Century Academy For Excellence: 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 3 bar

The state's math test uses one scale for every grade, so a score means the same thing in grade 3 as in grade 8.

6th The average 6th grader scores 102 points under the grade 3 bar. 2334 vs. 2436. The 6th-grade bar is 2552.
7th The average 7th grader scores 39 points under the grade 3 bar. 2397 vs. 2436. The 7th-grade bar is 2567.
8th The average 8th grader scores 19 points under the grade 3 bar. 2417 vs. 2436. The 8th-grade bar is 2586.

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
6	25,471	2414.5	− 2552	−137.5	× 94 / 249	−51.9
7	25,474	2434.0	− 2567	−133	× 71 / 249	−37.9
8	25,475	2424.0	− 2586	−162	× 84 / 249	−54.7
Sum, rounded to a whole point						−144

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	23,711	2370.9	− 2552	−181.1	× 61 / 209	−52.9
7	23,714	2438.4	− 2567	−128.6	× 84 / 209	−51.7
8	23,715	2420.9	− 2586	−165.1	× 64 / 209	−50.6
Sum, rounded to a whole point						−155

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	24,186	2420.5	− 2552	−131.5	× 56 / 212	−34.7
7	24,189	2423.4	− 2567	−143.6	× 70 / 212	−47.4
8	24,190	2457.8	− 2586	−128.2	× 86 / 212	−52
Sum, rounded to a whole point						−134

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	24,208	2398.2	− 2552	−153.8	× 58 / 201	−44.4
7	24,210	2446.8	− 2567	−120.2	× 66 / 201	−39.5
8	24,212	2433.4	− 2586	−152.6	× 77 / 201	−58.5
Sum, rounded to a whole point						−142

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	24,385	2333.9	− 2552	−218.1	× 50 / 184	−59.3
7	24,386	2396.9	− 2567	−170.1	× 63 / 184	−58.2
8	24,387	2416.7	− 2586	−169.3	× 71 / 184	−65.3
Sum, rounded to a whole point						−183

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −144, −155, −134, −142, −183 → −151.6
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 11 · 2016→2017: 21 · 2017→2018: 8 · 2018→2019: 41 → average 20.3
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 20.3 × 2.66 = 54. Upper limit −97.6, lower limit −205.6.

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.