There are $60$ students in a class. These students are divided into three groups $A, B$ and $C$ of $15, 20$ and $25$ students each. The groups $A$ and $C$ are combined to form group $D$.
If all the students of the class have the same weight, then which of the following is false?
- The average weight of all the four groups is the same.
- The total weight of A and C is twice the total weight of $B$.
- The average weight of D is greater than the average weight of $A$.
- The average weight of all the groups remains the same even if a number of students are shifted from one group to another.