Naranca 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.

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	70,291	2382.1	− 2436	−53.9	× 152 / 417	−19.6
4	70,293	2440.1	− 2485	−44.9	× 129 / 417	−13.9
5	70,294	2469.0	− 2528	−59	× 136 / 417	−19.2
Sum, rounded to a whole point						−53

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	65,167	2395.0	− 2436	−41	× 135 / 436	−12.7
4	65,170	2446.8	− 2485	−38.2	× 163 / 436	−14.3
5	65,172	2464.3	− 2528	−63.7	× 138 / 436	−20.2
Sum, rounded to a whole point						−47

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	66,983	2368.7	− 2436	−67.3	× 131 / 461	−19.1
4	66,985	2402.8	− 2485	−82.2	× 149 / 461	−26.6
5	66,987	2442.7	− 2528	−85.3	× 181 / 461	−33.5
Sum, rounded to a whole point						−79

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,088	2396.3	− 2436	−39.7	× 111 / 383	−11.5
4	67,090	2437.2	− 2485	−47.8	× 127 / 383	−15.9
5	67,092	2416.0	− 2528	−112	× 145 / 383	−42.4
Sum, rounded to a whole point						−70

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,584	2378.6	− 2436	−57.4	× 138 / 378	−21
4	67,585	2445.6	− 2485	−39.4	× 108 / 378	−11.3
5	67,586	2432.9	− 2528	−95.1	× 132 / 378	−33.2
Sum, rounded to a whole point						−65

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,730	2330.6	− 2436	−105.4	× 125 / 375	−35.1
4	67,731	2388.7	− 2485	−96.3	× 122 / 375	−31.3
5	67,732	2422.9	− 2528	−105.1	× 128 / 375	−35.9
Sum, rounded to a whole point						−102

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,739	2334.2	− 2436	−101.8	× 119 / 486	−24.9
4	67,740	2381.1	− 2485	−103.9	× 136 / 486	−29.1
5	67,741	2410.6	− 2528	−117.4	× 134 / 486	−32.4
6	67,742	2384.9	− 2552	−167.1	× 97 / 486	−33.4
Sum, rounded to a whole point						−120

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,733	2335.9	− 2436	−100.1	× 133 / 531	−25.1
4	67,734	2365.8	− 2485	−119.2	× 147 / 531	−33
5	67,735	2403.4	− 2528	−124.6	× 142 / 531	−33.3
6	67,736	2374.0	− 2552	−178	× 109 / 531	−36.5
Sum, rounded to a whole point						−128

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,491	2316.4	− 2436	−119.6	× 133 / 537	−29.6
4	67,492	2366.2	− 2485	−118.8	× 156 / 537	−34.5
5	67,493	2386.8	− 2528	−141.2	× 160 / 537	−42.1
6	67,494	2429.9	− 2552	−122.1	× 88 / 537	−20
Sum, rounded to a whole point						−126

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −53, −47, −79, −70, −65, −102, −120, −128, −126 → −87.8
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 6 · 2016→2017: 32 · 2017→2018: 9 · 2018→2019: 5 · 2019→2022: 37 · 2022→2023: 18 · 2023→2024: 8 · 2024→2025: 2 → average 14.6
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 14.6 × 2.66 = 38.8. Upper limit −49, lower limit −126.6.

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".

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, 2023–24, 2024–25, 2025–26.