Harder 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	1,472	2373.7	− 2436	−62.3	× 86 / 313	−17.1
4	1,473	2419.2	− 2485	−65.8	× 72 / 313	−15.1
5	1,476	2446.4	− 2528	−81.6	× 80 / 313	−20.9
6	1,477	2500.4	− 2552	−51.6	× 75 / 313	−12.4
Sum, rounded to a whole point						−65

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	1,276	2354.3	− 2436	−81.7	× 95 / 330	−23.5
4	1,279	2412.3	− 2485	−72.7	× 89 / 330	−19.6
5	1,280	2430.3	− 2528	−97.7	× 61 / 330	−18.1
6	1,283	2499.0	− 2552	−53	× 85 / 330	−13.7
Sum, rounded to a whole point						−75

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	1,315	2342.3	− 2436	−93.7	× 92 / 350	−24.6
4	1,316	2380.9	− 2485	−104.1	× 98 / 350	−29.1
5	1,319	2423.5	− 2528	−104.5	× 89 / 350	−26.6
6	1,321	2488.1	− 2552	−63.9	× 71 / 350	−13
Sum, rounded to a whole point						−93

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	1,344	2353.6	− 2436	−82.4	× 86 / 361	−19.6
4	1,347	2397.6	− 2485	−87.4	× 90 / 361	−21.8
5	1,348	2407.9	− 2528	−120.1	× 96 / 361	−31.9
6	1,351	2472.4	− 2552	−79.6	× 89 / 361	−19.6
Sum, rounded to a whole point						−93

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	1,371	2380.6	− 2436	−55.4	× 86 / 340	−14
4	1,372	2404.8	− 2485	−80.2	× 88 / 340	−20.8
5	1,373	2399.2	− 2528	−128.8	× 83 / 340	−31.4
6	1,374	2446.9	− 2552	−105.1	× 83 / 340	−25.7
Sum, rounded to a whole point						−92

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	1,355	2343.2	− 2436	−92.8	× 57 / 328	−16.1
4	1,356	2394.1	− 2485	−90.9	× 92 / 328	−25.5
5	1,357	2431.1	− 2528	−96.9	× 90 / 328	−26.6
6	1,358	2448.3	− 2552	−103.7	× 89 / 328	−28.1
Sum, rounded to a whole point						−96

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	1,351	2350.5	− 2436	−85.5	× 87 / 388	−19.2
4	1,352	2380.9	− 2485	−104.1	× 83 / 388	−22.3
5	1,353	2413.5	− 2528	−114.5	× 115 / 388	−33.9
6	1,354	2418.6	− 2552	−133.4	× 103 / 388	−35.4
Sum, rounded to a whole point						−111

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	1,319	2336.6	− 2436	−99.4	× 70 / 375	−18.6
4	1,320	2379.6	− 2485	−105.4	× 100 / 375	−28.1
5	1,321	2406.5	− 2528	−121.5	× 80 / 375	−25.9
6	1,322	2419.6	− 2552	−132.4	× 125 / 375	−44.1
Sum, rounded to a whole point						−117

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	1,311	2359.4	− 2436	−76.6	× 98 / 361	−20.8
4	1,312	2376.1	− 2485	−108.9	× 80 / 361	−24.1
5	1,313	2400.8	− 2528	−127.2	× 101 / 361	−35.6
6	1,314	2417.1	− 2552	−134.9	× 82 / 361	−30.6
Sum, rounded to a whole point						−111

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −65, −75, −93, −93, −92, −96, −111, −117, −111 → −94.8
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 10 · 2016→2017: 18 · 2017→2018: 0 · 2018→2019: 1 · 2019→2022: 4 · 2022→2023: 15 · 2023→2024: 6 · 2024→2025: 6 → average 7.5
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 7.5 × 2.66 = 20. Upper limit −74.8, lower limit −114.8.

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.