Arena Union Elementary: math

The shaded band is this district'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	43,144	2379.2	− 2436	−56.8	× 36 / 170	−12
4	43,145	2447.4	− 2485	−37.6	× 24 / 170	−5.3
5	43,148	2426.4	− 2528	−101.6	× 30 / 170	−17.9
6	43,149	2462.6	− 2552	−89.4	× 25 / 170	−13.1
7	43,152	2492.4	− 2567	−74.6	× 33 / 170	−14.5
8	43,153	2510.6	− 2586	−75.4	× 22 / 170	−9.8
Sum, rounded to a whole point						−73

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	39,836	2402.0	− 2436	−34	× 32 / 186	−5.8
4	39,837	2455.2	− 2485	−29.8	× 37 / 186	−5.9
5	39,839	2452.0	− 2528	−76	× 27 / 186	−11
6	39,841	2440.0	− 2552	−112	× 31 / 186	−18.7
7	39,843	2462.5	− 2567	−104.5	× 26 / 186	−14.6
8	39,846	2542.3	− 2586	−43.7	× 33 / 186	−7.8
Sum, rounded to a whole point						−64

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,858	2395.7	− 2436	−40.3	× 26 / 178	−5.9
4	40,861	2451.7	− 2485	−33.3	× 32 / 178	−6
5	40,862	2473.6	− 2528	−54.4	× 36 / 178	−11
6	40,865	2467.6	− 2552	−84.4	× 26 / 178	−12.3
7	40,867	2475.7	− 2567	−91.3	× 30 / 178	−15.4
8	40,869	2496.9	− 2586	−89.1	× 28 / 178	−14
Sum, rounded to a whole point						−65

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,875	2387.0	− 2436	−49	× 22 / 162	−6.7
4	40,877	2480.5	− 2485	−4.5	× 23 / 162	−0.6
5	40,879	2464.7	− 2528	−63.3	× 30 / 162	−11.7
6	40,881	2491.0	− 2552	−61	× 32 / 162	−12
7	40,884	2514.8	− 2567	−52.2	× 26 / 162	−8.4
8	40,886	2500.0	− 2586	−86	× 29 / 162	−15.4
Sum, rounded to a whole point						−55

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	41,028	2389.5	− 2436	−46.5	× 27 / 159	−7.9
4	41,029	2482.2	− 2485	−2.8	× 25 / 159	−0.4
5	41,030	2481.0	− 2528	−47	× 20 / 159	−5.9
6	41,031	2480.0	− 2552	−72	× 29 / 159	−13.1
7	41,032	2489.6	− 2567	−77.4	× 32 / 159	−15.6
8	41,033	2462.5	− 2586	−123.5	× 26 / 159	−20.2
Sum, rounded to a whole point						−63

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,793	2395.0	− 2436	−41	× 23 / 138	−6.8
4	40,794	2448.8	− 2485	−36.2	× 20 / 138	−5.2
5	40,795	2447.7	− 2528	−80.3	× 22 / 138	−12.8
6	40,796	2433.3	− 2552	−118.7	× 23 / 138	−19.8
7	40,797	2450.5	− 2567	−116.5	× 26 / 138	−21.9
8	40,798	2452.8	− 2586	−133.2	× 24 / 138	−23.2
Sum, rounded to a whole point						−90

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,824	2440.1	− 2436	4.1	× 19 / 131	0.6
4	40,825	2405.2	− 2485	−79.8	× 22 / 131	−13.4
5	40,826	2423.6	− 2528	−104.4	× 20 / 131	−15.9
6	40,827	2454.3	− 2552	−97.7	× 20 / 131	−14.9
7	40,828	2500.4	− 2567	−66.6	× 22 / 131	−11.2
8	40,829	2465.4	− 2586	−120.6	× 28 / 131	−25.8
Sum, rounded to a whole point						−81

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,647	2346.0	− 2436	−90	× 26 / 140	−16.7
4	40,648	2452.2	− 2485	−32.8	× 20 / 140	−4.7
5	40,649	2402.7	− 2528	−125.3	× 26 / 140	−23.3
6	40,650	2392.5	− 2552	−159.5	× 23 / 140	−26.2
7	40,651	2459.7	− 2567	−107.3	× 22 / 140	−16.9
8	40,652	2473.0	− 2586	−113	× 23 / 140	−18.6
Sum, rounded to a whole point						−106

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,432	2389.5	− 2436	−46.5	× 26 / 149	−8.1
4	40,433	2376.8	− 2485	−108.2	× 25 / 149	−18.2
5	40,434	2439.8	− 2528	−88.2	× 25 / 149	−14.8
6	40,435	2428.0	− 2552	−124	× 26 / 149	−21.6
7	40,436	2425.1	− 2567	−141.9	× 26 / 149	−24.8
8	40,437	2494.4	− 2586	−91.6	× 21 / 149	−12.9
Sum, rounded to a whole point						−100

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	40,342	2362.3	− 2436	−73.7	× 32 / 153	−15.4
4	40,343	2408.0	− 2485	−77	× 27 / 153	−13.6
5	40,344	2437.7	− 2528	−90.3	× 23 / 153	−13.6
6	40,345	2415.6	− 2552	−136.4	× 23 / 153	−20.5
7	40,346	2443.3	− 2567	−123.7	× 24 / 153	−19.4
8	40,347	2445.8	− 2586	−140.2	× 24 / 153	−22
Sum, rounded to a whole point						−104

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −73, −64, −65, −55, −63, −90, −81, −106, −100, −104 → −80.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 9 · 2016→2017: 1 · 2017→2018: 10 · 2018→2019: 8 · 2019→2022: 27 · 2022→2023: 9 · 2023→2024: 25 · 2024→2025: 6 · 2025→2026: 4 → average 11
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11 × 2.66 = 29.3. Upper limit −50.8, lower limit −109.4.

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 — for a district, the total across its schools. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.

Arena Union Elementary