The empirical relationship is 3 Median = Mode + 2 Mean, so $x = 3$, $y = 2$, $z = 1$.
Therefore, $x + y + z = 3 + 2 + 1 = \mathbf{6}$.
Answer: A — 6
Source: Chapter 13, Section 13.4 (Remarks)
The NCERT textbook states the empirical relation as: 3 Median = Mode + 2 Mean (i.e., 3 Median = 1 Mode + 2 Mean). Matching with $x$ Median + $y$ Mean = $z$ Mode gives $x=3$, $y=2$, $z=1$, so $x+y+z=6$. Examiners expect you to recall this standard formula exactly as given in the textbook.