Franklin Middle: 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 4 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 47 points under the grade 4 bar. 2438 vs. 2485. The 6th-grade bar is 2552.
7th The average 7th grader scores 47 points under the grade 4 bar. 2438 vs. 2485. The 7th-grade bar is 2567.
8th The average 8th grader scores 25 points under the grade 4 bar. 2460 vs. 2485. 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	93,671	2411.7	− 2552	−140.3	× 230 / 660	−48.9
7	93,672	2438.4	− 2567	−128.6	× 232 / 660	−45.2
8	93,675	2457.4	− 2586	−128.6	× 198 / 660	−38.6
Sum, rounded to a whole point						−133

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	87,048	2423.1	− 2552	−128.9	× 224 / 705	−41
7	87,049	2447.0	− 2567	−120	× 251 / 705	−42.7
8	87,051	2467.7	− 2586	−118.3	× 230 / 705	−38.6
Sum, rounded to a whole point						−122

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	89,511	2430.7	− 2552	−121.3	× 193 / 645	−36.3
7	89,512	2444.8	− 2567	−122.2	× 204 / 645	−38.6
8	89,514	2468.8	− 2586	−117.2	× 248 / 645	−45.1
Sum, rounded to a whole point						−120

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	89,721	2425.7	− 2552	−126.3	× 205 / 619	−41.8
7	89,724	2437.0	− 2567	−130	× 199 / 619	−41.8
8	89,725	2428.0	− 2586	−158	× 215 / 619	−54.9
Sum, rounded to a whole point						−139

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	90,347	2438.3	− 2552	−113.7	× 188 / 570	−37.5
7	90,348	2437.8	− 2567	−129.2	× 186 / 570	−42.2
8	90,349	2460.1	− 2586	−125.9	× 196 / 570	−43.3
Sum, rounded to a whole point						−123

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −133, −122, −120, −139, −123 → −127.4
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: 2 · 2017→2018: 19 · 2018→2019: 16 → average 12
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 12 × 2.66 = 31.9. Upper limit −95.5, lower limit −159.3.

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".

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.