Question

Making use of the data given below, calculate the coefficient of correlation.

X	10	6	9	10	12	13	11	9
Y	9	4	6	9	11	13	8	4

Answer 1

X	Y	X2	Y2	XY
10 6 9 10 12 13 11 9	9 4 6 9 11 13 8 4	100 36 81 100 144 169 121 81	81 16 36 81 121 169 64 16	90 24 54 90 132 169 88 36
$\mathit{\Sigma }\mathit{X}$=80	$\mathit{\Sigma }\mathit{Y}$=64	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=832	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=584	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=683

N = 8

$$\begin{gathered} r=\frac{\mathrm{N\Sigma XY}-\mathrm{\Sigma X\Sigma Y}}{\sqrt{{\mathrm{N\Sigma X}}^2-{\left(\mathrm{\Sigma X}\right)}^2}\sqrt{{\mathrm{N\Sigma Y}}^2-{\left(\mathrm{\Sigma Y}\right)}^2}} \\ \mathrm{or},r=\frac{8\times 683-80\times 64}{\sqrt{8\times 832-{\left(80\right)}^2}\sqrt{8\times 584-{\left(64\right)}^2}} \\ \mathrm{or},\mathrm{r}=\frac{344}{16\times 24} \\ \Rightarrow r=0.895 \end{gathered}$$

Therefore, coefficient of correlation= 0.895.