Palo Alto Unified: 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	88,531	2501.4	− 2436	65.4	× 952 / 6215	10
4	88,533	2560.8	− 2485	75.8	× 1018 / 6215	12.4
5	88,535	2592.1	− 2528	64.1	× 1025 / 6215	10.6
6	88,537	2622.7	− 2552	70.7	× 993 / 6215	11.3
7	88,539	2646.1	− 2567	79.1	× 936 / 6215	11.9
8	88,541	2690.9	− 2586	104.9	× 940 / 6215	15.9
11	88,543	2730.4	− 2628	102.4	× 351 / 6215	5.8
Sum, rounded to a whole point						78

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	82,168	2504.3	− 2436	68.3	× 897 / 6087	10.1
4	82,169	2559.5	− 2485	74.5	× 946 / 6087	11.6
5	82,171	2598.7	− 2528	70.7	× 1036 / 6087	12
6	82,174	2631.8	− 2552	79.8	× 965 / 6087	12.7
7	82,176	2650.3	− 2567	83.3	× 999 / 6087	13.7
8	82,177	2694.2	− 2586	108.2	× 920 / 6087	16.4
11	82,179	2751.9	− 2628	123.9	× 324 / 6087	6.6
Sum, rounded to a whole point						83

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	84,455	2500.8	− 2436	64.8	× 849 / 5812	9.5
4	84,457	2548.4	− 2485	63.4	× 922 / 5812	10.1
5	84,460	2586.8	− 2528	58.8	× 963 / 5812	9.7
6	84,462	2635.5	− 2552	83.5	× 1008 / 5812	14.5
7	84,464	2655.4	− 2567	88.4	× 951 / 5812	14.5
8	84,465	2686.5	− 2586	100.5	× 960 / 5812	16.6
11	84,467	2712.8	− 2628	84.8	× 159 / 5812	2.3
Sum, rounded to a whole point						77

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	84,671	2513.5	− 2436	77.5	× 843 / 5858	11.2
4	84,673	2555.5	− 2485	70.5	× 865 / 5858	10.4
5	84,675	2587.8	− 2528	59.8	× 909 / 5858	9.3
6	84,677	2636.0	− 2552	84	× 929 / 5858	13.3
7	84,679	2657.3	− 2567	90.3	× 997 / 5858	15.4
8	84,681	2683.7	− 2586	97.7	× 974 / 5858	16.2
11	84,683	2747.8	− 2628	119.8	× 341 / 5858	7
Sum, rounded to a whole point						83

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,269	2507.0	− 2436	71	× 798 / 5877	9.6
4	85,270	2557.0	− 2485	72	× 853 / 5877	10.5
5	85,271	2589.7	− 2528	61.7	× 864 / 5877	9.1
6	85,272	2627.3	− 2552	75.3	× 873 / 5877	11.2
7	85,273	2656.9	− 2567	89.9	× 910 / 5877	13.9
8	85,274	2684.4	− 2586	98.4	× 1000 / 5877	16.7
11	85,275	2726.6	− 2628	98.6	× 579 / 5877	9.7
Sum, rounded to a whole point						81

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	83,481	2501.7	− 2436	65.7	× 688 / 4705	9.6
4	83,482	2550.2	− 2485	65.2	× 677 / 4705	9.4
5	83,483	2583.3	− 2528	55.3	× 741 / 4705	8.7
6	83,484	2622.6	− 2552	70.6	× 713 / 4705	10.7
7	83,485	2652.7	− 2567	85.7	× 739 / 4705	13.5
8	83,486	2679.8	− 2586	93.8	× 735 / 4705	14.7
11	83,487	2769.8	− 2628	141.8	× 412 / 4705	12.4
Sum, rounded to a whole point						79

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,448	2507.7	− 2436	71.7	× 695 / 5057	9.9
4	85,449	2559.2	− 2485	74.2	× 731 / 5057	10.7
5	85,450	2592.2	− 2528	64.2	× 707 / 5057	9
6	85,451	2627.3	− 2552	75.3	× 743 / 5057	11.1
7	85,452	2640.4	− 2567	73.4	× 739 / 5057	10.7
8	85,453	2665.6	− 2586	79.6	× 786 / 5057	12.4
11	85,454	2746.8	− 2628	118.8	× 656 / 5057	15.4
Sum, rounded to a whole point						79

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,387	2516.3	− 2436	80.3	× 677 / 5259	10.3
4	85,388	2563.1	− 2485	78.1	× 693 / 5259	10.3
5	85,389	2600.0	− 2528	72	× 753 / 5259	10.3
6	85,390	2633.4	− 2552	81.4	× 716 / 5259	11.1
7	85,391	2655.4	− 2567	88.4	× 767 / 5259	12.9
8	85,392	2663.1	− 2586	77.1	× 770 / 5259	11.3
11	85,393	2712.0	− 2628	84	× 883 / 5259	14.1
Sum, rounded to a whole point						80

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,376	2515.1	− 2436	79.1	× 719 / 5246	10.8
4	85,377	2565.0	− 2485	80	× 706 / 5246	10.8
5	85,378	2592.1	− 2528	64.1	× 723 / 5246	8.8
6	85,379	2632.6	− 2552	80.6	× 767 / 5246	11.8
7	85,380	2652.9	− 2567	85.9	× 746 / 5246	12.2
8	85,381	2669.9	− 2586	83.9	× 792 / 5246	12.7
11	85,382	2714.1	− 2628	86.1	× 793 / 5246	13
Sum, rounded to a whole point						80

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	85,068	2516.1	− 2436	80.1	× 718 / 5230	11
4	85,069	2565.2	− 2485	80.2	× 730 / 5230	11.2
5	85,070	2605.9	− 2528	77.9	× 708 / 5230	10.5
6	85,071	2633.5	− 2552	81.5	× 718 / 5230	11.2
7	85,072	2663.7	− 2567	96.7	× 769 / 5230	14.2
8	85,073	2676.5	− 2586	90.5	× 758 / 5230	13.1
11	85,074	2725.6	− 2628	97.6	× 829 / 5230	15.5
Sum, rounded to a whole point						87

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	84,839	2517.9	− 2436	81.9	× 664 / 5137	10.6
4	84,840	2563.2	− 2485	78.2	× 728 / 5137	11.1
5	84,841	2599.9	− 2528	71.9	× 747 / 5137	10.5
6	84,842	2638.3	− 2552	86.3	× 734 / 5137	12.3
7	84,843	2660.2	− 2567	93.2	× 728 / 5137	13.2
8	84,844	2681.6	− 2586	95.6	× 785 / 5137	14.6
11	84,845	2728.5	− 2628	100.5	× 751 / 5137	14.7
Sum, rounded to a whole point						87

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 78, 83, 77, 83, 81, 79, 79, 80, 80, 87, 87 → 81.3
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: 6 · 2017→2018: 6 · 2018→2019: 2 · 2019→2021: 2 · 2021→2022: 0 · 2022→2023: 1 · 2023→2024: 0 · 2024→2025: 7 · 2025→2026: 0 → average 2.9
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 2.9 × 2.66 = 7.7. Upper limit 89, lower limit 73.6.

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.

Palo Alto Unified