Willard Intermediate: 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
6	51,957	2425.4	− 2552	−126.6	× 281 / 839	−42.4
7	51,958	2420.4	− 2567	−146.6	× 253 / 839	−44.2
8	51,961	2445.8	− 2586	−140.2	× 305 / 839	−51
Sum, rounded to a whole point						−138

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	48,274	2419.2	− 2552	−132.8	× 260 / 813	−42.5
7	48,276	2446.8	− 2567	−120.2	× 289 / 813	−42.7
8	48,277	2439.9	− 2586	−146.1	× 264 / 813	−47.4
Sum, rounded to a whole point						−133

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	49,601	2410.9	− 2552	−141.1	× 234 / 778	−42.4
7	49,604	2434.9	− 2567	−132.1	× 256 / 778	−43.5
8	49,606	2446.9	− 2586	−139.1	× 288 / 778	−51.5
Sum, rounded to a whole point						−137

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	49,615	2399.1	− 2552	−152.9	× 223 / 727	−46.9
7	49,618	2415.5	− 2567	−151.5	× 247 / 727	−51.5
8	49,619	2421.7	− 2586	−164.3	× 257 / 727	−58.1
Sum, rounded to a whole point						−156

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	49,814	2402.8	− 2552	−149.2	× 192 / 657	−43.6
7	49,815	2424.9	− 2567	−142.1	× 222 / 657	−48
8	49,816	2418.9	− 2586	−167.1	× 243 / 657	−61.8
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
6	49,732	2409.8	− 2552	−142.2	× 123 / 419	−41.7
7	49,733	2419.3	− 2567	−147.7	× 131 / 419	−46.2
8	49,734	2429.4	− 2586	−156.6	× 165 / 419	−61.7
Sum, rounded to a whole point						−150

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	49,694	2419.1	− 2552	−132.9	× 139 / 444	−41.6
7	49,695	2426.8	− 2567	−140.2	× 138 / 444	−43.6
8	49,696	2404.4	− 2586	−181.6	× 167 / 444	−68.3
Sum, rounded to a whole point						−153

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	49,545	2415.6	− 2552	−136.4	× 128 / 428	−40.8
7	49,546	2428.0	− 2567	−139	× 146 / 428	−47.4
8	49,547	2423.0	− 2586	−163	× 154 / 428	−58.6
Sum, rounded to a whole point						−147

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	49,303	2383.4	− 2552	−168.6	× 93 / 371	−42.3
7	49,304	2424.0	− 2567	−143	× 134 / 371	−51.6
8	49,305	2426.6	− 2586	−159.4	× 144 / 371	−61.9
Sum, rounded to a whole point						−156

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −138, −133, −137, −156, −153, −150, −153, −147, −156 → −147
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 5 · 2016→2017: 4 · 2017→2018: 19 · 2018→2019: 3 · 2019→2022: 3 · 2022→2023: 3 · 2023→2024: 6 · 2024→2025: 9 → average 6.5
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 6.5 × 2.66 = 17.3. Upper limit −129.7, lower limit −164.3.

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.