Question

In a dance competition, the marks given by two judges to $10$ participants are given below.

Participant	A	B	C	D	E	F	G	H	I	J
1st Judge	1	5	4	8	9	6	10	7	3	2
2nd Judge	4	8	7	6	5	9	10	3	2	1

Find the rank correlation coefficient.

• A. $0.5515$
• B. $0.4485$
• C. $0.3995$
• D. $0.2348$

Answer 1

The correct option is A $0.5515$

Rank Correlation Coefficient,$r_s=1-\frac{6\sum {\rho }_i^2}{n(n^2-1)}$

where, ${\rho }_i=$Difference between two ranks of each observation.

Here, $n=10$

$r_s=1-\frac{6\sum {\rho }_i^2}{n(n^2-1)}$

$=1-\frac{6(9+9+9+4+16+9+0+16+1+1)}{10(100-1)}$

$=1-\frac{6\times 74}{10\times 99}$

$=1-0.4484848$

$=0.5515$

Hence, A is correct option.