Answer
(a) See the picture below.
(b) $r=-0.933$
(c) There is a negative linear relation between x and y.
Work Step by Step
(b) $x ̅=\frac{2+3+5+6+6}{5}=4.4$
$s_x=\sqrt {\frac{(2-4.4)^2+(3-4.4)^2+(5-4.4)^2+(6-4.4)^2+(6-4.4)^2}{5-1}}=1.8166$
$y ̅=\frac{10+9+7+4+2}{5}=6.4$
$s_y=\sqrt {\frac{(10-6.4)^2+(9-6.4)^2+(7-6.4)^2+(4-6.4)^2+(2-6.4)^2}{5-1}}=3.3615$
$r=\frac{Σ(\frac{x_i-x ̅}{s_x})(\frac{y_i-y ̅}{s_y})}{n-1}=\frac{(\frac{2-4.4}{1.8166})(\frac{10-6.4}{3.3615})+(\frac{3-4.4}{1.8166})(\frac{9-6.4}{3.3615})+(\frac{5-4.4}{1.8166})(\frac{7-6.4}{3.3615})+(\frac{6-4.4}{1.8166})(\frac{4-6.4}{3.3615})+(\frac{6-4.4}{1.8166})(\frac{2-6.4}{3.3615})}{5-1}=-0.933$
(c) The scatter diagram looks like Figure 4 (e) on page 194. $r\approx-0.9$ indicates a strong negative linear relation.
