EXPLANATION:
Given;
We are given a table of x and y values in order to calculate the correlation coefficient.
Required;
We are required to calculate and populate the tables for the values;
[tex]\begin{gathered} (i)\frac{X-\bar{X}\text{ }}{S_x} \\ (ii)\frac{Y-\bar{Y}}{S_y} \\ (iii)\frac{(X-\bar{X})(Y-\bar{Y})\text{ }}{S_xS_y} \end{gathered}[/tex]
The variables here are;
[tex]\begin{gathered} \bar{X}=mean\text{ }value\text{ }of\text{ }x \\ \bar{Y}=mean\text{ }value\text{ }of\text{ }y \\ S_x=standard\text{ }deviation\text{ }of\text{ }x \\ S_y=standard\text{ }deviation\text{ }of\text{ }y \end{gathered}[/tex]
With the use of a calculator the mean and standrd deeviations are as follows;
[tex]\begin{gathered} \bar{X}=31 \\ \bar{Y}=10.77 \\ S_x=10.68 \\ S_{y=2.17} \end{gathered}[/tex]
The values that goes in the column;
[tex]\begin{gathered} \frac{X-\bar{X}}{S_x} \\ (i)\frac{18-31}{10.68}=-1.2172 \\ (ii)\frac{20-31}{10.68}=-1.0299 \\ (iii)\frac{22-31}{10.68}=-0.8427 \\ (iv)\frac{25-31}{10.68}=-0.5618 \\ (v)\frac{31-31}{10.68}=0 \end{gathered}[/tex]
For the next column;
[tex]\begin{gathered} \frac{Y-\bar{Y}}{S_y} \\ \\ (i)\frac{14-10.77}{2.17}=1.4885 \\ \\ (ii)\frac{14-10.77}{2.17}=1.4855 \\ \\ (iii)\frac{12-10.77}{2.17}=0.5668 \\ \\ (iv)\frac{11-10.77}{2.17}=0.1059 \\ \\ (iv)\frac{10-10.77}{2.17}=-0.3548 \end{gathered}[/tex]
For the last column;
[tex]\begin{gathered} \frac{(X-\bar{X})(Y-\bar{Y})}{S_xS_y} \\ \\ (i)\frac{(-1.2127)(1.4885)}{(10.68)(2.17)}=-0.0779 \\ \\ (ii)\frac{(-1.0299)(1.4885)}{(10.68)(2.17)}=-0.0661 \\ \\ (iii)\frac{(-0.8427)(0.5668)}{(10.68)(2.17)}=-0.0206 \\ \\ (iv)\frac{(-0.5618)(0.1059)}{(10.68)(2.17)}=-0.0026 \\ \\ (v)\frac{(0)(-0.3548)}{(10.68)(2.17)}=0 \end{gathered}[/tex]
