Columbia 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	23,205	2394.3	− 2436	−41.7	× 71 / 647	−4.6
4	23,206	2470.7	− 2485	−14.3	× 50 / 647	−1.1
5	23,209	2476.3	− 2528	−51.7	× 58 / 647	−4.6
6	23,210	2481.8	− 2552	−70.2	× 60 / 647	−6.5
7	23,213	2516.9	− 2567	−50.1	× 207 / 647	−16
8	23,214	2525.6	− 2586	−60.4	× 201 / 647	−18.8
Sum, rounded to a whole point						−52

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	21,795	2398.0	− 2436	−38	× 78 / 695	−4.3
4	21,797	2430.1	− 2485	−54.9	× 76 / 695	−6
5	21,799	2497.3	− 2528	−30.7	× 59 / 695	−2.6
6	21,801	2467.1	− 2552	−84.9	× 62 / 695	−7.6
7	21,804	2520.7	− 2567	−46.3	× 201 / 695	−13.4
8	21,806	2542.4	− 2586	−43.6	× 219 / 695	−13.7
Sum, rounded to a whole point						−48

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,213	2396.4	− 2436	−39.6	× 67 / 708	−3.7
4	22,215	2432.2	− 2485	−52.8	× 83 / 708	−6.2
5	22,216	2453.4	− 2528	−74.6	× 86 / 708	−9.1
6	22,219	2533.5	− 2552	−18.5	× 56 / 708	−1.5
7	22,220	2511.4	− 2567	−55.6	× 212 / 708	−16.6
8	22,222	2549.8	− 2586	−36.2	× 204 / 708	−10.4
Sum, rounded to a whole point						−48

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,199	2391.6	− 2436	−44.4	× 61 / 692	−3.9
4	22,202	2434.7	− 2485	−50.3	× 66 / 692	−4.8
5	22,203	2465.1	− 2528	−62.9	× 79 / 692	−7.2
6	22,206	2483.3	− 2552	−68.7	× 89 / 692	−8.8
7	22,208	2506.1	− 2567	−60.9	× 184 / 692	−16.2
8	22,210	2552.6	− 2586	−33.4	× 213 / 692	−10.3
Sum, rounded to a whole point						−51

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,380	2426.2	− 2436	−9.8	× 66 / 656	−1
4	22,381	2445.0	− 2485	−40	× 61 / 656	−3.7
5	22,382	2462.7	− 2528	−65.3	× 69 / 656	−6.9
6	22,383	2486.7	− 2552	−65.3	× 81 / 656	−8.1
7	22,384	2518.9	− 2567	−48.1	× 194 / 656	−14.2
8	22,385	2543.3	− 2586	−42.7	× 185 / 656	−12
Sum, rounded to a whole point						−46

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,347	2394.5	− 2436	−41.5	× 57 / 575	−4.1
4	22,348	2420.5	− 2485	−64.5	× 77 / 575	−8.6
5	22,349	2459.9	− 2528	−68.1	× 55 / 575	−6.5
6	22,350	2515.0	− 2552	−37	× 60 / 575	−3.9
7	22,351	2497.4	− 2567	−69.6	× 151 / 575	−18.3
8	22,352	2511.4	− 2586	−74.6	× 175 / 575	−22.7
Sum, rounded to a whole point						−64

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,322	2389.5	− 2436	−46.5	× 55 / 544	−4.7
4	22,323	2434.6	− 2485	−50.4	× 59 / 544	−5.5
5	22,324	2458.4	− 2528	−69.6	× 76 / 544	−9.7
6	22,325	2496.8	− 2552	−55.2	× 53 / 544	−5.4
7	22,326	2514.3	− 2567	−52.7	× 155 / 544	−15
8	22,327	2515.4	− 2586	−70.6	× 146 / 544	−18.9
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	22,172	2388.0	− 2436	−48	× 63 / 549	−5.5
4	22,173	2431.8	− 2485	−53.2	× 58 / 549	−5.6
5	22,174	2471.1	− 2528	−56.9	× 56 / 549	−5.8
6	22,175	2482.1	− 2552	−69.9	× 79 / 549	−10.1
7	22,176	2491.8	− 2567	−75.2	× 146 / 549	−20
8	22,177	2523.2	− 2586	−62.8	× 147 / 549	−16.8
Sum, rounded to a whole point						−64

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	22,083	2411.3	− 2436	−24.7	× 56 / 571	−2.4
4	22,084	2423.8	− 2485	−61.2	× 75 / 571	−8
5	22,085	2451.5	− 2528	−76.5	× 60 / 571	−8
6	22,086	2515.1	− 2552	−36.9	× 60 / 571	−3.9
7	22,087	2487.9	− 2567	−79.1	× 175 / 571	−24.2
8	22,088	2504.5	− 2586	−81.5	× 145 / 571	−20.7
Sum, rounded to a whole point						−67

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −52, −48, −48, −51, −46, −64, −59, −64, −67 → −55.4
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 4 · 2016→2017: 0 · 2017→2018: 3 · 2018→2019: 5 · 2019→2022: 18 · 2022→2023: 5 · 2023→2024: 5 · 2024→2025: 3 → average 5.4
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 5.4 × 2.66 = 14.4. Upper limit −41, lower limit −69.8.

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.