Question

Following are the ranks of $10$ students in Maths and Biology projects given by $2$ professors. Find the rank correlation coefficient.

Maths	4	8	5	3	1	2	10	7	6	9
Biology	1	4	5	6	2	3	8	9	7	10

• A. $0.2787$
• B. $0.7213$
• C. $0.8232$
• D. $0.9031$

Answer 1

Answer: (B)

$0.7213$

Let the ranks of students obtained in Maths be $x$ and the ranks of students obtained in Biology be $y$.

$x$	$4$	$8$	$5$	$3$	$1$	$2$	$10$	$7$	$6$	$9$
$y$	$1$	$4$	$5$	$6$	$2$	$3$	$8$	$9$	$7$	$10$
$d=x-y$	$3$	$4$	$0$	$-3$	$-1$	$-1$	$2$	$-2$	$-1$	$-1$
$d^2$	$9$	$16$	$0$	$9$	$1$	$1$	$4$	$4$	$1$	$1$
					$\sum d^2$ $=46$

The rank correlation coefficient is given by

$r=1-\frac{6\sum d^2}{n(n^2-1)}$

$=1-\frac{6\times 46}{10(100-1)}$

$=1-\frac{276}{10\times 99}$

$=1-\frac{276}{990}$

$=1-0.2787$

$=0.7213$

Therefore, the rank correlation coefficient is $0.7213$.