Lowell 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	88,908	2378.7	− 2436	−57.3	× 84 / 208	−23.1
4	88,910	2408.4	− 2485	−76.6	× 73 / 208	−26.9
5	88,912	2420.9	− 2528	−107.1	× 51 / 208	−26.3
Sum, rounded to a whole point						−76

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	82,509	2399.5	− 2436	−36.5	× 50 / 196	−9.3
4	82,512	2420.7	− 2485	−64.3	× 78 / 196	−25.6
5	82,514	2425.1	− 2528	−102.9	× 68 / 196	−35.7
Sum, rounded to a whole point						−71

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	84,801	2373.3	− 2436	−62.7	× 50 / 163	−19.2
4	84,804	2417.6	− 2485	−67.4	× 43 / 163	−17.8
5	84,806	2427.3	− 2528	−100.7	× 70 / 163	−43.2
Sum, rounded to a whole point						−80

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,017	2394.6	− 2436	−41.4	× 60 / 159	−15.6
4	85,019	2414.5	− 2485	−70.5	× 51 / 159	−22.6
5	85,021	2414.0	− 2528	−114	× 48 / 159	−34.4
Sum, rounded to a whole point						−73

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,611	2352.9	− 2436	−83.1	× 50 / 157	−26.5
4	85,612	2420.3	− 2485	−64.7	× 58 / 157	−23.9
5	85,613	2444.1	− 2528	−83.9	× 49 / 157	−26.2
Sum, rounded to a whole point						−77

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,837	2345.3	− 2436	−90.7	× 45 / 127	−32.1
4	83,838	2391.2	− 2485	−93.8	× 40 / 127	−29.5
5	83,839	2402.2	− 2528	−125.8	× 42 / 127	−41.6
Sum, rounded to a whole point						−103

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,806	2335.6	− 2436	−100.4	× 37 / 119	−31.2
4	85,807	2396.2	− 2485	−88.8	× 47 / 119	−35.1
5	85,808	2410.1	− 2528	−117.9	× 35 / 119	−34.7
Sum, rounded to a whole point						−101

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,724	2336.7	− 2436	−99.3	× 48 / 127	−37.5
4	85,725	2387.8	− 2485	−97.2	× 34 / 127	−26
5	85,726	2398.4	− 2528	−129.6	× 45 / 127	−45.9
Sum, rounded to a whole point						−109

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,716	2339.4	− 2436	−96.6	× 39 / 138	−27.3
4	85,717	2385.5	− 2485	−99.5	× 49 / 138	−35.3
5	85,718	2402.7	− 2528	−125.3	× 50 / 138	−45.4
Sum, rounded to a whole point						−108

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,402	2329.2	− 2436	−106.8	× 42 / 124	−36.2
4	85,403	2384.7	− 2485	−100.3	× 35 / 124	−28.3
5	85,404	2391.3	− 2528	−136.7	× 47 / 124	−51.8
Sum, rounded to a whole point						−116

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −76, −71, −80, −73, −77, −103, −101, −109, −108, −116 → −91.4
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 5 · 2016→2017: 9 · 2017→2018: 7 · 2018→2019: 4 · 2019→2021: 26 · 2021→2022: 2 · 2022→2023: 8 · 2023→2024: 1 · 2024→2025: 8 → 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 −70.7, lower limit −112.1.

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.