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Q:  

I am looking for the size of the 18-19 year old population in the US over time. This must be available from the Census Bureau but I am not finding anything.

A:  

You are correct. This is found on the Census Bureau website under Estimates. Information for dates in the past, can be found under the Archives link on the top navigation banner. Unfortunately, the format differs by era, but here are the specific paths for each time period:

1900 - 1980 has single years of age*sex*race:

http://www.census.gov/popest/data/national/asrh/pre-1980/PE-11.html

The 1980s table has age*sex. If you need race, you lose age detail. This link is not to look at, but to use with some sort of software as it is a compilation of single years of age starting with Alabama and ending with Wyoming:

http://www.census.gov/popest/data/historical/1980s/state.html

The 1990s data presents the information as US totals first, followed by each state (Alabama, Alaska. . . Wyoming).

http://www.census.gov/popest/data/historical/1990s/index.html

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