Is there any information on what numbers of American families have what numbers of children, for any time period?

score:6

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You can download Census microdata at IPUMS USA here: https://usa.ipums.org/usa/

Since a large number of births occurred to married women historically in the United States, you could also use completed birth parities by birth cohort of women for an estimation: cdc.gov/nchs/nvss/cohort_fertility_tables.htm

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