Calculate coefficient of correlation by means of ranking method from the following data :

Explanation

In this question in X series, the values 60 and 50 are repeated thrice and twice. The averages rank for the value 60 is `4(3+4+5 div 3)` while for the value 50 it is 6.5 `(6+7 div 2)`. In both the cases, the correlation factor will be `(1)/(12)(3^(3)-3) " and " (1)/(12)(2^(3)-2)` respectively . In series Y, the 130 is repeated twice. The average rank for the value 130 is 5.5 `(5+6 div 2)`. In this case, correlation factor will be `(1)/(12)(2^(3)-2)`.
`r_(k)=1-(6[sumD^(2)+(1)/(12)(m_(1)^(3)-m_(1))+(1)/(12)(m_(2)^(3)-m_(2))+(1)/(12)(m_(3)^(3)-m_(3))])/(N^(3)-N)`
Here, `sumD^(2)=45,m_(1)=3,m_(2)=2,m_(3)=2N=8`
By substituting values in the above formula, we get
`r_(k)=1-(6[45+(1)/(12)(3^(3)-3)+(1)/(12)(2^(3)-2)+(1)/(12)(2^(3)-2)])/((8)^(3)-8)`
`=1-(6[45+(1)/(12)(24)+(1)/(12)(6)+(1)/(12)(6)])/(512-8)`
`=1-(6(45+2+(1)/(2)+(1)/(2)))/(504)=1-(6(48))/(504)=1-(288)/(504)=1-0.571=0.429`
Coefficient of Rank Correlation `(r_(k))=0.429`