Explanation

(b)
[table] $\mathbf{x}$ | $\mathbf{y}$ | $\mathbf{d = x - y}$ | $\mathbf{d}^{\mathbf{2}}$ ; 1 | 10 | -9 | 81 ; 2 | 9 | -7 | 49 ; 3 | 8 | -5 | 25 ; 4 | 7 | -3 | 9 ; 5 | 6 | -1 | 1 ; 6 | 5 | 1 | 1 ; 7 | 4 | 3 | 9 ; 8 | 3 | 5 | 25 ; 9 | 2 | 7 | 49 ; 10 | 1 | 9 | 81 ; | | | $\sum_{}^{}d^{2} = 330$ [/table]
$\therefore$ Rank correlation $R = 1 - \frac{6d^{2}}{n(n^{2} - 1)}$
$= 1 - \frac{6 \times 330}{10(10^{2} - 1)}$
$= 1 - \frac{198}{99} = - 1$