Answer to Question #163508 in Statistics and Probability for Alen

Question #163508

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.


1
Expert's answer
2021-02-22T13:21:52-0500

The enteries by two judges are:-


Here N=12N=12 ,

Rank correlation coefficient =16×D2N3N1-\dfrac{6\times \sum D^2}{N^3-N}


=16×416(12)3121-\dfrac{6\times 416}{(12)^3-12}


=16×4161728121-\dfrac{6\times 416}{1728-12}


=1-6×4161716\dfrac{6\times 416}{1716}

=1416280=11.45=0.451-\dfrac{416}{280}=1-1.45=-0.45


Hence Rank correlation coefficient is 0.45.-0.45.


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