Ans: B
I may be false. Suppose the mark of the students in Group $A$ are $60$ and $60$, that in Group $B$ are $70$ and $70$, and that in Group $C$ are $80$, $80$ and $80$. Then the mean mark of Group $A$, $B$ and $C$ are still $60$, $70$ and $80$ respectively. However, the mean mark of all students
I may be false. Suppose the mark of the students in Group $A$ are $60$ and $60$, that in Group $B$ are $70$ and $70$, and that in Group $C$ are $80$, $80$ and $80$. Then the mean mark of Group $A$, $B$ and $C$ are still $60$, $70$ and $80$ respectively. However, the mean mark of all students
$\begin{array}{cl}
= & \dfrac{60 + 60 + \cdots + 80}{7} \\
= & 71.428~571~43
\end{array}$
II must be true. Note that the mean mark of all students of Group $A$ and $B$ must be higher than $60$ and lower than $70$, and that of Group $B$ and $C$ must be higher than $70$ and lower than $80$. Therefore, the mean mark of all students of Group $A$ and Group $B$ is lower than the mean mark of all students of Group $B$ and Group $C$.
III may be false. Suppose the mark of students in Group $A$ are $45$, $45$ and $90$, and that in Group $C$ are $80$ and $80$. The mean marks are still $60$ and $80$. But the highest mark $90$ is in Group $A$.
