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Calculate coefficient of rank correlation between the marks in Economics and Statistics, as indicated byanswer books of each of the two examiners. |
Answer» Solution :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` |
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