Install Spyder3 without Anaconda on ubuntu 16.04
After trial and error I can suggest the following:
sudo apt-get install python3-pip python3-pyqt4 \
python3-pyqt5 python3-pyqt5.qtsvg python3-pyqt5.qtwebkit
sudo pip3 install -U spyder
The result: you have Spyder3 installed and its About Spyder window contains
Spyder 3.2.4
...
Python 3.5.2 64bits, Qt 5.5.1, PyQt5 5.5.1 on Linux
Tested on clean Ubuntu 16.04.3 LTS amd64 install.