Ans: C
I cannot be determine. The median of $A=\dfrac{\beta+\gamma}{2}$ while that of $B=\mu +2$. There is not enough information to determine.
I cannot be determine. The median of $A=\dfrac{\beta+\gamma}{2}$ while that of $B=\mu +2$. There is not enough information to determine.
II is true. The range of $A=\delta-\alpha$ while that of $B=(\delta+2)-(\alpha+2)=\delta-\alpha$.
III is true. Let $\overline{x}$ be the mean of $\alpha+2$, $\beta+2$, $\gamma+2$ and $\delta+2$. It is obviously that $\alpha+2<\beta+2\le \overline{x} \le \gamma+2<\delta+2$. The more the numbers near the mean, the smaller the standard deviation.
