Be sure to assign your dwellers to rooms that match their stats. So, if someone's highest stat is Charisma, put them in the Living Quarters or Radio Station, etc. Training rooms are the exception. You can put anybody here with no negative impact to their morale. If a dweller is not assigned to any room - resourceful, training or whatever else - their morale will go down. Their morale will also go down if assigned to a room which they don't have good stats for. So, if you are assigning a 1-Strength dweller to the Power Station, you're doing it wrong. Plus, your overall vault resources matter too as do disasters. If your vault is low on power, food or water then it can affect the morale of everybody.
