Howard Pence 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	75,944	2388.1	− 2436	−47.9	× 103 / 401	−12.3
4	75,947	2421.5	− 2485	−63.5	× 102 / 401	−16.2
5	75,948	2449.6	− 2528	−78.4	× 101 / 401	−19.7
6	75,951	2444.8	− 2552	−107.2	× 95 / 401	−25.4
Sum, rounded to a whole point						−74

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	70,437	2413.2	− 2436	−22.8	× 97 / 424	−5.2
4	70,439	2425.3	− 2485	−59.7	× 104 / 424	−14.6
5	70,440	2445.5	− 2528	−82.5	× 108 / 424	−21
6	70,442	2456.5	− 2552	−95.5	× 115 / 424	−25.9
Sum, rounded to a whole point						−67

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,300	2430.7	− 2436	−5.3	× 98 / 404	−1.3
4	72,302	2448.4	− 2485	−36.6	× 90 / 404	−8.2
5	72,303	2465.1	− 2528	−62.9	× 109 / 404	−17
6	72,305	2485.2	− 2552	−66.8	× 107 / 404	−17.7
Sum, rounded to a whole point						−44

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,439	2410.6	− 2436	−25.4	× 76 / 391	−4.9
4	72,441	2420.9	− 2485	−64.1	× 104 / 391	−17
5	72,443	2476.7	− 2528	−51.3	× 102 / 391	−13.4
6	72,445	2484.0	− 2552	−68	× 109 / 391	−19
Sum, rounded to a whole point						−54

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,939	2427.3	− 2436	−8.7	× 97 / 387	−2.2
4	72,940	2425.2	− 2485	−59.8	× 83 / 387	−12.8
5	72,941	2477.8	− 2528	−50.2	× 109 / 387	−14.1
6	72,942	2505.9	− 2552	−46.1	× 98 / 387	−11.7
Sum, rounded to a whole point						−41

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	71,426	2344.3	− 2436	−91.7	× 87 / 298	−26.8
4	71,427	2382.2	− 2485	−102.8	× 76 / 298	−26.2
5	71,428	2424.0	− 2528	−104	× 73 / 298	−25.5
6	71,429	2423.0	− 2552	−129	× 62 / 298	−26.8
Sum, rounded to a whole point						−105

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	73,029	2360.8	− 2436	−75.2	× 73 / 327	−16.8
4	73,030	2392.5	− 2485	−92.5	× 96 / 327	−27.2
5	73,031	2422.9	− 2528	−105.1	× 78 / 327	−25.1
6	73,032	2428.8	− 2552	−123.2	× 80 / 327	−30.1
Sum, rounded to a whole point						−99

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	73,023	2337.8	− 2436	−98.2	× 73 / 319	−22.5
4	73,024	2377.5	− 2485	−107.5	× 66 / 319	−22.2
5	73,025	2417.6	− 2528	−110.4	× 94 / 319	−32.5
6	73,026	2438.1	− 2552	−113.9	× 86 / 319	−30.7
Sum, rounded to a whole point						−108

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	73,013	2354.4	− 2436	−81.6	× 60 / 280	−17.5
4	73,014	2390.0	− 2485	−95	× 62 / 280	−21
5	73,015	2395.6	− 2528	−132.4	× 67 / 280	−31.7
6	73,016	2439.2	− 2552	−112.8	× 91 / 280	−36.7
Sum, rounded to a whole point						−107

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,709	2356.2	− 2436	−79.8	× 46 / 241	−15.2
4	72,710	2396.1	− 2485	−88.9	× 60 / 241	−22.1
5	72,711	2439.6	− 2528	−88.4	× 65 / 241	−23.8
6	72,712	2418.7	− 2552	−133.3	× 70 / 241	−38.7
Sum, rounded to a whole point						−100

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −74, −67, −44, −54, −41, −105, −99, −108, −107, −100 → −79.9
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 7 · 2016→2017: 23 · 2017→2018: 10 · 2018→2019: 13 · 2019→2021: 64 · 2021→2022: 6 · 2022→2023: 9 · 2023→2024: 1 · 2024→2025: 7 → average 15.6
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 15.6 × 2.66 = 41.5. Upper limit −38.4, lower limit −121.4.

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. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.