Tibby 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	39,079	2370.6	− 2436	−65.4	× 83 / 304	−17.9
4	39,081	2422.2	− 2485	−62.8	× 68 / 304	−14
5	39,083	2438.0	− 2528	−90	× 79 / 304	−23.4
6	39,085	2509.7	− 2552	−42.3	× 74 / 304	−10.3
Sum, rounded to a whole point						−66

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	36,259	2470.6	− 2436	34.6	× 69 / 365	6.5
4	36,260	2496.7	− 2485	11.7	× 86 / 365	2.8
5	36,263	2487.3	− 2528	−40.7	× 75 / 365	−8.4
6	36,265	2489.7	− 2552	−62.3	× 68 / 365	−11.6
7	36,266	2532.6	− 2567	−34.4	× 67 / 365	−6.3
Sum, rounded to a whole point						−17

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	37,017	2430.0	− 2436	−6	× 98 / 446	−1.3
4	37,019	2440.3	− 2485	−44.7	× 73 / 446	−7.3
5	37,021	2462.1	− 2528	−65.9	× 87 / 446	−12.9
6	37,022	2504.5	− 2552	−47.5	× 67 / 446	−7.1
7	37,025	2540.6	− 2567	−26.4	× 64 / 446	−3.8
8	37,026	2537.6	− 2586	−48.4	× 57 / 446	−6.2
Sum, rounded to a whole point						−39

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	36,986	2495.4	− 2436	59.4	× 78 / 441	10.5
4	36,988	2424.7	− 2485	−60.3	× 100 / 441	−13.7
5	36,990	2492.1	− 2528	−35.9	× 67 / 441	−5.5
6	36,992	2491.2	− 2552	−60.8	× 71 / 441	−9.8
7	36,994	2472.3	− 2567	−94.7	× 64 / 441	−13.7
8	36,996	2558.8	− 2586	−27.2	× 61 / 441	−3.8
Sum, rounded to a whole point						−36

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	37,186	2523.5	− 2436	87.5	× 92 / 448	18
4	37,187	2459.1	− 2485	−25.9	× 74 / 448	−4.3
5	37,188	2456.7	− 2528	−71.3	× 93 / 448	−14.8
6	37,189	2518.1	− 2552	−33.9	× 61 / 448	−4.6
7	37,190	2471.8	− 2567	−95.2	× 66 / 448	−14
8	37,191	2463.7	− 2586	−122.3	× 62 / 448	−16.9
Sum, rounded to a whole point						−37

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	37,107	2445.1	− 2436	9.1	× 91 / 396	2.1
4	37,108	2471.2	− 2485	−13.8	× 92 / 396	−3.2
5	37,109	2441.6	− 2528	−86.4	× 62 / 396	−13.5
6	37,110	2512.6	− 2552	−39.4	× 57 / 396	−5.7
7	37,111	2536.6	− 2567	−30.4	× 46 / 396	−3.5
8	37,112	2487.3	− 2586	−98.7	× 48 / 396	−12
Sum, rounded to a whole point						−36

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	37,140	2474.9	− 2436	38.9	× 58 / 370	6.1
4	37,141	2497.8	− 2485	12.8	× 94 / 370	3.3
5	37,142	2518.5	− 2528	−9.5	× 91 / 370	−2.3
6	37,143	2486.0	− 2552	−66	× 43 / 370	−7.7
7	37,144	2518.8	− 2567	−48.2	× 48 / 370	−6.3
8	37,145	2491.9	− 2586	−94.1	× 36 / 370	−9.2
Sum, rounded to a whole point						−16

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	36,990	2470.9	− 2436	34.9	× 71 / 350	7.1
4	36,991	2501.5	− 2485	16.5	× 59 / 350	2.8
5	36,992	2533.8	− 2528	5.8	× 84 / 350	1.4
6	36,993	2541.9	− 2552	−10.1	× 60 / 350	−1.7
7	36,994	2550.2	− 2567	−16.8	× 35 / 350	−1.7
8	36,995	2584.8	− 2586	−1.2	× 41 / 350	−0.1
Sum, rounded to a whole point						8

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	36,827	2483.5	− 2436	47.5	× 74 / 332	10.6
4	36,828	2497.2	− 2485	12.2	× 61 / 332	2.2
5	36,829	2493.7	− 2528	−34.3	× 59 / 332	−6.1
6	36,830	2606.7	− 2552	54.7	× 49 / 332	8.1
7	36,831	2565.0	− 2567	−2	× 56 / 332	−0.3
8	36,832	2610.2	− 2586	24.2	× 33 / 332	2.4
Sum, rounded to a whole point						17

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −66, −17, −39, −36, −37, −36, −16, 8, 17 → −24.7
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 49 · 2016→2017: 22 · 2017→2018: 3 · 2018→2019: 1 · 2019→2022: 1 · 2022→2023: 20 · 2023→2024: 24 · 2024→2025: 9 → average 16.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 16.1 × 2.66 = 42.8. Upper limit 18.1, lower limit −67.5.

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.