Montague 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	89,303	2435.7	− 2436	−0.3	× 54 / 150	−0.1
4	89,305	2435.7	− 2485	−49.3	× 44 / 150	−14.5
5	89,307	2488.0	− 2528	−40	× 52 / 150	−13.9
Sum, rounded to a whole point						−28

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	82,840	2418.3	− 2436	−17.7	× 40 / 136	−5.2
4	82,841	2482.9	− 2485	−2.1	× 49 / 136	−0.8
5	82,843	2487.3	− 2528	−40.7	× 47 / 136	−14.1
Sum, rounded to a whole point						−20

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,149	2409.3	− 2436	−26.7	× 51 / 130	−10.5
4	85,152	2445.6	− 2485	−39.4	× 36 / 130	−10.9
5	85,154	2517.2	− 2528	−10.8	× 43 / 130	−3.6
Sum, rounded to a whole point						−25

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,367	2425.7	− 2436	−10.3	× 51 / 131	−4
4	85,369	2443.9	− 2485	−41.1	× 45 / 131	−14.1
5	85,371	2487.1	− 2528	−40.9	× 35 / 131	−10.9
Sum, rounded to a whole point						−29

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,963	2399.4	− 2436	−36.6	× 50 / 147	−12.4
4	85,964	2448.2	− 2485	−36.8	× 50 / 147	−12.5
5	85,965	2488.9	− 2528	−39.1	× 47 / 147	−12.5
Sum, rounded to a whole point						−37

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	86,174	2449.9	− 2436	13.9	× 48 / 145	4.6
4	86,175	2468.2	− 2485	−16.8	× 41 / 145	−4.8
5	86,176	2460.5	− 2528	−67.5	× 56 / 145	−26.1
Sum, rounded to a whole point						−26

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	86,096	2430.4	− 2436	−5.6	× 32 / 118	−1.5
4	86,097	2455.8	− 2485	−29.2	× 47 / 118	−11.6
5	86,098	2492.5	− 2528	−35.5	× 39 / 118	−11.7
Sum, rounded to a whole point						−25

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	86,082	2427.9	− 2436	−8.1	× 31 / 106	−2.4
4	86,083	2450.2	− 2485	−34.8	× 38 / 106	−12.5
5	86,084	2512.2	− 2528	−15.8	× 37 / 106	−5.5
Sum, rounded to a whole point						−20

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,770	2402.1	− 2436	−33.9	× 38 / 112	−11.5
4	85,771	2475.3	− 2485	−9.7	× 36 / 112	−3.1
5	85,772	2477.0	− 2528	−51	× 38 / 112	−17.3
Sum, rounded to a whole point						−32

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −28, −20, −25, −29, −37, −26, −25, −20, −32 → −26.9
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 8 · 2016→2017: 5 · 2017→2018: 4 · 2018→2019: 8 · 2019→2022: 11 · 2022→2023: 1 · 2023→2024: 5 · 2024→2025: 12 → average 6.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 6.8 × 2.66 = 18.1. Upper limit −8.8, lower limit −45.

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.