California Steam San Bernardino: 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 11.

3rd The average 3rd grader scores 66 points under the grade 3 bar. 2370 vs. 2436.
4th The average 4th grader scores 58 points under the grade 3 bar. 2378 vs. 2436. The 4th-grade bar is 2485.
5th The average 5th grader scores 38 points under the grade 3 bar. 2398 vs. 2436. The 5th-grade bar is 2528.
6th The average 6th grader scores 25 points under the grade 3 bar. 2411 vs. 2436. The 6th-grade bar is 2552.
7th The average 7th grader scores 37 points under the grade 4 bar. 2448 vs. 2485. The 7th-grade bar is 2567.
8th The average 8th grader scores just under the grade 3 bar. 2430 vs. 2436. The 8th-grade bar is 2586.
11th The average 11th grader scores just under the grade 4 bar. 2483 vs. 2485. The 11th-grade bar is 2628.

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.

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	65,208	2387.4	− 2436	−48.6	× 37 / 362	−5
4	65,209	2390.5	− 2485	−94.5	× 31 / 362	−8.1
5	65,212	2425.9	− 2528	−102.1	× 33 / 362	−9.3
6	65,213	2471.1	− 2552	−80.9	× 43 / 362	−9.6
7	65,215	2482.7	− 2567	−84.3	× 54 / 362	−12.6
8	65,218	2462.2	− 2586	−123.8	× 44 / 362	−15
11	65,220	2508.5	− 2628	−119.5	× 120 / 362	−39.6
Sum, rounded to a whole point						−99

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	65,293	2345.0	− 2436	−91	× 43 / 413	−9.5
4	65,295	2400.6	− 2485	−84.4	× 54 / 413	−11
5	65,297	2387.4	− 2528	−140.6	× 49 / 413	−16.7
6	65,299	2417.3	− 2552	−134.7	× 49 / 413	−16
7	65,301	2473.4	− 2567	−93.6	× 67 / 413	−15.2
8	65,303	2440.3	− 2586	−145.7	× 62 / 413	−21.9
11	65,305	2467.6	− 2628	−160.4	× 89 / 413	−34.6
Sum, rounded to a whole point						−125

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	65,666	2369.8	− 2436	−66.2	× 92 / 865	−7
4	65,667	2378.0	− 2485	−107	× 100 / 865	−12.4
5	65,668	2398.3	− 2528	−129.7	× 115 / 865	−17.2
6	65,669	2410.7	− 2552	−141.3	× 107 / 865	−17.5
7	65,670	2448.3	− 2567	−118.7	× 155 / 865	−21.3
8	65,671	2430.0	− 2586	−156	× 146 / 865	−26.3
11	65,672	2482.8	− 2628	−145.2	× 150 / 865	−25.2
Sum, rounded to a whole point						−127

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −99, −125, −127 → −117
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2017→2018: 26 · 2018→2019: 2 → average 14
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 14 × 2.66 = 37.2. Upper limit −79.8, lower limit −154.2.

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 2016–17, 2017–18, 2018–19.