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	89,559	2482.0	− 2436	46	× 606 / 3648	7.6
4	89,562	2528.4	− 2485	43.4	× 616 / 3648	7.3
5	89,563	2558.6	− 2528	30.6	× 629 / 3648	5.3
6	89,566	2586.7	− 2552	34.7	× 625 / 3648	5.9
7	89,567	2596.5	− 2567	29.5	× 600 / 3648	4.9
8	89,570	2615.9	− 2586	29.9	× 572 / 3648	4.7
Sum, rounded to a whole point						36

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,051	2499.9	− 2436	63.9	× 686 / 3818	11.5
4	83,053	2531.2	− 2485	46.2	× 629 / 3818	7.6
5	83,056	2574.6	− 2528	46.6	× 618 / 3818	7.5
6	83,058	2588.0	− 2552	36	× 655 / 3818	6.2
7	83,059	2615.5	− 2567	48.5	× 618 / 3818	7.9
8	83,062	2640.8	− 2586	54.8	× 612 / 3818	8.8
Sum, rounded to a whole point						49

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,373	2505.1	− 2436	69.1	× 644 / 3906	11.4
4	85,376	2542.3	− 2485	57.3	× 712 / 3906	10.4
5	85,378	2580.4	− 2528	52.4	× 648 / 3906	8.7
6	85,379	2598.0	− 2552	46	× 629 / 3906	7.4
7	85,381	2616.2	− 2567	49.2	× 653 / 3906	8.2
8	85,384	2648.6	− 2586	62.6	× 620 / 3906	9.9
Sum, rounded to a whole point						56

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,594	2497.2	− 2436	61.2	× 608 / 3938	9.4
4	85,595	2540.5	− 2485	55.5	× 672 / 3938	9.5
5	85,598	2588.0	− 2528	60	× 715 / 3938	10.9
6	85,599	2601.0	− 2552	49	× 670 / 3938	8.3
7	85,602	2630.8	− 2567	63.8	× 616 / 3938	10
8	85,603	2631.5	− 2586	45.5	× 657 / 3938	7.6
Sum, rounded to a whole point						56

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	86,186	2502.1	− 2436	66.1	× 610 / 3955	10.2
4	86,187	2535.0	− 2485	50	× 626 / 3955	7.9
5	86,188	2582.6	− 2528	54.6	× 696 / 3955	9.6
6	86,189	2616.4	− 2552	64.4	× 728 / 3955	11.9
7	86,190	2632.0	− 2567	65	× 668 / 3955	11
8	86,191	2646.4	− 2586	60.4	× 627 / 3955	9.6
Sum, rounded to a whole point						60

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	86,407	2503.5	− 2436	67.5	× 618 / 3709	11.2
4	86,408	2542.2	− 2485	57.2	× 651 / 3709	10
5	86,409	2573.1	− 2528	45.1	× 595 / 3709	7.2
6	86,410	2610.8	− 2552	58.8	× 590 / 3709	9.4
7	86,411	2616.9	− 2567	49.9	× 594 / 3709	8
8	86,412	2647.1	− 2586	61.1	× 661 / 3709	10.9
Sum, rounded to a whole point						57

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	86,321	2504.3	− 2436	68.3	× 545 / 3622	10.3
4	86,322	2544.8	− 2485	59.8	× 629 / 3622	10.4
5	86,323	2583.3	− 2528	55.3	× 650 / 3622	9.9
6	86,324	2612.7	− 2552	60.7	× 618 / 3622	10.4
7	86,325	2628.2	− 2567	61.2	× 594 / 3622	10
8	86,326	2639.7	− 2586	53.7	× 586 / 3622	8.7
Sum, rounded to a whole point						60

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	86,313	2501.7	− 2436	65.7	× 596 / 3675	10.7
4	86,314	2545.2	− 2485	60.2	× 560 / 3675	9.2
5	86,315	2576.1	− 2528	48.1	× 625 / 3675	8.2
6	86,316	2619.7	− 2552	67.7	× 657 / 3675	12.1
7	86,317	2630.4	− 2567	63.4	× 628 / 3675	10.8
8	86,318	2657.1	− 2586	71.1	× 609 / 3675	11.8
Sum, rounded to a whole point						63

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	86,001	2507.1	− 2436	71.1	× 549 / 3655	10.7
4	86,002	2549.1	− 2485	64.1	× 597 / 3655	10.5
5	86,003	2579.9	− 2528	51.9	× 578 / 3655	8.2
6	86,004	2613.1	− 2552	61.1	× 646 / 3655	10.8
7	86,005	2649.3	− 2567	82.3	× 667 / 3655	15
8	86,006	2661.0	− 2586	75	× 618 / 3655	12.7
Sum, rounded to a whole point						68

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,756	2513.2	− 2436	77.2	× 523 / 3592	11.2
4	85,757	2551.6	− 2485	66.6	× 564 / 3592	10.5
5	85,758	2589.6	− 2528	61.6	× 611 / 3592	10.5
6	85,759	2624.9	− 2552	72.9	× 596 / 3592	12.1
7	85,760	2638.9	− 2567	71.9	× 641 / 3592	12.8
8	85,761	2687.1	− 2586	101.1	× 657 / 3592	18.5
Sum, rounded to a whole point						76

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 36, 49, 56, 56, 60, 57, 60, 63, 68, 76 → 58.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 13 · 2016→2017: 7 · 2017→2018: 0 · 2018→2019: 4 · 2019→2022: 3 · 2022→2023: 3 · 2023→2024: 3 · 2024→2025: 5 · 2025→2026: 8 → average 5.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 5.1 × 2.66 = 13.6. Upper limit 71.7, lower limit 44.5.

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.

Union Elementary