Calculate coefficient of rank correlation between the marks in Economics and Statistics, as indicated by answer books of each of the two examiners.

Explanation

There are 8 answer books each in Economics and Statistics indicating different marks. Rank 1 is accorded to the highest score. In Statistics, two answer books indicate 10 marsk each. Hence, the first answer book has been given Rank 8 and the second 7. Thus, the average rank `=(8+7)/(2)=7.5` has been accorded to both. Likewise, in Economics two answer books indicate 12 marks each. The average rank `=(6+5)/(2)=5.5` has, therefore, been accorded to both.

Here, number 10 is repeated twice in series X and number 12 is repeated twice in series Y. Therefore,in X, m=2 and in Y, m=2.
`1-(6[sumD^(2)+(1)/(12)(m_(1)^(3)-m_(1))+(1)/(12)(m_(2)^(3)-m_(2))])/(N^(3)-N)`
`=1-(6[114+(1)/(12)(2^(3)-2)+(1)/(12)(2^(3)-2)])/(8^(3)-8)`
`1-(6[114+(1)/(2)(6)+(1)/(12)(6)])/(512-8)`
`=1-(6[114+(1)/(2)+(1)/(2)])/(504)`
`=1-(6[115])/(504)=1-(690)/(504)`
`=1-1.36=-0.36`
Coefficient of Rank Correlation `(r_(k))=-0.36`