Question

Calculate Karl Pearson's Coefficient of Correlation on the following data:

X	:	15	18	21	24	27	30	36	39	42	48
Y	:	25	25	27	27	31	33	35	41	41	45

Answer 1

X	Y	$\left(\mathit{X}\mathit{-}\overline{\mathit{X}}\right)$ (x)	x2	$\left(\mathit{Y}\mathit{-}\overline{\mathit{Y}}\right)$ (y)	y2	xy
15	25	−15	225	−8	64	120
18	25	−12	144	−8	64	96
21	27	−9	81	−6	36	54
24	27	−6	36	−6	36	36
27	31	−3	9	−2	4	6
30	33	0	0	0	0	0
36	35	6	36	2	4	12
39	41	9	81	8	64	72
42	41	12	144	8	64	96
48	45	18	324	12	144	216
ƩX = 300	ƩY =330		Ʃx2 =1080		Ʃy2 =480	Ʃxy =708

N = 10

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }X}{N}=\frac{300}{10}=30 \\ \overline{Y}=\frac{\mathrm{\Sigma }Y}{N}=\frac{330}{10}=33 \\ r=\frac{\mathrm{\Sigma }xy}{\sqrt{\mathrm{\Sigma }{x}^2}\times \sqrt{\mathrm{\Sigma }{y}^2}} \\ =\frac{708}{\sqrt{1080}\times \sqrt{480}}=\frac{708}{32.86\times 21.91} \\ =\frac{708}{720} \\ =0.983 \end{gathered}$$
Thus, the value of correlation coefficient is 0.983.