Mark Twain Union Elementary: 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	5,457	2419.4	− 2436	−16.6	× 91 / 520	−2.9
4	5,460	2460.9	− 2485	−24.1	× 95 / 520	−4.4
5	5,461	2495.9	− 2528	−32.1	× 77 / 520	−4.8
6	5,464	2502.7	− 2552	−49.3	× 83 / 520	−7.9
7	5,465	2547.0	− 2567	−20	× 80 / 520	−3.1
8	5,468	2553.2	− 2586	−32.8	× 94 / 520	−5.9
Sum, rounded to a whole point						−29

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	4,925	2427.3	− 2436	−8.7	× 97 / 540	−1.6
4	4,927	2450.1	− 2485	−34.9	× 97 / 540	−6.3
5	4,928	2481.0	− 2528	−47	× 95 / 540	−8.3
6	4,931	2515.3	− 2552	−36.7	× 78 / 540	−5.3
7	4,932	2521.8	− 2567	−45.2	× 85 / 540	−7.1
8	4,935	2548.5	− 2586	−37.5	× 88 / 540	−6.1
Sum, rounded to a whole point						−35

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,018	2423.0	− 2436	−13	× 86 / 527	−2.1
4	5,020	2446.0	− 2485	−39	× 94 / 527	−7
5	5,022	2448.9	− 2528	−79.1	× 90 / 527	−13.5
6	5,024	2519.0	− 2552	−33	× 98 / 527	−6.1
7	5,026	2534.4	− 2567	−32.6	× 79 / 527	−4.9
8	5,029	2514.4	− 2586	−71.6	× 80 / 527	−10.9
Sum, rounded to a whole point						−44

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,006	2400.4	− 2436	−35.6	× 73 / 501	−5.2
4	5,009	2471.5	− 2485	−13.5	× 85 / 501	−2.3
5	5,010	2467.4	− 2528	−60.6	× 84 / 501	−10.2
6	5,013	2481.2	− 2552	−70.8	× 87 / 501	−12.3
7	5,014	2530.0	− 2567	−37	× 95 / 501	−7
8	5,017	2529.5	− 2586	−56.5	× 77 / 501	−8.7
Sum, rounded to a whole point						−46

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	5,039	2414.4	− 2436	−21.6	× 76 / 476	−3.4
4	5,040	2450.3	− 2485	−34.7	× 70 / 476	−5.1
5	5,041	2482.6	− 2528	−45.4	× 86 / 476	−8.2
6	5,042	2474.6	− 2552	−77.4	× 87 / 476	−14.1
7	5,043	2504.8	− 2567	−62.2	× 78 / 476	−10.2
8	5,044	2550.1	− 2586	−35.9	× 79 / 476	−6
Sum, rounded to a whole point						−47

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	4,880	2392.2	− 2436	−43.8	× 69 / 427	−7.1
4	4,881	2401.5	− 2485	−83.5	× 74 / 427	−14.5
5	4,882	2453.4	− 2528	−74.6	× 86 / 427	−15
6	4,883	2465.0	− 2552	−87	× 70 / 427	−14.3
7	4,884	2466.3	− 2567	−100.7	× 71 / 427	−16.7
8	4,885	2479.5	− 2586	−106.5	× 57 / 427	−14.2
Sum, rounded to a whole point						−82

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	4,864	2366.3	− 2436	−69.7	× 74 / 452	−11.4
4	4,865	2398.2	− 2485	−86.8	× 74 / 452	−14.2
5	4,866	2397.1	− 2528	−130.9	× 78 / 452	−22.6
6	4,867	2452.8	− 2552	−99.2	× 92 / 452	−20.2
7	4,868	2470.8	− 2567	−96.2	× 72 / 452	−15.3
8	4,869	2471.4	− 2586	−114.6	× 62 / 452	−15.7
Sum, rounded to a whole point						−99

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	4,819	2369.4	− 2436	−66.6	× 88 / 480	−12.2
4	4,820	2394.3	− 2485	−90.7	× 80 / 480	−15.1
5	4,821	2408.7	− 2528	−119.3	× 78 / 480	−19.4
6	4,822	2434.7	− 2552	−117.3	× 74 / 480	−18.1
7	4,823	2466.2	− 2567	−100.8	× 93 / 480	−19.5
8	4,824	2467.0	− 2586	−119	× 67 / 480	−16.6
Sum, rounded to a whole point						−101

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	4,783	2393.6	− 2436	−42.4	× 58 / 462	−5.3
4	4,784	2438.9	− 2485	−46.1	× 87 / 462	−8.7
5	4,785	2420.5	− 2528	−107.5	× 73 / 462	−17
6	4,786	2443.2	− 2552	−108.8	× 81 / 462	−19.1
7	4,787	2475.6	− 2567	−91.4	× 73 / 462	−14.4
8	4,788	2488.7	− 2586	−97.3	× 90 / 462	−19
Sum, rounded to a whole point						−83

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −29, −35, −44, −46, −47, −82, −99, −101, −83 → −62.9
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 6 · 2016→2017: 9 · 2017→2018: 2 · 2018→2019: 1 · 2019→2022: 35 · 2022→2023: 17 · 2023→2024: 2 · 2024→2025: 18 → average 11.3
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11.3 × 2.66 = 30.1. Upper limit −32.8, lower limit −93.

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.