1.

Find out coefficient of rank correlation between X and Y

Answer»

Solution :
Here NUMBERS 30,50 and 70 are REPEATED twice in series Y.
Therefore, m=2 in Y.
`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)`
`=1-(6[19.5+(1)/(12)(2^(3)-2)+(1)/(12)(2^(3)-2)+(1)/(12)(2^(3)-2)])/((8)^(3)-8)`
`=1-(6[19.5+(1)/(12)(6)+(1)/(12)(6)+(1)/(12)(6)])/(512-8)`
`=1-(6[19.5+0.5+0.5+0.5+])/(504)`
`=1-(6[21])/(504)=1-(126)/(504)`
`=1-0.25=0.75`
Coefficient of Rank Correlation `(r_(k))=0.75`.


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