Natomas Middle: 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	63,050	2448.4	− 2552	−103.6	× 139 / 734	−19.6
7	63,052	2468.7	− 2567	−98.3	× 254 / 734	−34
8	63,054	2465.9	− 2586	−120.1	× 341 / 734	−55.8
Sum, rounded to a whole point						−109

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	58,493	2457.5	− 2552	−94.5	× 239 / 764	−29.6
7	58,496	2458.5	− 2567	−108.5	× 278 / 764	−39.5
8	58,498	2486.5	− 2586	−99.5	× 247 / 764	−32.2
Sum, rounded to a whole point						−101

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	60,195	2444.9	− 2552	−107.1	× 225 / 717	−33.6
7	60,197	2470.3	− 2567	−96.7	× 227 / 717	−30.6
8	60,199	2472.2	− 2586	−113.8	× 265 / 717	−42.1
Sum, rounded to a whole point						−106

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	60,319	2455.9	− 2552	−96.1	× 276 / 750	−35.4
7	60,322	2467.0	− 2567	−100	× 239 / 750	−31.9
8	60,323	2479.9	− 2586	−106.1	× 235 / 750	−33.2
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
6	60,574	2448.4	− 2552	−103.6	× 189 / 724	−27
7	60,575	2468.4	− 2567	−98.6	× 284 / 724	−38.7
8	60,576	2490.9	− 2586	−95.1	× 251 / 724	−33
Sum, rounded to a whole point						−99

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	60,668	2433.5	− 2552	−118.5	× 182 / 597	−36.1
7	60,669	2447.0	− 2567	−120	× 218 / 597	−43.8
8	60,670	2454.2	− 2586	−131.8	× 197 / 597	−43.5
Sum, rounded to a whole point						−123

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	60,613	2408.4	− 2552	−143.6	× 176 / 609	−41.5
7	60,614	2456.2	− 2567	−110.8	× 202 / 609	−36.8
8	60,615	2450.3	− 2586	−135.7	× 231 / 609	−51.5
Sum, rounded to a whole point						−130

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	60,560	2416.4	− 2552	−135.6	× 187 / 598	−42.4
7	60,561	2424.6	− 2567	−142.4	× 195 / 598	−46.4
8	60,562	2448.3	− 2586	−137.7	× 216 / 598	−49.7
Sum, rounded to a whole point						−139

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	60,313	2419.7	− 2552	−132.3	× 210 / 627	−44.3
7	60,314	2433.6	− 2567	−133.4	× 197 / 627	−41.9
8	60,315	2448.8	− 2586	−137.2	× 220 / 627	−48.1
Sum, rounded to a whole point						−134

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −109, −101, −106, −100, −99, −123, −130, −139, −134 → −115.7
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: 6 · 2018→2019: 1 · 2019→2022: 24 · 2022→2023: 7 · 2023→2024: 9 · 2024→2025: 5 → average 8.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 8.1 × 2.66 = 21.5. Upper limit −94.2, lower limit −137.2.

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.