You could also compile the latest source and install Python to an alternative path from the default (so that applications don't get messed up). Basically you would download the latest Python, configure it, compile, then install.
$> wget https://www.python.org/ftp/python/2.7.11/Python-2.7.11.tgz
$> tar xvhf Python-2.7.11.tgz
$> cd Python-2.7.11
$> ./configure
$> make
$> sudo make altinstall
Update
To see all the available options for Python configuration execute ./config --help
. This is important to know because, by default, many options are left out (especially in Python 2.x) such as unicode or IPv6 support. Features can also be disabled if required.
Reference