John Muir 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.

Measured against the grade bars

The state's math test uses one scale for every grade, so a score means the same thing in grade 3 as in grade 5.

3rd The average 3rd grader scores 13 points under the grade 3 bar. 2423 vs. 2436.
4th The average 4th grader scores 46 points under the grade 4 bar. 2439 vs. 2485.
5th The average 5th grader scores 14 points under the grade 5 bar. 2514 vs. 2528.

2022 results. "Meets standard" is the state's mark for being on track for that grade.

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	37,175	2404.7	− 2436	−31.3	× 51 / 130	−12.3
4	37,177	2445.4	− 2485	−39.6	× 23 / 130	−7
5	37,179	2497.6	− 2528	−30.4	× 56 / 130	−13.1
Sum, rounded to a whole point						−32

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	34,615	2403.9	− 2436	−32.1	× 47 / 116	−13
4	34,617	2490.0	− 2485	5	× 44 / 116	1.9
5	34,619	2496.7	− 2528	−31.3	× 25 / 116	−6.7
Sum, rounded to a whole point						−18

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	35,253	2415.5	− 2436	−20.5	× 46 / 137	−6.9
4	35,254	2441.6	− 2485	−43.4	× 42 / 137	−13.3
5	35,256	2521.1	− 2528	−6.9	× 49 / 137	−2.5
Sum, rounded to a whole point						−23

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	35,264	2413.0	− 2436	−23	× 40 / 125	−7.4
4	35,266	2448.2	− 2485	−36.8	× 42 / 125	−12.4
5	35,268	2470.8	− 2528	−57.2	× 43 / 125	−19.7
Sum, rounded to a whole point						−39

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	35,433	2443.3	− 2436	7.3	× 39 / 120	2.4
4	35,434	2467.9	− 2485	−17.1	× 41 / 120	−5.8
5	35,435	2493.3	− 2528	−34.7	× 40 / 120	−11.6
Sum, rounded to a whole point						−15

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	35,320	2423.0	− 2436	−13	× 40 / 115	−4.5
4	35,321	2438.8	− 2485	−46.2	× 28 / 115	−11.2
5	35,322	2514.2	− 2528	−13.8	× 47 / 115	−5.6
Sum, rounded to a whole point						−21

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −32, −18, −23, −39, −15, −21 → −24.7
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 14 · 2016→2017: 5 · 2017→2018: 16 · 2018→2019: 24 · 2019→2022: 6 → average 13
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 13 × 2.66 = 34.6. Upper limit 9.9, lower limit −59.3.

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.