Answer
(a) See the picture below.
(b) $r=-0.496$
(c) There is a moderate negative linear relation between x and y.
Work Step by Step
(b) $x ̅=\frac{2+6+6+7+9}{5}=6$
$s_x=\sqrt {\frac{(2-6)^2+(6-6)^2+(6-6)^2+(7-6)^2+(9-6)^2}{5-1}}=2.5495$
$y ̅=\frac{8+7+6+9+5}{5}=7$
$s_y=\sqrt {\frac{(8-7)^2+(7-7)^2+(6-7)^2+(9-7)^2+(5-7)^2}{5-1}}=1.5811$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{2-6}{2.5495})(\frac{8-7}{1.5811})+(\frac{6-6}{2.5495})(\frac{7-7}{1.5811})+(\frac{6-6}{2.5495})(\frac{6-7}{1.5811})+(\frac{7-6}{2.5495})(\frac{9-7}{1.5811})+(\frac{9-6}{2.5495})(\frac{5-7}{1.5811})}{5-1}=-0.496$
(c) The scatter diagram looks like Figure 4 (f) on page 194. $r\approx-0.4$ indicates a moderate negative linear relation.