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I need a table that will map each US zip code to either the mean age or the median age of the population in that zip code.

I see that https://www.census.gov/popest/data/counties/asrh/2015 provides estimates of this data at the county level. I am ok with estimated data, but I need to be able to look up the data by zip code.

Alternatively, perhaps there is a way to get the info from the census demographic profile (http://www2.census.gov/census_2010/03-Demographic_Profile/), but I haven't been able to figure it out.

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I did a quick export of data from the 2014 5-year ACS of the population and median age of every ZIP code: https://numeracy.co/public/2lZ9jKZoehr

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    Data need met. Fish provided. Bonus points for teaching them how to fish... – Shawn Mehan Aug 12 '16 at 19:14
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American Fact Finder includes median age in their General Population and Housing Statistics reports;
General Population and Housing Statistics for Zip Code 23662 is one such table, from the 2010 US Census.
To get them all: not sure if American Fact Finder offers bulk download, but almost positive they do; if for some reason that is not an option, find a list of all US zip codes, and swap them out in the URL; the above example actually points to: http://factfinder.census.gov/bkmk/table/1.0/en/DEC/10_DP/DPDP1/8600000US23662
US23662 is the zip code variable being used, replace/append zip codes as desired.

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