Install MySQL on Ubuntu without a password prompt

sudo debconf-set-selections <<< 'mysql-server mysql-server/root_password password your_password'
sudo debconf-set-selections <<< 'mysql-server mysql-server/root_password_again password your_password'
sudo apt-get -y install mysql-server

For specific versions, such as mysql-server-5.6, you'll need to specify the version in like this:

sudo debconf-set-selections <<< 'mysql-server-5.6 mysql-server/root_password password your_password'
sudo debconf-set-selections <<< 'mysql-server-5.6 mysql-server/root_password_again password your_password'
sudo apt-get -y install mysql-server-5.6

For mysql-community-server, the keys are slightly different:

sudo debconf-set-selections <<< 'mysql-community-server mysql-community-server/root-pass password your_password'
sudo debconf-set-selections <<< 'mysql-community-server mysql-community-server/re-root-pass password your_password'
sudo apt-get -y install mysql-community-server

Replace your_password with the desired root password. (it seems your_password can also be left blank for a blank root password.)

If your shell doesn't support here-strings (zsh, ksh93 and bash support them), use:

echo ... | sudo debconf-set-selections 

This should do the trick

export DEBIAN_FRONTEND=noninteractive
sudo -E apt-get -q -y install mysql-server

Of course, it leaves you with a blank root password - so you'll want to run something like

mysqladmin -u root password mysecretpasswordgoeshere

Afterwards to add a password to the account.