Capital City Independent Study: 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
5	61,412	2423.9	− 2528	−104.1	× 12 / 152	−8.2
7	61,416	2484.2	− 2567	−82.8	× 15 / 152	−8.2
8	61,418	2478.3	− 2586	−107.7	× 33 / 152	−23.4
11	61,420	2444.5	− 2628	−183.5	× 92 / 152	−111.1
Sum, rounded to a whole point						−151

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	56,975	2444.1	− 2528	−83.9	× 11 / 137	−6.7
6	56,978	2462.1	− 2552	−89.9	× 18 / 137	−11.8
7	56,979	2475.2	− 2567	−91.8	× 22 / 137	−14.7
8	56,982	2421.1	− 2586	−164.9	× 27 / 137	−32.5
11	56,983	2481.2	− 2628	−146.8	× 59 / 137	−63.2
Sum, rounded to a whole point						−129

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	58,647	2419.4	− 2528	−108.6	× 16 / 164	−10.6
6	58,649	2423.3	− 2552	−128.7	× 18 / 164	−14.1
7	58,651	2484.3	− 2567	−82.7	× 16 / 164	−8.1
8	58,653	2447.7	− 2586	−138.3	× 28 / 164	−23.6
11	58,654	2460.2	− 2628	−167.8	× 86 / 164	−88
Sum, rounded to a whole point						−144

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	58,763	2359.3	− 2528	−168.7	× 11 / 152	−12.2
6	58,766	2460.7	− 2552	−91.3	× 20 / 152	−12
7	58,767	2478.0	− 2567	−89	× 23 / 152	−13.5
8	58,770	2490.2	− 2586	−95.8	× 19 / 152	−12
11	58,771	2440.5	− 2628	−187.5	× 79 / 152	−97.5
Sum, rounded to a whole point						−147

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	59,021	2391.4	− 2552	−160.6	× 17 / 155	−17.6
7	59,022	2454.4	− 2567	−112.6	× 19 / 155	−13.8
8	59,023	2461.7	− 2586	−124.3	× 26 / 155	−20.9
11	59,024	2459.9	− 2628	−168.1	× 93 / 155	−100.9
Sum, rounded to a whole point						−153

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,101	2410.0	− 2436	−26	× 57 / 430	−3.4
4	59,102	2421.8	− 2485	−63.2	× 74 / 430	−10.9
5	59,103	2423.6	− 2528	−104.4	× 79 / 430	−19.2
6	59,104	2466.7	− 2552	−85.3	× 66 / 430	−13.1
7	59,105	2480.2	− 2567	−86.8	× 53 / 430	−10.7
8	59,106	2487.9	− 2586	−98.1	× 76 / 430	−17.3
11	59,107	2487.0	− 2628	−141	× 25 / 430	−8.2
Sum, rounded to a whole point						−83

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,059	2369.8	− 2436	−66.2	× 32 / 300	−7.1
4	59,060	2393.3	− 2485	−91.7	× 29 / 300	−8.9
5	59,061	2432.9	− 2528	−95.1	× 43 / 300	−13.6
6	59,062	2432.7	− 2552	−119.3	× 36 / 300	−14.3
7	59,063	2476.4	− 2567	−90.6	× 52 / 300	−15.7
8	59,064	2471.0	− 2586	−115	× 45 / 300	−17.3
11	59,065	2476.6	− 2628	−151.4	× 63 / 300	−31.8
Sum, rounded to a whole point						−109

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
4	58,991	2394.9	− 2485	−90.1	× 15 / 129	−10.5
6	58,993	2407.3	− 2552	−144.7	× 32 / 129	−35.9
7	58,994	2448.0	− 2567	−119	× 25 / 129	−23.1
8	58,995	2474.6	− 2586	−111.4	× 35 / 129	−30.2
11	58,996	2465.0	− 2628	−163	× 22 / 129	−27.8
Sum, rounded to a whole point						−127

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
5	58,749	2362.9	− 2528	−165.1	× 15 / 112	−22.1
6	58,750	2372.1	− 2552	−179.9	× 17 / 112	−27.3
7	58,751	2406.0	− 2567	−161	× 25 / 112	−35.9
8	58,752	2424.5	− 2586	−161.5	× 26 / 112	−37.5
11	58,753	2446.3	− 2628	−181.7	× 29 / 112	−47
Sum, rounded to a whole point						−170

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −151, −129, −144, −147, −153, −83, −109, −127, −170 → −134.8
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 22 · 2016→2017: 15 · 2017→2018: 3 · 2018→2019: 6 · 2019→2022: 70 · 2022→2023: 26 · 2023→2024: 18 · 2024→2025: 43 → average 25.4
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 25.4 × 2.66 = 67.6. Upper limit −67.2, lower limit −202.4.

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.