Warren Lane 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	24,644	2356.4	− 2436	−79.6	× 56 / 202	−22.1
4	24,645	2393.8	− 2485	−91.2	× 51 / 202	−23
5	24,648	2389.8	− 2528	−138.2	× 48 / 202	−32.8
6	24,650	2478.8	− 2552	−73.2	× 47 / 202	−17
Sum, rounded to a whole point						−95

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	23,002	2353.6	− 2436	−82.4	× 43 / 178	−19.9
4	23,003	2361.7	− 2485	−123.3	× 47 / 178	−32.6
5	23,005	2402.5	− 2528	−125.5	× 51 / 178	−36
6	23,008	2448.0	− 2552	−104	× 37 / 178	−21.6
Sum, rounded to a whole point						−110

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	23,452	2339.5	− 2436	−96.5	× 35 / 154	−21.9
4	23,455	2374.8	− 2485	−110.2	× 39 / 154	−27.9
5	23,456	2359.9	− 2528	−168.1	× 28 / 154	−30.6
6	23,458	2396.6	− 2552	−155.4	× 52 / 154	−52.5
Sum, rounded to a whole point						−133

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	23,461	2365.2	− 2436	−70.8	× 37 / 131	−20
4	23,463	2416.0	− 2485	−69	× 34 / 131	−17.9
5	23,465	2402.2	− 2528	−125.8	× 40 / 131	−38.4
6	23,467	2395.7	− 2552	−156.3	× 20 / 131	−23.9
Sum, rounded to a whole point						−100

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	23,636	2328.7	− 2436	−107.3	× 20 / 105	−20.4
4	23,637	2408.1	− 2485	−76.9	× 33 / 105	−24.2
5	23,638	2401.3	− 2528	−126.7	× 23 / 105	−27.8
6	23,639	2447.9	− 2552	−104.1	× 29 / 105	−28.8
Sum, rounded to a whole point						−101

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	23,033	2337.0	− 2436	−99	× 23 / 79	−28.8
4	23,034	2344.6	− 2485	−140.4	× 18 / 79	−32
5	23,035	2340.4	− 2528	−187.6	× 20 / 79	−47.5
6	23,036	2385.5	− 2552	−166.5	× 18 / 79	−37.9
Sum, rounded to a whole point						−146

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	23,571	2322.0	− 2436	−114	× 13 / 63	−23.5
4	23,572	2383.3	− 2485	−101.7	× 20 / 63	−32.3
5	23,573	2382.6	− 2528	−145.4	× 17 / 63	−39.2
6	23,574	2352.2	− 2552	−199.8	× 13 / 63	−41.2
Sum, rounded to a whole point						−136

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −95, −110, −133, −100, −101, −146, −136 → −117.3
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 15 · 2016→2017: 23 · 2017→2018: 33 · 2018→2019: 1 · 2019→2021: 45 · 2021→2022: 10 → average 21.2
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 21.2 × 2.66 = 56.4. Upper limit −60.9, lower limit −173.7.

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.