Harding 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	7,721	2436.1	− 2436	0.1	× 40 / 205	0
4	7,722	2465.9	− 2485	−19.1	× 48 / 205	−4.5
5	7,725	2483.0	− 2528	−45	× 67 / 205	−14.7
6	7,726	2480.8	− 2552	−71.2	× 50 / 205	−17.4
Sum, rounded to a whole point						−37

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	6,904	2436.9	− 2436	0.9	× 55 / 237	0.2
4	6,906	2492.5	− 2485	7.5	× 53 / 237	1.7
5	6,908	2488.9	− 2528	−39.1	× 59 / 237	−9.7
6	6,910	2488.2	− 2552	−63.8	× 70 / 237	−18.8
Sum, rounded to a whole point						−27

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	7,117	2473.4	− 2436	37.4	× 44 / 220	7.5
4	7,119	2482.9	− 2485	−2.1	× 56 / 220	−0.5
5	7,121	2511.2	− 2528	−16.8	× 57 / 220	−4.4
6	7,122	2499.1	− 2552	−52.9	× 63 / 220	−15.1
Sum, rounded to a whole point						−13

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	7,134	2442.6	− 2436	6.6	× 43 / 210	1.4
4	7,137	2463.0	− 2485	−22	× 59 / 210	−6.2
5	7,138	2490.7	− 2528	−37.3	× 52 / 210	−9.2
6	7,141	2521.9	− 2552	−30.1	× 56 / 210	−8
Sum, rounded to a whole point						−22

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	7,181	2457.8	− 2436	21.8	× 63 / 220	6.2
4	7,182	2509.0	− 2485	24	× 43 / 220	4.7
5	7,183	2511.2	− 2528	−16.8	× 57 / 220	−4.4
6	7,184	2510.4	− 2552	−41.6	× 57 / 220	−10.8
Sum, rounded to a whole point						−4

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	7,122	2431.1	− 2436	−4.9	× 60 / 232	−1.3
4	7,123	2458.1	− 2485	−26.9	× 56 / 232	−6.5
5	7,124	2495.5	− 2528	−32.5	× 57 / 232	−8
6	7,125	2523.6	− 2552	−28.4	× 59 / 232	−7.2
Sum, rounded to a whole point						−23

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	7,110	2475.4	− 2436	39.4	× 62 / 234	10.4
4	7,111	2494.7	− 2485	9.7	× 58 / 234	2.4
5	7,112	2496.9	− 2528	−31.1	× 58 / 234	−7.7
6	7,113	2513.1	− 2552	−38.9	× 56 / 234	−9.3
Sum, rounded to a whole point						−4

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	7,057	2441.2	− 2436	5.2	× 87 / 260	1.7
4	7,058	2523.7	− 2485	38.7	× 61 / 260	9.1
5	7,059	2503.6	− 2528	−24.4	× 55 / 260	−5.2
6	7,060	2488.7	− 2552	−63.3	× 57 / 260	−13.9
Sum, rounded to a whole point						−8

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	7,017	2435.7	− 2436	−0.3	× 64 / 270	−0.1
4	7,018	2480.2	− 2485	−4.8	× 87 / 270	−1.5
5	7,019	2537.5	− 2528	9.5	× 62 / 270	2.2
6	7,020	2518.3	− 2552	−33.7	× 57 / 270	−7.1
Sum, rounded to a whole point						−7

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −37, −27, −13, −22, −4, −23, −4, −8, −7 → −16.1
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 10 · 2016→2017: 14 · 2017→2018: 9 · 2018→2019: 18 · 2019→2022: 19 · 2022→2023: 19 · 2023→2024: 4 · 2024→2025: 1 → average 11.8
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 11.8 × 2.66 = 31.4. Upper limit 15.3, lower limit −47.5.

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.