Alpine 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 17 points under the grade 3 bar. 2419 vs. 2436.
4th The average 4th grader scores 44 points under the grade 4 bar. 2441 vs. 2485.
5th The average 5th grader scores 36 points under the grade 5 bar. 2492 vs. 2528.

2019 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	70,010	2416.4	− 2436	−19.6	× 99 / 264	−7.4
4	70,013	2468.5	− 2485	−16.5	× 87 / 264	−5.4
5	70,014	2476.4	− 2528	−51.6	× 78 / 264	−15.2
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	64,900	2441.2	− 2436	5.2	× 70 / 250	1.5
4	64,902	2465.4	− 2485	−19.6	× 91 / 250	−7.1
5	64,904	2471.6	− 2528	−56.4	× 89 / 250	−20.1
Sum, rounded to a whole point						−26

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	66,716	2447.1	− 2436	11.1	× 44 / 182	2.7
4	66,717	2458.6	− 2485	−26.4	× 52 / 182	−7.5
5	66,720	2468.3	− 2528	−59.7	× 86 / 182	−28.2
Sum, rounded to a whole point						−33

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	66,803	2424.4	− 2436	−11.6	× 43 / 146	−3.4
4	66,806	2469.9	− 2485	−15.1	× 44 / 146	−4.6
5	66,807	2509.2	− 2528	−18.8	× 59 / 146	−7.6
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	67,322	2419.4	− 2436	−16.6	× 20 / 99	−3.4
4	67,323	2440.9	− 2485	−44.1	× 36 / 99	−16
5	67,324	2492.2	− 2528	−35.8	× 43 / 99	−15.5
Sum, rounded to a whole point						−35

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −28, −26, −33, −16, −35 → −27.6
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 2 · 2016→2017: 7 · 2017→2018: 17 · 2018→2019: 19 → average 11.3
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11.3 × 2.66 = 30.1. Upper limit 2.5, lower limit −57.7.

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".

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.