Here is a first-differences plot for Grade 3 Reading, 2013-14 through 2015-16. It is typical of those for other grades and other years.

There are four “base years,” beginning with 2013-14 and going through 2017-18, and three grades, for a total of twelve instances where schools might be involved when considering Reading and Math separately. The following table shows the number of schools that had N appearances amongst the outliers, the maximim possible being twelve.

For Reading:

0 1 2 3 4 5 6 7 8 9 10 (all)
477 292 182 123 94 68 23 14 9 5 2 1289

For Math:

0 1 2 3 4 5 6 7 8 9 10 (all)
482 284 197 123 81 64 30 17 7 1 3 1289

For the 2013-14-based first differences, specifically for Grade 3 Reading in Traditional public schools, there was a total of 1234 schools, of which 173 were outside the putative 90 percent ellipse. There were altogether 115 LEAs, with the outlying schools being in 73 LEAs.

Comparing that with the more recent 2016-17-based first differences, there was a total of 1234 schools, of which 194 were outside the 90 percent ellipse associated with 80 LEAs.

Some of the difference between the observations for these is due to computational difficulties in constructing the ellipses. However, the ellipses are only guides and are not to be used for anything of a precise character. Generally speaking the proportion of outliers is about ten percent of the total number of schools. That more or less holds by grade, although with considerable variation.

What Can Be Said About These Schools?

The following tables group together grades 3, 4 and 5, and presents these by academic year from 2013-14 (“A”) to 2018-19 (“F”). It appears that, for the schools lying outside the 90% ellipse, only the EDS category is even approximately normally distributed.

For schools lying outside the 90% ellipses at least six times:

f_acYear BLCKpct_mean BLCKpct_sd BLCKpct_med EDSpct_mean EDSpct_sd EDSpct_med HISPpct_mean HISPpct_sd HISPpct_med WHTEpct_mean WHTEpct_sd WHTEpct_med
A 18.23 21.40 6.74 64.21 15.64 64.81 9.55 11.56 5.23 62.84 25.85 66.55
B 18.72 22.67 5.83 54.84 15.88 55.00 10.06 12.11 5.86 62.20 26.50 68.79
C 16.90 23.02 0.00 54.76 15.57 55.04 6.59 13.05 0.00 61.29 27.69 67.36
D 16.58 22.34 0.00 58.78 15.88 61.19 7.34 13.74 0.00 59.51 28.99 65.26
E 17.05 22.41 0.00 53.04 15.14 57.06 7.02 13.85 0.00 58.62 28.81 66.86
F 17.34 23.05 0.00 56.03 16.25 59.02 7.52 14.16 0.00 58.63 29.79 62.50

For schools lying outside the 90% ellipses fewer than six times (including never being outside):

f_acYear BLCKpct_mean BLCKpct_sd BLCKpct_med EDSpct_mean EDSpct_sd EDSpct_med HISPpct_mean HISPpct_sd HISPpct_med WHTEpct_mean WHTEpct_sd WHTEpct_med
A 25.85 24.01 19.73 60.88 23.17 62.48 15.05 13.94 11.41 49.33 28.35 52.22
B 25.75 23.85 19.74 54.76 20.64 56.87 15.98 14.31 12.32 48.47 28.21 51.20
C 24.73 24.56 18.84 54.55 19.41 57.03 14.70 15.92 10.73 46.63 28.97 49.39
D 24.90 24.50 19.09 55.56 20.10 58.09 15.27 16.07 11.21 45.63 28.78 48.80
E 24.87 24.37 19.25 50.65 18.14 52.22 16.03 16.31 12.62 44.66 28.73 47.89
F 24.87 24.34 19.54 53.91 19.73 55.61 16.34 16.51 13.03 43.96 28.68 46.58

Here are several histograms that present the data for EDS percent, White percent, and Black percent, rolled up over the academic years from 2013-14 through 2018-19.

For schools lying outside the 90% ellipses at least six times:

For schools lying outside the 90% ellipses fewer than six times (including never being outside):