Question

Find Karl Pearson's correlation coefficient for the following data:

X	3	2	1	5	4
Y	8	4	10	2	6

Answer 1

Table 1.

X	3	2	1	5	4
Y	8	4	10	2	6

Table2.

$\therefore X$	$Y$	$X^2$	$Y^2$	$XY$
$3$	$8$	$9$	$64$	$24$
$2$	$4$	$4$	$16$	$8$
$1$	$10$	$1$	$100$	$10$
$5$	$2$	$25$	$4$	$10$
$4$	$6$	$16$	$36$	$24$
$\sum X=15$	$\sum Y=30$	$\sum X^2=55$	$\sum Y^2=220$	$\sum XY=76$

Table 1

Table 2

Correlation co efficient $r(x,y)=\frac{(\sum xy)-\frac{1}{n}(\sum x.\sum y)}{\sqrt{\sum x^2-\frac{1}{n}{(\sum x)}^2}\sqrt{\sum y^2-\frac{1}{n}\sum y^2}}$

$=\frac{76-\frac{15\times 30}{5}}{\sqrt{55-\frac{225}{5}}\sqrt{220-\frac{900}{5}}}$

$=\frac{76-90}{\sqrt{10}\sqrt{40}}$

$=\frac{-14}{\sqrt{400}}$

$=\frac{-14}{20}$

$=\frac{-7}{10}$

$=-0.7$

$r(x,y)=-0.7$