The solution is as follows. Given that the ranks of items of the same quality are equal to the arithmetic mean of the ordinal numbers of the items: $(3+4+5) / 3=4, \quad(6+7+8+9) / 4=7.5, \quad(6+7) / 2=6.5$, we can write the sequences of ranks assigned to the items by the controllers:

$$
\begin{array}{cccccccccc}
x_{i} & 1 & 2 & 4 & 4 & 4 & 7.5 & 7.5 & 7.5 & 7.5 \\
y_{i} & 2 & 1 & 4 & 3 & 5 & 6.5 & 6.5 & 8 & 9
\end{array}
$$

We will find the sample rank correlation coefficient of Spearman, given that $\sum d_{i}^{2}=8.5, n=9$:

$$
\rho_{\mathrm{B}}=1-\frac{6 \sum d_{i}^{2}}{(n-1) n(n+1)}=1-\frac{6 \cdot 8.5}{8 \cdot 9 \cdot 10}=0.93
$$

Thus, $\rho_{\mathrm{B}}=0.93$.
546. Two controllers $A$ and $B$ arranged samples of products made by nine masters in the order of decreasing quality (in parentheses are the ordinal numbers of products of the same quality):
(A)
$\begin{array}{llll}\text { (A) } & 1 & 2 \\ \text { (B) } & 2 & 1\end{array}$
$\left.\begin{array}{ccc}(3, & 4 & 5 \\ 4 & 3 & 5\end{array}\right)$
$(6$,
$7,8,9)$
$(6,7) \quad 8 \quad 9$

Find the sample rank correlation coefficient of Spearman between the ranks of the products assigned by the two controllers.