942	2485.1	− 2485	0.1	× 4256 / 28509	0
5	73,945	2507.1	− 2528	−20.9	× 4346 / 28509	−3.2
6	73,946	2521.6	− 2552	−30.4	× 3924 / 28509	−4.2
7	73,949	2550.6	− 2567	−16.4	× 3957 / 28509	−2.3
8	73,950	2576.8	− 2586	−9.2	× 3971 / 28509	−1.3
11	73,953	2602.5	− 2628	−25.5	× 3815 / 28509	−3.4
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	74,474	2448.0	− 2436	12	× 4291 / 28458	1.8
4	74,475	2482.1	− 2485	−2.9	× 4254 / 28458	−0.4
5	74,476	2514.9	− 2528	−13.1	× 4256 / 28458	−2
6	74,477	2517.1	− 2552	−34.9	× 3950 / 28458	−4.8
7	74,478	2557.4	− 2567	−9.6	× 3937 / 28458	−1.3
8	74,479	2569.0	− 2586	−17	× 3936 / 28458	−2.4
11	74,480	2601.7	− 2628	−26.3	× 3834 / 28458	−3.5
Sum, rounded to a whole point						−13

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	73,005	2410.4	− 2436	−25.6	× 114 / 1176	−2.5
4	73,006	2472.8	− 2485	−12.2	× 70 / 1176	−0.7
5	73,007	2483.6	− 2528	−44.4	× 147 / 1176	−5.6
6	73,008	2479.5	− 2552	−72.5	× 232 / 1176	−14.3
7	73,009	2517.5	− 2567	−49.5	× 242 / 1176	−10.2
8	73,010	2538.7	− 2586	−47.3	× 236 / 1176	−9.5
11	73,011	2559.9	− 2628	−68.1	× 135 / 1176	−7.8
Sum, rounded to a whole point						−51

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,654	2441.5	− 2436	5.5	× 3890 / 26114	0.8
4	74,655	2469.7	− 2485	−15.3	× 3937 / 26114	−2.3
5	74,656	2498.1	− 2528	−29.9	× 4013 / 26114	−4.6
6	74,657	2502.5	− 2552	−49.5	× 3507 / 26114	−6.6
7	74,658	2527.8	− 2567	−39.2	× 3552 / 26114	−5.3
8	74,659	2543.5	− 2586	−42.5	× 3630 / 26114	−5.9
11	74,660	2588.7	− 2628	−39.3	× 3585 / 26114	−5.4
Sum, rounded to a whole point						−29

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,640	2439.2	− 2436	3.2	× 3848 / 25937	0.5
4	74,641	2479.4	− 2485	−5.6	× 3911 / 25937	−0.8
5	74,642	2498.1	− 2528	−29.9	× 3963 / 25937	−4.6
6	74,643	2500.1	− 2552	−51.9	× 3667 / 25937	−7.3
7	74,644	2535.2	− 2567	−31.8	× 3513 / 25937	−4.3
8	74,645	2538.4	− 2586	−47.6	× 3569 / 25937	−6.5
11	74,646	2590.7	− 2628	−37.3	× 3466 / 25937	−5
Sum, rounded to a whole point						−28

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,626	2434.7	− 2436	−1.3	× 3921 / 25871	−0.2
4	74,627	2475.9	− 2485	−9.1	× 3865 / 25871	−1.4
5	74,628	2504.1	− 2528	−23.9	× 3903 / 25871	−3.6
6	74,629	2503.3	− 2552	−48.7	× 3587 / 25871	−6.8
7	74,630	2529.9	− 2567	−37.1	× 3621 / 25871	−5.2
8	74,631	2543.6	− 2586	−42.4	× 3568 / 25871	−5.8
11	74,632	2576.0	− 2628	−52	× 3406 / 25871	−6.8
Sum, rounded to a whole point						−30

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,294	2432.9	− 2436	−3.1	× 3901 / 25868	−0.5
4	74,295	2475.5	− 2485	−9.5	× 3932 / 25868	−1.4
5	74,296	2501.3	− 2528	−26.7	× 3877 / 25868	−4
6	74,297	2511.4	− 2552	−40.6	× 3566 / 25868	−5.6
7	74,298	2540.1	− 2567	−26.9	× 3571 / 25868	−3.7
8	74,299	2547.7	− 2586	−38.3	× 3641 / 25868	−5.4
11	74,300	2579.6	− 2628	−48.4	× 3380 / 25868	−6.3
Sum, rounded to a whole point						−27

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	74,198	2436.6	− 2436	0.6	× 3867 / 25556	0.1
4	74,199	2473.0	− 2485	−12	× 3864 / 25556	−1.8
5	74,200	2502.5	− 2528	−25.5	× 3881 / 25556	−3.9
6	74,201	2510.9	− 2552	−41.1	× 3541 / 25556	−5.7
7	74,202	2545.8	− 2567	−21.2	× 3566 / 25556	−3
8	74,203	2554.5	− 2586	−31.5	× 3570 / 25556	−4.4
11	74,204	2577.3	− 2628	−50.7	× 3267 / 25556	−6.5
Sum, rounded to a whole point						−25

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −17, −13, −11, −13, −13, −51, −29, −28, −30, −27, −25 → −23.4
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 4 · 2016→2017: 2 · 2017→2018: 2 · 2018→2019: 0 · 2019→2021: 38 · 2021→2022: 22 · 2022→2023: 1 · 2023→2024: 2 · 2024→2025: 3 · 2025→2026: 2 → average 7.6
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 7.6 × 2.66 = 20.2. Upper limit −3.2, lower limit −43.6.

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 county, 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.