Penn Valley 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	47,640	2410.7	− 2436	−25.3	× 64 / 410	−3.9
4	47,643	2435.5	− 2485	−49.5	× 68 / 410	−8.2
5	47,644	2463.9	− 2528	−64.1	× 58 / 410	−9.1
6	47,647	2494.3	− 2552	−57.7	× 63 / 410	−8.9
7	47,648	2539.5	− 2567	−27.5	× 75 / 410	−5
8	47,651	2553.0	− 2586	−33	× 82 / 410	−6.6
Sum, rounded to a whole point						−42

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	44,287	2425.3	− 2436	−10.7	× 73 / 407	−1.9
4	44,289	2471.5	− 2485	−13.5	× 64 / 407	−2.1
5	44,291	2466.6	− 2528	−61.4	× 71 / 407	−10.7
6	44,293	2507.7	− 2552	−44.3	× 52 / 407	−5.7
7	44,295	2517.1	− 2567	−49.9	× 58 / 407	−7.1
8	44,297	2572.9	− 2586	−13.1	× 75 / 407	−2.4
11	44,300	2527.3	− 2628	−100.7	× 14 / 407	−3.5
Sum, rounded to a whole point						−33

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	45,375	2444.0	− 2436	8	× 68 / 385	1.4
4	45,377	2458.2	− 2485	−26.8	× 77 / 385	−5.4
5	45,378	2492.7	− 2528	−35.3	× 57 / 385	−5.2
6	45,380	2491.8	− 2552	−60.2	× 64 / 385	−10
7	45,383	2547.1	− 2567	−19.9	× 50 / 385	−2.6
8	45,384	2531.9	− 2586	−54.1	× 57 / 385	−8
11	45,386	2485.2	− 2628	−142.8	× 12 / 385	−4.5
Sum, rounded to a whole point						−34

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	45,399	2445.0	− 2436	9	× 67 / 356	1.7
4	45,402	2488.1	− 2485	3.1	× 70 / 356	0.6
5	45,403	2492.9	− 2528	−35.1	× 62 / 356	−6.1
6	45,406	2547.5	− 2552	−4.5	× 53 / 356	−0.7
7	45,407	2544.5	− 2567	−22.5	× 58 / 356	−3.7
8	45,410	2574.6	− 2586	−11.4	× 46 / 356	−1.5
Sum, rounded to a whole point						−10

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	45,538	2431.1	− 2436	−4.9	× 49 / 349	−0.7
4	45,539	2477.7	− 2485	−7.3	× 70 / 349	−1.5
5	45,540	2509.8	− 2528	−18.2	× 64 / 349	−3.3
6	45,541	2515.0	− 2552	−37	× 61 / 349	−6.5
7	45,542	2532.2	− 2567	−34.8	× 49 / 349	−4.9
8	45,543	2541.3	− 2586	−44.7	× 56 / 349	−7.2
Sum, rounded to a whole point						−24

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	44,175	2413.0	− 2436	−23	× 44 / 308	−3.3
4	44,176	2443.9	− 2485	−41.1	× 49 / 308	−6.5
5	44,177	2478.2	− 2528	−49.8	× 53 / 308	−8.6
6	44,178	2485.2	− 2552	−66.8	× 57 / 308	−12.4
7	44,179	2532.0	− 2567	−35	× 56 / 308	−6.4
8	44,180	2531.1	− 2586	−54.9	× 49 / 308	−8.7
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	45,230	2421.6	− 2436	−14.4	× 67 / 361	−2.7
4	45,231	2458.6	− 2485	−26.4	× 47 / 361	−3.4
5	45,232	2484.9	− 2528	−43.1	× 58 / 361	−6.9
6	45,233	2497.7	− 2552	−54.3	× 63 / 361	−9.5
7	45,234	2503.4	− 2567	−63.6	× 66 / 361	−11.6
8	45,235	2512.7	− 2586	−73.3	× 60 / 361	−12.2
Sum, rounded to a whole point						−46

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	45,192	2450.4	− 2436	14.4	× 64 / 364	2.5
4	45,193	2466.5	− 2485	−18.5	× 70 / 364	−3.6
5	45,194	2487.8	− 2528	−40.2	× 51 / 364	−5.6
6	45,195	2486.0	− 2552	−66	× 59 / 364	−10.7
7	45,196	2511.6	− 2567	−55.4	× 58 / 364	−8.8
8	45,197	2502.1	− 2586	−83.9	× 62 / 364	−14.3
Sum, rounded to a whole point						−40

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	45,037	2487.5	− 2436	51.5	× 51 / 340	7.7
4	45,038	2474.0	− 2485	−11	× 55 / 340	−1.8
5	45,039	2500.2	− 2528	−27.8	× 74 / 340	−6.1
6	45,040	2477.7	− 2552	−74.3	× 42 / 340	−9.2
7	45,041	2505.6	− 2567	−61.4	× 53 / 340	−9.6
8	45,042	2500.7	− 2586	−85.3	× 65 / 340	−16.3
Sum, rounded to a whole point						−35

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	44,783	2450.4	− 2436	14.4	× 50 / 305	2.4
4	44,784	2468.8	− 2485	−16.2	× 49 / 305	−2.6
5	44,785	2477.4	− 2528	−50.6	× 52 / 305	−8.6
6	44,786	2483.9	− 2552	−68.1	× 68 / 305	−15.2
7	44,787	2535.2	− 2567	−31.8	× 43 / 305	−4.5
8	44,788	2578.6	− 2586	−7.4	× 43 / 305	−1
Sum, rounded to a whole point						−30

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	44,644	2420.2	− 2436	−15.8	× 59 / 327	−2.9
4	44,645	2432.1	− 2485	−52.9	× 49 / 327	−7.9
5	44,646	2503.1	− 2528	−24.9	× 46 / 327	−3.5
6	44,647	2480.3	− 2552	−71.7	× 54 / 327	−11.8
7	44,648	2472.5	− 2567	−94.5	× 72 / 327	−20.8
8	44,649	2475.1	− 2586	−110.9	× 47 / 327	−15.9
Sum, rounded to a whole point						−63

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −42, −33, −34, −10, −24, −46, −46, −40, −35, −30, −63 → −36.6
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: 24 · 2018→2019: 14 · 2019→2021: 22 · 2021→2022: 0 · 2022→2023: 6 · 2023→2024: 5 · 2024→2025: 5 · 2025→2026: 33 → average 11.9
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11.9 × 2.66 = 31.7. Upper limit −4.9, lower limit −68.3.

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.

Penn Valley Union Elementary