Charles Hoffman 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	67,537	2396.5	− 2436	−39.5	× 60 / 160	−14.8
4	67,538	2429.5	− 2485	−55.5	× 59 / 160	−20.5
5	67,541	2444.1	− 2528	−83.9	× 41 / 160	−21.5
Sum, rounded to a whole point						−57

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	62,591	2415.0	− 2436	−21	× 56 / 177	−6.6
4	62,594	2430.2	− 2485	−54.8	× 63 / 177	−19.5
5	62,595	2451.0	− 2528	−77	× 58 / 177	−25.2
Sum, rounded to a whole point						−51

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	64,387	2390.7	− 2436	−45.3	× 43 / 155	−12.6
4	64,390	2450.1	− 2485	−34.9	× 56 / 155	−12.6
5	64,391	2457.4	− 2528	−70.6	× 56 / 155	−25.5
Sum, rounded to a whole point						−51

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	64,497	2426.5	− 2436	−9.5	× 44 / 152	−2.8
4	64,498	2447.2	− 2485	−37.8	× 47 / 152	−11.7
5	64,501	2478.9	− 2528	−49.1	× 61 / 152	−19.7
Sum, rounded to a whole point						−34

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	64,862	2386.9	− 2436	−49.1	× 49 / 137	−17.6
4	64,863	2474.1	− 2485	−10.9	× 42 / 137	−3.3
5	64,864	2470.1	− 2528	−57.9	× 46 / 137	−19.4
Sum, rounded to a whole point						−40

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	64,949	2401.0	− 2436	−35	× 48 / 143	−11.7
4	64,950	2453.1	− 2485	−31.9	× 43 / 143	−9.6
5	64,951	2487.3	− 2528	−40.7	× 52 / 143	−14.8
Sum, rounded to a whole point						−36

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	64,944	2378.7	− 2436	−57.3	× 44 / 142	−17.8
4	64,945	2427.8	− 2485	−57.2	× 50 / 142	−20.1
5	64,946	2465.5	− 2528	−62.5	× 48 / 142	−21.1
Sum, rounded to a whole point						−59

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	64,910	2440.8	− 2436	4.8	× 46 / 139	1.6
4	64,911	2460.5	− 2485	−24.5	× 42 / 139	−7.4
5	64,912	2480.9	− 2528	−47.1	× 51 / 139	−17.3
Sum, rounded to a whole point						−23

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	64,668	2435.2	− 2436	−0.8	× 38 / 128	−0.2
4	64,669	2487.5	− 2485	2.5	× 46 / 128	0.9
5	64,670	2500.0	− 2528	−28	× 44 / 128	−9.6
Sum, rounded to a whole point						−9

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −57, −51, −51, −34, −40, −36, −59, −23, −9 → −40
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 6 · 2016→2017: 0 · 2017→2018: 17 · 2018→2019: 6 · 2019→2022: 4 · 2022→2023: 23 · 2023→2024: 36 · 2024→2025: 14 → average 13.3
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 13.3 × 2.66 = 35.4. Upper limit −4.6, lower limit −75.4.

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.