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Is there a way to get a count of the number of single women over 40 who moved in the past year?
The American Community Survey (ACS) asks a question about residential mobility in the past year. You will have to use microdata to make the specific table you are interested in as the pre-tabulated tables do not have a table that includes age categories, sex, marital status, and migration status. The most recent ACS is the 2011 file, which was collected in calendar year 2010.
As a note, there are several migration variables available. The simplest variable indicates whether or not the respondent lived in the same house, a different house, or lived abroad.
You can add more detail by looking at the current state of residence and the migration place of residence, which allows you to differentiate among: live in same house, in-state move, between state move, or lived abroad. Further detail of the in-state moves can be determined with the current PUMA of residence and the migration PUMA of residence. PUMAs are geographic aggregations of census tracts or counties to a population of around 100,000.