Question

Find the product moment correlation of the following data:

X	:	1	2	3	4	5
Y	:	9	8	10	12	11

Answer 1

X	Y	$\left(\mathit{X}\mathit{-}\overline{X}\right)$ x	$\left(\mathit{Y}\mathit{-}\overline{\mathit{Y}}\right)$ y	x2	y2	xy
1	9	−2	−1	4	1	2
2	8	−1	−2	1	4	2
3	10	0	0	0	0	0
4	12	1	2	1	4	2
5	11	2	1	4	1	2
ƩX =15	ƩY =50			Ʃx2 = 10	Ʃy2 = 10	Ʃxy = 8

N = 5

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{15}{5}=3 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{50}{5}=10 \\ r=\frac{\mathrm{\Sigma }xy}{\mathrm{\Sigma }{x}^2\times \mathrm{\Sigma }{y}^2}=\frac{8}{\sqrt{10}\times \sqrt{10}}=\frac{8}{10} \\ =0.80 \end{gathered}$$
Thus, the product moment correlation is 0.80.