I have a shape file created as per the answer to my previous question, which includes county level means for each county in the US.
How can I now export this data in a .csv file, e.g. with just the state, county, and county_mean fields?
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ArcGIS will export a .dbf to .txt. You can then rename it to .csv. First turn off the fields you do not want exported under Properties, Fields. Right-click the table, data, export. Select the browse folder button, change the "save to type" to .txt.
Step-by-step instructions to follow comment by @Brandon (ArcMap 10.1)