Lillian Larsen 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	82,069	2399.5	− 2436	−36.5	× 45 / 218	−7.5
4	82,070	2441.3	− 2485	−43.7	× 40 / 218	−8
5	82,073	2426.8	− 2528	−101.2	× 41 / 218	−19
6	82,074	2468.4	− 2552	−83.6	× 37 / 218	−14.2
7	82,077	2505.1	− 2567	−61.9	× 28 / 218	−8
8	82,078	2487.8	− 2586	−98.2	× 27 / 218	−12.2
Sum, rounded to a whole point						−69

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	76,115	2419.9	− 2436	−16.1	× 37 / 223	−2.7
4	76,116	2455.0	− 2485	−30	× 43 / 223	−5.8
5	76,119	2461.6	− 2528	−66.4	× 37 / 223	−11
6	76,121	2480.2	− 2552	−71.8	× 37 / 223	−11.9
7	76,123	2504.9	− 2567	−62.1	× 38 / 223	−10.6
8	76,124	2511.9	− 2586	−74.1	× 31 / 223	−10.3
Sum, rounded to a whole point						−52

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	78,152	2403.1	− 2436	−32.9	× 36 / 220	−5.4
4	78,153	2457.7	− 2485	−27.3	× 36 / 220	−4.5
5	78,155	2465.9	− 2528	−62.1	× 39 / 220	−11
6	78,157	2454.3	− 2552	−97.7	× 40 / 220	−17.8
7	78,159	2517.0	− 2567	−50	× 35 / 220	−8
8	78,161	2543.5	− 2586	−42.5	× 34 / 220	−6.6
Sum, rounded to a whole point						−53

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	78,307	2428.4	− 2436	−7.6	× 34 / 230	−1.1
4	78,308	2442.0	− 2485	−43	× 42 / 230	−7.9
5	78,311	2435.8	− 2528	−92.2	× 38 / 230	−15.2
6	78,312	2408.8	− 2552	−143.2	× 37 / 230	−23
7	78,315	2519.9	− 2567	−47.1	× 42 / 230	−8.6
8	78,316	2544.8	− 2586	−41.2	× 37 / 230	−6.6
Sum, rounded to a whole point						−62

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	78,839	2400.5	− 2436	−35.5	× 40 / 239	−5.9
4	78,840	2468.3	− 2485	−16.7	× 37 / 239	−2.6
5	78,841	2462.1	− 2528	−65.9	× 38 / 239	−10.5
6	78,842	2437.7	− 2552	−114.3	× 47 / 239	−22.5
7	78,843	2522.7	− 2567	−44.3	× 38 / 239	−7
8	78,844	2534.8	− 2586	−51.2	× 39 / 239	−8.4
Sum, rounded to a whole point						−57

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	79,093	2399.3	− 2436	−36.7	× 52 / 260	−7.3
4	79,094	2463.6	− 2485	−21.4	× 47 / 260	−3.9
5	79,095	2453.3	− 2528	−74.7	× 45 / 260	−12.9
6	79,096	2441.8	− 2552	−110.2	× 46 / 260	−19.5
7	79,097	2471.7	− 2567	−95.3	× 35 / 260	−12.8
8	79,098	2488.3	− 2586	−97.7	× 35 / 260	−13.2
Sum, rounded to a whole point						−70

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	79,075	2430.9	− 2436	−5.1	× 39 / 262	−0.8
4	79,076	2424.6	− 2485	−60.4	× 54 / 262	−12.4
5	79,077	2451.9	− 2528	−76.1	× 46 / 262	−13.4
6	79,078	2474.9	− 2552	−77.1	× 46 / 262	−13.5
7	79,079	2490.0	− 2567	−77	× 44 / 262	−12.9
8	79,080	2496.7	− 2586	−89.3	× 33 / 262	−11.2
Sum, rounded to a whole point						−64

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	79,101	2412.7	− 2436	−23.3	× 40 / 266	−3.5
4	79,102	2481.9	− 2485	−3.1	× 40 / 266	−0.5
5	79,103	2437.4	− 2528	−90.6	× 48 / 266	−16.3
6	79,104	2459.3	− 2552	−92.7	× 44 / 266	−15.3
7	79,105	2495.6	− 2567	−71.4	× 45 / 266	−12.1
8	79,106	2493.8	− 2586	−92.2	× 49 / 266	−17
Sum, rounded to a whole point						−65

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	78,779	2416.1	− 2436	−19.9	× 35 / 257	−2.7
4	78,780	2463.6	− 2485	−21.4	× 39 / 257	−3.2
5	78,781	2482.4	− 2528	−45.6	× 45 / 257	−8
6	78,782	2452.5	− 2552	−99.5	× 54 / 257	−20.9
7	78,783	2494.0	− 2567	−73	× 42 / 257	−11.9
8	78,784	2539.5	− 2586	−46.5	× 42 / 257	−7.6
Sum, rounded to a whole point						−54

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −69, −52, −53, −62, −57, −70, −64, −65, −54 → −60.7
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: 1 · 2017→2018: 9 · 2018→2019: 5 · 2019→2022: 13 · 2022→2023: 6 · 2023→2024: 1 · 2024→2025: 11 → average 7.9
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 7.9 × 2.66 = 21. Upper limit −39.7, lower limit −81.7.

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.