Hamilton 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.

Measured against the grade 3 bar

The state's math test uses one scale for every grade, so a score means the same thing in grade 3 as in grade 5.

3rd The average 3rd grader scores 69 points under the grade 3 bar. 2367 vs. 2436.
4th The average 4th grader scores 49 points under the grade 3 bar. 2387 vs. 2436. The 4th-grade bar is 2485.
5th The average 5th grader scores 14 points under the grade 3 bar. 2422 vs. 2436. The 5th-grade bar is 2528.

2026 results. "Meets standard" is the state's mark for being on track for that grade.

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	56,473	2373.5	− 2436	−62.5	× 47 / 278	−10.6
4	56,475	2423.4	− 2485	−61.6	× 47 / 278	−10.4
5	56,477	2446.5	− 2528	−81.5	× 51 / 278	−15
6	56,479	2472.5	− 2552	−79.5	× 40 / 278	−11.4
7	56,481	2517.7	− 2567	−49.3	× 43 / 278	−7.6
8	56,483	2495.3	− 2586	−90.7	× 50 / 278	−16.3
Sum, rounded to a whole point						−71

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	52,444	2396.9	− 2436	−39.1	× 39 / 274	−5.6
4	52,446	2434.6	− 2485	−50.4	× 43 / 274	−7.9
5	52,447	2467.2	− 2528	−60.8	× 44 / 274	−9.8
6	52,449	2484.5	− 2552	−67.5	× 54 / 274	−13.3
7	52,451	2508.3	− 2567	−58.7	× 45 / 274	−9.6
8	52,454	2541.4	− 2586	−44.6	× 49 / 274	−8
Sum, rounded to a whole point						−54

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	53,943	2379.0	− 2436	−57	× 47 / 268	−10
4	53,945	2445.3	− 2485	−39.7	× 35 / 268	−5.2
5	53,946	2445.1	− 2528	−82.9	× 43 / 268	−13.3
6	53,948	2489.0	− 2552	−63	× 44 / 268	−10.3
7	53,950	2500.3	− 2567	−66.7	× 52 / 268	−12.9
8	53,953	2504.8	− 2586	−81.2	× 47 / 268	−14.2
Sum, rounded to a whole point						−66

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,041	2403.0	− 2436	−33	× 44 / 267	−5.4
4	54,043	2423.5	− 2485	−61.5	× 48 / 267	−11.1
5	54,045	2494.6	− 2528	−33.4	× 36 / 267	−4.5
6	54,047	2442.5	− 2552	−109.5	× 43 / 267	−17.6
7	54,049	2472.6	− 2567	−94.4	× 45 / 267	−15.9
8	54,051	2484.5	− 2586	−101.5	× 51 / 267	−19.4
Sum, rounded to a whole point						−74

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,283	2386.2	− 2436	−49.8	× 53 / 270	−9.8
4	54,284	2433.9	− 2485	−51.1	× 45 / 270	−8.5
5	54,285	2454.1	− 2528	−73.9	× 48 / 270	−13.1
6	54,286	2481.1	− 2552	−70.9	× 35 / 270	−9.2
7	54,287	2475.0	− 2567	−92	× 43 / 270	−14.7
8	54,288	2488.2	− 2586	−97.8	× 46 / 270	−16.7
Sum, rounded to a whole point						−72

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,342	2364.6	− 2436	−71.4	× 42 / 128	−23.4
4	54,343	2382.5	− 2485	−102.5	× 49 / 128	−39.2
5	54,344	2452.9	− 2528	−75.1	× 37 / 128	−21.7
Sum, rounded to a whole point						−84

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,285	2375.3	− 2436	−60.7	× 53 / 158	−20.4
4	54,286	2404.6	− 2485	−80.4	× 51 / 158	−26
5	54,287	2440.2	− 2528	−87.8	× 54 / 158	−30
Sum, rounded to a whole point						−76

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	54,153	2391.9	− 2436	−44.1	× 47 / 162	−12.8
4	54,154	2421.3	− 2485	−63.7	× 53 / 162	−20.8
5	54,155	2411.6	− 2528	−116.4	× 62 / 162	−44.5
Sum, rounded to a whole point						−78

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	53,889	2376.8	− 2436	−59.2	× 66 / 170	−23
4	53,890	2405.3	− 2485	−79.7	× 50 / 170	−23.4
5	53,891	2431.1	− 2528	−96.9	× 54 / 170	−30.8
Sum, rounded to a whole point						−77

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	53,826	2366.8	− 2436	−69.2	× 56 / 180	−21.5
4	53,827	2387.2	− 2485	−97.8	× 71 / 180	−38.6
5	53,828	2422.3	− 2528	−105.7	× 53 / 180	−31.1
Sum, rounded to a whole point						−91

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −71, −54, −66, −74, −72, −84, −76, −78, −77, −91 → −74.3
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 17 · 2016→2017: 12 · 2017→2018: 8 · 2018→2019: 2 · 2019→2022: 12 · 2022→2023: 8 · 2023→2024: 2 · 2024→2025: 1 · 2025→2026: 14 → average 8.4
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 8.4 × 2.66 = 22.3. Upper limit −52, lower limit −96.6.

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.