Carnelian 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	64,460	2440.8	− 2436	4.8	× 57 / 244	1.1
4	64,463	2451.1	− 2485	−33.9	× 57 / 244	−7.9
5	64,464	2487.7	− 2528	−40.3	× 64 / 244	−10.6
6	64,467	2513.2	− 2552	−38.8	× 66 / 244	−10.5
Sum, rounded to a whole point						−28

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	59,791	2449.5	− 2436	13.5	× 64 / 245	3.5
4	59,794	2489.8	− 2485	4.8	× 54 / 245	1.1
5	59,796	2479.7	− 2528	−48.3	× 59 / 245	−11.6
6	59,797	2506.2	− 2552	−45.8	× 68 / 245	−12.7
Sum, rounded to a whole point						−20

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	61,509	2428.1	− 2436	−7.9	× 69 / 252	−2.2
4	61,510	2465.5	− 2485	−19.5	× 64 / 252	−5
5	61,512	2504.4	− 2528	−23.6	× 55 / 252	−5.2
6	61,515	2520.5	− 2552	−31.5	× 64 / 252	−8
Sum, rounded to a whole point						−20

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	61,609	2471.3	− 2436	35.3	× 61 / 256	8.4
4	61,612	2482.0	− 2485	−3	× 74 / 256	−0.9
5	61,613	2541.3	− 2528	13.3	× 63 / 256	3.3
6	61,616	2572.8	− 2552	20.8	× 58 / 256	4.7
Sum, rounded to a whole point						16

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	61,875	2458.1	− 2436	22.1	× 60 / 262	5.1
4	61,876	2509.5	− 2485	24.5	× 65 / 262	6.1
5	61,877	2509.1	− 2528	−18.9	× 71 / 262	−5.1
6	61,878	2579.9	− 2552	27.9	× 66 / 262	7
Sum, rounded to a whole point						13

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	61,960	2461.8	− 2436	25.8	× 75 / 267	7.2
4	61,961	2509.6	− 2485	24.6	× 52 / 267	4.8
5	61,962	2518.0	− 2528	−10	× 75 / 267	−2.8
6	61,963	2524.0	− 2552	−28	× 65 / 267	−6.8
Sum, rounded to a whole point						2

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	61,908	2457.0	− 2436	21	× 67 / 273	5.2
4	61,909	2509.1	− 2485	24.1	× 76 / 273	6.7
5	61,910	2526.8	− 2528	−1.2	× 60 / 273	−0.3
6	61,911	2527.5	− 2552	−24.5	× 70 / 273	−6.3
Sum, rounded to a whole point						5

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	61,863	2452.5	− 2436	16.5	× 69 / 281	4.1
4	61,864	2483.6	− 2485	−1.4	× 71 / 281	−0.4
5	61,865	2531.8	− 2528	3.8	× 81 / 281	1.1
6	61,866	2535.1	− 2552	−16.9	× 60 / 281	−3.6
Sum, rounded to a whole point						1

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	61,628	2462.3	− 2436	26.3	× 56 / 263	5.6
4	61,629	2483.5	− 2485	−1.5	× 72 / 263	−0.4
5	61,630	2519.6	− 2528	−8.4	× 72 / 263	−2.3
6	61,631	2553.5	− 2552	1.5	× 63 / 263	0.4
Sum, rounded to a whole point						3

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −28, −20, −20, 16, 13, 2, 5, 1, 3 → −3.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 8 · 2016→2017: 0 · 2017→2018: 36 · 2018→2019: 3 · 2019→2022: 11 · 2022→2023: 3 · 2023→2024: 4 · 2024→2025: 2 → average 8.4
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 8.4 × 2.66 = 22.3. Upper limit 19.2, lower limit −25.4.

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.