Approximately 250,000 per year always seems like it the most accurate way of describing our immigration tradition before the 1965 Act reopened Mass Immigration.
All of those very different numerical traditions shown above average out to an overall tradition before the 1965 Act (that our movement is sworn to overturn) of around a quarter-million immigrants a year.
It also is a level that is part of our very recent immigration tradition, at time when nearly all Americans told pollsters they felt good about immigration. As it turns out, 250,000 is almost exactly the average of the 1945-1970 quarter century that ran from the end of WWII to the beginning of population-stabilization-level fertility shortly after the passage of the 1965 Act.
It is unclear where the 300,000 figure that is often referenced as our traditional average came from. It may be based on our immigration tradition after we started keeping federal records (1820) and until the 1965 Act. The average for that 145-year period was about 295,000. That also coincidentally happens to be almost exactly the level of immigration in 1965 when Congress changed the law and inadvertently unleashed levels of immigration totally out of proportion to our immigration tradition to that point.
All of the immigration totals from 1820 through the present are from federal immihration records that were provided by the immigration and Naturalization Service (now the Department of Homeland Securities.)