Charts, graphs, and tables are not subject to copyright protection because they do not meet one of the key requirements for copyright protection, which is that they are not “original works of authorship” under the definitions in the Copyright Act. Facts and data aren't considered original works of authorship and therefore are generally not under copyright protection because they are regarded as “discovered” and “recorded” natural phenomena rather than “created.” Keep in mind however, that some countries do protect data and data sets, so if you are planning on taking your data abroad, be aware that the rules may not be the same as in the U.S. But, your use of data within the United States, for example, on servers in the U.S., is acceptable. Only in cases where a chart, table, or graph creatively represents more than just an expression of the underlying data, would the works be considered under copyright (e.g., a bar graph on U.S. immigration data created in the likeness of a U.S. flag). If you do need permission, refer to WPI's webpage on Requesting permission for information and a sample letter to adapt.
For examples of charts, tables and graphs that are NOT subject to copyright, as well as an example of a graph that IS subject to copyright, see the examples listed at the University of Michigan's Copyright website: http://www.lib.umich.edu/copyright/copyright-info/charts-tables-graphs
The APA Style Blog takes you through the four steps of navigating copyright for reproduced images: