CentOS 7 ships with python 2.7.5 by default. We have some software that requires 2.7.11. It's generally a bad idea to clobber your system python, since other system-supplied software may rely on it being a particular version.
Our strategy for running 2.7.11 alongside the system python is to build it from source, then create virtualenvs that will run our software.
Step 1. Update CentOS and install development tools
Step 2. Download the Python source tarball
Step 3. Configure, build and install into /opt (replace with /usr/local/ if you prefer)
Step 4. Install pip and virtualenv for the system Python
You have to be root for this.