Norman Liddell 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	12,494	2411.8	− 2436	−24.2	× 83 / 356	−5.6
4	12,496	2475.1	− 2485	−9.9	× 82 / 356	−2.3
5	12,498	2484.9	− 2528	−43.1	× 94 / 356	−11.4
6	12,500	2495.7	− 2552	−56.3	× 97 / 356	−15.3
Sum, rounded to a whole point						−35

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,520	2403.6	− 2436	−32.4	× 83 / 360	−7.5
4	11,523	2464.1	− 2485	−20.9	× 85 / 360	−4.9
5	11,525	2490.5	− 2528	−37.5	× 95 / 360	−9.9
6	11,527	2531.5	− 2552	−20.5	× 97 / 360	−5.5
Sum, rounded to a whole point						−28

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,852	2432.4	− 2436	−3.6	× 98 / 361	−1
4	11,855	2502.2	− 2485	17.2	× 81 / 361	3.9
5	11,856	2485.5	− 2528	−42.5	× 87 / 361	−10.2
6	11,859	2535.0	− 2552	−17	× 95 / 361	−4.5
Sum, rounded to a whole point						−12

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,888	2457.4	− 2436	21.4	× 106 / 372	6.1
4	11,890	2489.9	− 2485	4.9	× 100 / 372	1.3
5	11,892	2503.5	− 2528	−24.5	× 81 / 372	−5.3
6	11,894	2514.7	− 2552	−37.3	× 85 / 372	−8.5
Sum, rounded to a whole point						−6

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,981	2452.2	− 2436	16.2	× 104 / 384	4.4
4	11,982	2499.8	− 2485	14.8	× 99 / 384	3.8
5	11,983	2489.5	− 2528	−38.5	× 100 / 384	−10
6	11,984	2530.6	− 2552	−21.4	× 81 / 384	−4.5
Sum, rounded to a whole point						−6

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,972	2433.4	− 2436	−2.6	× 85 / 373	−0.6
4	11,973	2488.5	− 2485	3.5	× 92 / 373	0.9
5	11,974	2504.3	− 2528	−23.7	× 95 / 373	−6
6	11,975	2515.9	− 2552	−36.1	× 101 / 373	−9.8
Sum, rounded to a whole point						−16

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,955	2424.2	− 2436	−11.8	× 88 / 350	−3
4	11,956	2506.7	− 2485	21.7	× 79 / 350	4.9
5	11,957	2500.7	− 2528	−27.3	× 94 / 350	−7.3
6	11,958	2542.9	− 2552	−9.1	× 89 / 350	−2.3
Sum, rounded to a whole point						−8

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,918	2454.5	− 2436	18.5	× 70 / 334	3.9
4	11,919	2501.4	− 2485	16.4	× 90 / 334	4.4
5	11,920	2521.6	− 2528	−6.4	× 79 / 334	−1.5
6	11,921	2537.8	− 2552	−14.2	× 95 / 334	−4
Sum, rounded to a whole point						3

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	11,861	2439.4	− 2436	3.4	× 83 / 336	0.8
4	11,862	2512.9	− 2485	27.9	× 78 / 336	6.5
5	11,863	2510.3	− 2528	−17.7	× 91 / 336	−4.8
6	11,864	2538.7	− 2552	−13.3	× 84 / 336	−3.3
Sum, rounded to a whole point						−1

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −35, −28, −12, −6, −6, −16, −8, 3, −1 → −12.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 7 · 2016→2017: 16 · 2017→2018: 6 · 2018→2019: 0 · 2019→2022: 10 · 2022→2023: 8 · 2023→2024: 11 · 2024→2025: 4 → average 7.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 7.8 × 2.66 = 20.7. Upper limit 8.6, lower limit −32.8.

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.