Ans: A
Note that the second group of numbers is formed by multiply $8$ to each of the data in the first group. Therefore, the new mode, the new inter-quartile range and the new standard deviation are $8$ times the original mode, the inter-quartile range and the original standard deviation.
Note that the second group of numbers is formed by multiply $8$ to each of the data in the first group. Therefore, the new mode, the new inter-quartile range and the new standard deviation are $8$ times the original mode, the inter-quartile range and the original standard deviation.
Hence, I and II must be true.
III must not be true.
$\begin{array}{rcl}
v_2 & = & (\text{the new standard deviation})^2 \\
v_2 & = & (8 \times \text{the original standard deviation})^2 \\
v_2 & = & 64 \times (\text{the original standard deviation})^2 \\
v_2 & = & 64v_1
\end{array}$
