Carlton Hills 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	75,549	2460.7	− 2436	24.7	× 46 / 316	3.6
4	75,551	2476.0	− 2485	−9	× 42 / 316	−1.2
5	75,553	2497.5	− 2528	−30.5	× 44 / 316	−4.2
6	75,555	2499.5	− 2552	−52.5	× 41 / 316	−6.8
7	75,557	2581.1	− 2567	14.1	× 81 / 316	3.6
8	75,559	2637.8	− 2586	51.8	× 62 / 316	10.2
Sum, rounded to a whole point						5

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	70,067	2416.9	− 2436	−19.1	× 48 / 305	−3
4	70,068	2487.1	− 2485	2.1	× 46 / 305	0.3
5	70,071	2519.6	− 2528	−8.4	× 44 / 305	−1.2
6	70,072	2505.1	− 2552	−46.9	× 46 / 305	−7.1
7	70,074	2573.1	− 2567	6.1	× 53 / 305	1.1
8	70,077	2647.5	− 2586	61.5	× 68 / 305	13.7
Sum, rounded to a whole point						4

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	71,920	2442.7	− 2436	6.7	× 58 / 309	1.3
4	71,921	2456.0	− 2485	−29	× 44 / 309	−4.1
5	71,924	2522.3	− 2528	−5.7	× 47 / 309	−0.9
6	71,925	2521.9	− 2552	−30.1	× 42 / 309	−4.1
7	71,928	2579.4	− 2567	12.4	× 65 / 309	2.6
8	71,930	2621.3	− 2586	35.3	× 53 / 309	6.1
Sum, rounded to a whole point						1

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,060	2470.4	− 2436	34.4	× 72 / 350	7.1
4	72,062	2496.5	− 2485	11.5	× 60 / 350	2
5	72,064	2486.6	− 2528	−41.4	× 48 / 350	−5.7
6	72,066	2525.1	− 2552	−26.9	× 48 / 350	−3.7
7	72,068	2582.4	− 2567	15.4	× 59 / 350	2.6
8	72,070	2622.8	− 2586	36.8	× 63 / 350	6.6
Sum, rounded to a whole point						9

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,553	2454.2	− 2436	18.2	× 67 / 374	3.3
4	72,554	2514.6	− 2485	29.6	× 75 / 374	5.9
5	72,555	2509.8	− 2528	−18.2	× 57 / 374	−2.8
6	72,556	2511.5	− 2552	−40.5	× 54 / 374	−5.8
7	72,557	2579.7	− 2567	12.7	× 64 / 374	2.2
8	72,558	2623.3	− 2586	37.3	× 57 / 374	5.7
Sum, rounded to a whole point						8

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	71,036	2457.3	− 2436	21.3	× 56 / 417	2.9
4	71,037	2475.0	− 2485	−10	× 76 / 417	−1.8
5	71,038	2502.5	− 2528	−25.5	× 78 / 417	−4.8
6	71,039	2535.8	− 2552	−16.2	× 87 / 417	−3.4
7	71,040	2558.1	− 2567	−8.9	× 52 / 417	−1.1
8	71,041	2579.6	− 2586	−6.4	× 68 / 417	−1
Sum, rounded to a whole point						−9

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,631	2462.2	− 2436	26.2	× 53 / 369	3.8
4	72,632	2457.8	− 2485	−27.2	× 59 / 369	−4.3
5	72,633	2503.9	− 2528	−24.1	× 56 / 369	−3.7
6	72,634	2525.3	− 2552	−26.7	× 60 / 369	−4.3
7	72,635	2548.1	− 2567	−18.9	× 73 / 369	−3.7
8	72,636	2601.3	− 2586	15.3	× 68 / 369	2.8
Sum, rounded to a whole point						−10

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,629	2447.5	− 2436	11.5	× 47 / 350	1.5
4	72,630	2485.4	− 2485	0.4	× 57 / 350	0.1
5	72,631	2486.3	− 2528	−41.7	× 57 / 350	−6.8
6	72,632	2492.1	− 2552	−59.9	× 53 / 350	−9.1
7	72,633	2575.6	− 2567	8.6	× 63 / 350	1.5
8	72,634	2628.1	− 2586	42.1	× 73 / 350	8.8
Sum, rounded to a whole point						−4

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,611	2471.3	− 2436	35.3	× 56 / 341	5.8
4	72,612	2497.0	− 2485	12	× 51 / 341	1.8
5	72,613	2505.4	− 2528	−22.6	× 55 / 341	−3.6
6	72,614	2539.0	− 2552	−13	× 56 / 341	−2.1
7	72,615	2571.6	− 2567	4.6	× 58 / 341	0.8
8	72,616	2629.0	− 2586	43	× 65 / 341	8.2
Sum, rounded to a whole point						11

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	72,325	2468.8	− 2436	32.8	× 47 / 363	4.2
4	72,326	2515.0	− 2485	30	× 56 / 363	4.6
5	72,327	2519.6	− 2528	−8.4	× 50 / 363	−1.2
6	72,328	2540.5	− 2552	−11.5	× 61 / 363	−1.9
7	72,329	2570.6	− 2567	3.6	× 87 / 363	0.9
8	72,330	2631.7	− 2586	45.7	× 62 / 363	7.8
Sum, rounded to a whole point						14

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 5, 4, 1, 9, 8, −9, −10, −4, 11, 14 → 2.9
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 1 · 2016→2017: 3 · 2017→2018: 8 · 2018→2019: 1 · 2019→2021: 17 · 2021→2022: 1 · 2022→2023: 6 · 2023→2024: 15 · 2024→2025: 3 → average 6.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 6.1 × 2.66 = 16.2. Upper limit 19.1, lower limit −13.3.

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