See my final edit. If it was 10 men in a shul, that’s 50 souls (say a wife and three children each on average), in some instances up to double that figure. You’d still need 6,500 such “communities” for the claim to be true. I’d believe it if the date was 1950-1980, but 1880-1924 sounds less likely.
I don't know where
@chevron got that specific figure. Is it 1/3 of people were in small communities? Or 1/3 of communities were small? Here's one source:
Religion and Secularism in America’s Small-Town Jewish Communities, Lee Shai Weissbach
Revue française d’études américaines 2014/4 (n° 141), pages 95 à 106
"....scholars have long focused their attention almost exclusively on America’s larger urban centers, places such as New York, Boston, Philadelphia, and Chicago. As a result, the experience of small-town Jewish communities in the United States has been largely ignored. This is unfortunate, for up until the period between World War I and World War II, the United States was still an essentially rural country and many observers of American life considered small towns to be the heart and soul of American society, whether they thought of them as ideal dwelling places (reflecting a sort of Jeffersonian worldview) or whether they criticized them for their insularity and provincialism.
"Moreover, smaller Jewish communities in small-town settings actually constituted the vast majority of Jewish settlements in the United States throughout the late nineteenth century and well into the twentieth. As early as the 1870s, there were already some 136 smaller cities and towns in the U.S. with Jewish populations of at least 100 but fewer than 1,000 individuals, and by 1927 there were nearly 500 triple-digit Jewish communities in America. Some of these smaller communities had been founded by Jewish pioneers from the German states and adjacent areas in the middle decades of the nineteenth century, while the majority were established in the era of mass migration at the turn of the twentieth century by East European immigrants as they fanned out across the land.
"In Massachusetts in the 1920s, for example, when there was a community of some 90,000 Jews in Boston, there were also Jewish settlements of somewhere between 100 and 1,000 individuals in 33 other towns, places such as Chicopee, Fitchburg, Newburyport, North Adams, and Plymouth, locations not usually associated with the American Jewish experience. In Michigan in the 1920s, to take another example, there was a Jewish community of some 75,000 in Detroit, but there were also triple-digit Jewish communities in 19 other places, including towns such as Benton Harbor, Iron Mountain, Kalamazoo, and Muskegon. Small-town Jewish communities were not large enough to command much attention on the national scene, but they were large enough to develop their own identities and their own internal dynamics."
https://www.cairn.info/revue-francaise-d-etudes-americaines-2014-4-page-95.htm?contenu=article