Question

From the following data, calculate coefficient of correlation.

X	57	59	62	63	64	65	58	66	70	72
Y	113	117	126	125	130	128	110	132	140	149

Answer 1

X	Y	X2	Y2	XY
57 59 62 63 64 65 58 66 70 72	113 117 126 125 130 128 110 132 140 149	3249 3481 3844 3969 4096 4225 3364 4356 4900 5184	12769 13689 15876 15625 16900 16384 12100 17424 19600 22201	6441 6903 7812 7875 8320 8320 6380 8712 9800 10728
$\Sigma X$=636	$\Sigma Y$=1270	$\Sigma X^2$=40668	$\Sigma Y^2$=162568	$\Sigma XY$=81291

N = 10

$$\begin{gathered} r=\frac{N\Sigma XY-\Sigma X\Sigma Y}{\sqrt{\mathrm{N\Sigma }{X}^2-{\left(\Sigma X\right)}^2}\sqrt{N\Sigma Y^2-{\left(\Sigma Y\right)}^2}} \\ \mathrm{or},r=\frac{10\times 81291-636\times 1270}{\sqrt{10\times 40668-{\left(636\right)}^2}\sqrt{10\times 162568-{\left(1270\right)}^2}} \\ \mathrm{or},r=\frac{5190}{46.733\times 113.04} \\ \Rightarrow r=0.982 \end{gathered}$$

Hence, coefficient of correlation is 0.982.