Foothill 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.

7th The average 7th grader scores just under the grade 4 bar. 2480 vs. 2485. The 7th-grade bar is 2567.
8th The average 8th grader scores 16 points under the grade 4 bar. 2469 vs. 2485. The 8th-grade bar is 2586.

2023 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	20,931	2480.5	− 2552	−71.5	× 175 / 566	−22.1
7	20,934	2465.2	− 2567	−101.8	× 191 / 566	−34.4
8	20,935	2463.8	− 2586	−122.2	× 200 / 566	−43.2
Sum, rounded to a whole point						−100

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	19,874	2466.2	− 2552	−85.8	× 167 / 528	−27.1
7	19,876	2468.2	− 2567	−98.8	× 172 / 528	−32.2
8	19,879	2451.1	− 2586	−134.9	× 189 / 528	−48.3
Sum, rounded to a whole point						−108

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	20,187	2441.8	− 2552	−110.2	× 188 / 549	−37.7
7	20,188	2481.9	− 2567	−85.1	× 170 / 549	−26.4
8	20,191	2472.0	− 2586	−114	× 191 / 549	−39.7
Sum, rounded to a whole point						−104

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	20,187	2459.9	− 2552	−92.1	× 188 / 534	−32.4
7	20,189	2488.7	− 2567	−78.3	× 179 / 534	−26.2
8	20,191	2440.1	− 2586	−145.9	× 167 / 534	−45.6
Sum, rounded to a whole point						−104

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
6	20,365	2499.1	− 2552	−52.9	× 143 / 510	−14.8
7	20,366	2485.3	− 2567	−81.7	× 195 / 510	−31.2
8	20,367	2458.0	− 2586	−128	× 172 / 510	−43.2
Sum, rounded to a whole point						−89

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	20,399	2496.1	− 2567	−70.9	× 134 / 276	−34.4
8	20,400	2456.2	− 2586	−129.8	× 142 / 276	−66.8
Sum, rounded to a whole point						−101

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
7	20,370	2479.9	− 2567	−87.1	× 130 / 258	−43.9
8	20,371	2469.4	− 2586	−116.6	× 128 / 258	−57.8
Sum, rounded to a whole point						−102

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −100, −108, −104, −104, −89, −101, −102 → −101.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 8 · 2016→2017: 4 · 2017→2018: 0 · 2018→2019: 15 · 2019→2022: 12 · 2022→2023: 1 → average 6.7
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 6.7 × 2.66 = 17.8. Upper limit −83.3, lower limit −118.9.

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, 2022–23.