Over the years, I have conducted a series of censuses of day schools in the United States for the Avi Chai Foundation. This research is painstaking and involves direct contact with every yeshiva and day school, as well as with government agencies, Jewish communal organizations and federations. The statistics that emerge are the actual count, school-by-school and grade-by-grade, and not estimates or extrapolations.
It is possible that a very small number of schools with tiny enrollments fall through the cracks and are not reported. It is also at least as likely that some schools for one reason or another overestimated their enrollment. The data published by the Avi Chai Foundation are reliable.
Those who conducted the UJA-Federation of New York population study of the eight counties in the federation catchment area did not think it necessary to refer to this research. How this accords with even minimal standards of scholarship is a mystery. What is certain is that the number of day school enrollees living in the eight counties is significantly below what the demographers Steven Cohen, Jack Ukeles and Ron Miller have reported.