How can I upgrade Python from 2.7.10 to 2.7.11 on OSX (Yosemite)?
You should not replace the Python version that comes with OS X. If you do, you may break something in your system. Instead, you should install a new instance of Python.
You could use brew whenever they are offering 2.7.11:
brew install python
However, it is likely that they still only offer 2.7.10. In that case, you can download the source code and compile it yourself. Unpack into a directory and run:
./configure --prefix=/opt/python2.7.11 && make && make install