Gratton 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	96,728	2477.1	− 2436	41.1	× 15 / 88	7
4	96,731	2503.9	− 2485	18.9	× 14 / 88	3
5	96,732	2541.9	− 2528	13.9	× 15 / 88	2.4
6	96,735	2539.4	− 2552	−12.6	× 15 / 88	−2.1
7	96,736	2570.0	− 2567	3	× 15 / 88	0.5
8	96,739	2569.6	− 2586	−16.4	× 14 / 88	−2.6
Sum, rounded to a whole point						8

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	89,691	2471.6	− 2436	35.6	× 13 / 89	5.2
4	89,692	2502.8	− 2485	17.8	× 16 / 89	3.2
5	89,695	2526.4	− 2528	−1.6	× 15 / 89	−0.3
6	89,696	2563.7	− 2552	11.7	× 15 / 89	2
7	89,699	2565.5	− 2567	−1.5	× 14 / 89	−0.2
8	89,700	2614.7	− 2586	28.7	× 16 / 89	5.2
Sum, rounded to a whole point						15

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	92,315	2450.1	− 2436	14.1	× 16 / 89	2.5
4	92,317	2501.1	− 2485	16.1	× 14 / 89	2.5
5	92,318	2541.3	− 2528	13.3	× 16 / 89	2.4
6	92,320	2546.3	− 2552	−5.7	× 14 / 89	−0.9
7	92,322	2548.4	− 2567	−18.6	× 14 / 89	−2.9
8	92,325	2567.9	− 2586	−18.1	× 15 / 89	−3.1
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	92,511	2511.3	− 2436	75.3	× 15 / 89	12.7
4	92,514	2503.3	− 2485	18.3	× 16 / 89	3.3
5	92,515	2527.6	− 2528	−0.4	× 16 / 89	−0.1
6	92,518	2550.4	− 2552	−1.6	× 16 / 89	−0.3
7	92,519	2538.0	− 2567	−29	× 13 / 89	−4.2
8	92,522	2597.2	− 2586	11.2	× 13 / 89	1.6
Sum, rounded to a whole point						13

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,145	2472.7	− 2436	36.7	× 19 / 93	7.5
4	93,146	2546.5	− 2485	61.5	× 14 / 93	9.3
5	93,147	2539.1	− 2528	11.1	× 15 / 93	1.8
6	93,148	2566.0	− 2552	14	× 16 / 93	2.4
7	93,149	2550.6	− 2567	−16.4	× 15 / 93	−2.6
8	93,150	2613.4	− 2586	27.4	× 14 / 93	4.1
Sum, rounded to a whole point						22

2021 from sb_ca2021_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	91,170	2425.6	− 2436	−10.4	× 15 / 94	−1.7
4	91,171	2498.1	− 2485	13.1	× 16 / 94	2.2
5	91,172	2549.7	− 2528	21.7	× 20 / 94	4.6
6	91,173	2580.6	− 2552	28.6	× 14 / 94	4.3
7	91,174	2541.4	− 2567	−25.6	× 16 / 94	−4.4
8	91,175	2639.2	− 2586	53.2	× 13 / 94	7.4
Sum, rounded to a whole point						12

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,380	2436.5	− 2436	0.5	× 16 / 94	0.1
4	93,381	2507.9	− 2485	22.9	× 16 / 94	3.9
5	93,382	2566.5	− 2528	38.5	× 15 / 94	6.1
6	93,383	2505.9	− 2552	−46.1	× 19 / 94	−9.3
7	93,384	2567.6	− 2567	0.6	× 12 / 94	0.1
8	93,385	2625.6	− 2586	39.6	× 16 / 94	6.7
Sum, rounded to a whole point						8

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,274	2442.7	− 2436	6.7	× 14 / 91	1
4	93,275	2510.4	− 2485	25.4	× 16 / 91	4.5
5	93,276	2579.4	− 2528	51.4	× 17 / 91	9.6
6	93,277	2562.0	− 2552	10	× 14 / 91	1.5
7	93,278	2554.1	− 2567	−12.9	× 17 / 91	−2.4
8	93,279	2620.1	− 2586	34.1	× 13 / 91	4.9
Sum, rounded to a whole point						19

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	93,169	2407.1	− 2436	−28.9	× 17 / 84	−5.8
4	93,170	2495.6	− 2485	10.6	× 13 / 84	1.6
5	93,171	2569.1	− 2528	41.1	× 15 / 84	7.3
6	93,172	2546.9	− 2552	−5.1	× 16 / 84	−1
7	93,173	2573.7	− 2567	6.7	× 11 / 84	0.9
8	93,174	2599.3	− 2586	13.3	× 12 / 84	1.9
Sum, rounded to a whole point						5

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	92,895	2466.9	− 2436	30.9	× 16 / 87	5.7
4	92,896	2476.8	− 2485	−8.2	× 16 / 87	−1.5
5	92,897	2585.5	− 2528	57.5	× 13 / 87	8.6
6	92,898	2572.4	− 2552	20.4	× 14 / 87	3.3
7	92,899	2606.1	− 2567	39.1	× 16 / 87	7.2
8	92,900	2581.9	− 2586	−4.1	× 12 / 87	−0.6
Sum, rounded to a whole point						23

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. 8, 15, 1, 13, 22, 12, 8, 19, 5, 23 → 12.6
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: 14 · 2017→2018: 12 · 2018→2019: 9 · 2019→2021: 10 · 2021→2022: 4 · 2022→2023: 11 · 2023→2024: 14 · 2024→2025: 18 → average 11
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11 × 2.66 = 29.3. Upper limit 41.9, lower limit −16.7.

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 — 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.

Schools in Gratton Elementary

Gratton Charter Charter