Hearthstone School: 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	4,265	2348.1	− 2436	−87.9	× 27 / 148	−16
4	4,266	2403.2	− 2485	−81.8	× 17 / 148	−9.4
5	4,269	2422.8	− 2528	−105.2	× 12 / 148	−8.5
6	4,270	2417.6	− 2552	−134.4	× 20 / 148	−18.2
7	4,273	2462.5	− 2567	−104.5	× 15 / 148	−10.6
8	4,274	2442.0	− 2586	−144	× 17 / 148	−16.5
11	4,277	2540.8	− 2628	−87.2	× 40 / 148	−23.6
Sum, rounded to a whole point						−103

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	3,769	2374.2	− 2436	−61.8	× 13 / 154	−5.2
4	3,771	2388.3	− 2485	−96.7	× 28 / 154	−17.6
5	3,772	2442.2	− 2528	−85.8	× 17 / 154	−9.5
6	3,774	2453.6	− 2552	−98.4	× 13 / 154	−8.3
7	3,777	2465.4	− 2567	−101.6	× 25 / 154	−16.5
8	3,779	2464.4	− 2586	−121.6	× 19 / 154	−15
11	3,781	2527.4	− 2628	−100.6	× 39 / 154	−25.5
Sum, rounded to a whole point						−98

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	3,859	2364.0	− 2436	−72	× 13 / 140	−6.7
4	3,860	2388.3	− 2485	−96.7	× 11 / 140	−7.6
5	3,862	2407.4	− 2528	−120.6	× 21 / 140	−18.1
6	3,865	2449.0	− 2552	−103	× 17 / 140	−12.5
7	3,867	2458.8	− 2567	−108.2	× 16 / 140	−12.4
8	3,869	2467.7	− 2586	−118.3	× 27 / 140	−22.8
11	3,870	2535.1	− 2628	−92.9	× 35 / 140	−23.2
Sum, rounded to a whole point						−103

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
4	3,858	2415.5	− 2485	−69.5	× 13 / 124	−7.3
5	3,861	2411.7	− 2528	−116.3	× 17 / 124	−15.9
6	3,862	2390.1	− 2552	−161.9	× 20 / 124	−26.1
7	3,865	2500.2	− 2567	−66.8	× 18 / 124	−9.7
8	3,866	2458.8	− 2586	−127.2	× 17 / 124	−17.4
11	3,869	2526.5	− 2628	−101.5	× 39 / 124	−31.9
Sum, rounded to a whole point						−108

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	3,907	2400.9	− 2552	−151.1	× 12 / 75	−24.2
7	3,908	2482.2	− 2567	−84.8	× 17 / 75	−19.2
8	3,909	2502.4	− 2586	−83.6	× 17 / 75	−18.9
11	3,910	2511.4	− 2628	−116.6	× 29 / 75	−45.1
Sum, rounded to a whole point						−107

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	3,761	2462.9	− 2552	−89.1	× 11 / 45	−21.8
8	3,763	2479.8	− 2586	−106.2	× 16 / 45	−37.8
11	3,764	2501.7	− 2628	−126.3	× 18 / 45	−50.5
Sum, rounded to a whole point						−110

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	3,806	2496.9	− 2567	−70.1	× 15 / 48	−21.9
8	3,807	2415.7	− 2586	−170.3	× 11 / 48	−39
11	3,808	2451.6	− 2628	−176.4	× 22 / 48	−80.9
Sum, rounded to a whole point						−142

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	3,789	2496.6	− 2567	−70.4	× 18 / 50	−25.3
8	3,790	2486.9	− 2586	−99.1	× 16 / 50	−31.7
11	3,791	2526.1	− 2628	−101.9	× 16 / 50	−32.6
Sum, rounded to a whole point						−90

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	3,755	2434.6	− 2552	−117.4	× 13 / 73	−20.9
7	3,756	2465.3	− 2567	−101.7	× 12 / 73	−16.7
8	3,757	2434.1	− 2586	−151.9	× 22 / 73	−45.8
11	3,758	2465.5	− 2628	−162.5	× 26 / 73	−57.9
Sum, rounded to a whole point						−141

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	3,709	2479.2	− 2552	−72.8	× 14 / 67	−15.2
7	3,710	2515.3	− 2567	−51.7	× 15 / 67	−11.6
8	3,711	2486.4	− 2586	−99.6	× 17 / 67	−25.3
11	3,712	2457.2	− 2628	−170.8	× 21 / 67	−53.5
Sum, rounded to a whole point						−106

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −103, −98, −103, −108, −107, −110, −142, −90, −141, −106 → −110.8
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: 5 · 2017→2018: 5 · 2018→2019: 1 · 2019→2021: 3 · 2021→2022: 32 · 2022→2023: 52 · 2023→2024: 51 · 2024→2025: 35 → average 21
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 21 × 2.66 = 55.9. Upper limit −54.9, lower limit −166.7.

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.