Updated January 14, 2016
1. Install the following, in this order:
sudo yum install gcc
sudo yum install mysql mysql-devel mysql-libs
sudo yum install python-devel
sudo yum install MySQL-python
sudo pip install mysql-python
2. Upgrade pip and set the correct path
sudo pip install --upgrade
When you upgrade pip on an EC2 instance, your sudo pip will be broken. To set the correct path, look at my answer on StackOverflow: http://stackoverflow.com/questions/34103119/upgrade-pip-in-amazon-linux/34584537#34584537
3. Install numpy
sudo yum install python27-numpy
4. Install scipy
sudo yum install python27-scipy
5. Install matplotlib
sudo yum install python27-matplotlib