Answer to Question #163508 in Statistics and Probability for Alen

Question

Two judges in a beauty contest rank the 12 entries as follows

12 Y 12 9 6 10 3 5 4 7 8 2 11 1

Calculate the rank correlation coefficient between X and Y.

Answer 1

The enteries by two judges are:-

Here $N=12$ ,

Rank correlation coefficient =$1-\dfrac{6\times \sum D^2}{N^3-N}$

=$1-\dfrac{6\times 416}{(12)^3-12}$

=$1-\dfrac{6\times 416}{1728-12}$

=1-$\dfrac{6\times 416}{1716}$

=$1-\dfrac{416}{280}=1-1.45=-0.45$

Hence Rank correlation coefficient is $-0.45.$