A student asks five friends how many cups of coffee they drank in a day and how many hours they…

Step 1. The means. $\bar{x} = \dfrac{15}{5} = 3$ cups and $\bar{y} = \dfrac{23}{5} = 4.6$ hours.

Step 2. The sums. The deviations of $y$ are $2.4, 0.4, 1.4, -1.6, -2.6$. Then $S_{xy} = (-2)(2.4) + (-1)(0.4) + 0 + (1)(-1.6) + (2)(-2.6) = -4.8 - 0.4 - 1.6 - 5.2 = -12$. Also $S_{xx} = 10$ and $S_{yy} = 5.76 + 0.16 + 1.96 + 2.56 + 6.76 = 17.2$.

Step 3. The correlation. $r = \dfrac{-12}{\sqrt{10 \times 17.2}} = \dfrac{-12}{13.115} = -0.915$.