Training sessions will help to identify those who might be unable to understand the evidence for whatever reason, or who may be too emotional to come to an analytical decision, either just their nature or maybe trauma in their life which resurfaces when they are faced with someone else's trauma. It's very difficult, but every attempt should be made to find suitable jurors especially when murder is involved.
I agree that education and common sense are definitely not connected, but there must be a good level of education involved in order to understand what may be very complex evidence.
As things are, with the jury having no training, the foreman should not be one of the jurors! The foreman should be a trained person who will give everyone a fair hearing and stop any bullying. If the foreman is one of the jurors there's a good chance they may direct people to vote their way, or be unable to control some of the stronger characters.