Question

Calculate coefficient of rank correlation with the help of these data :

$\begin{array}{cccccccc}\text{Economics}& 66& 90& 89& 55& 58& 44& 42\\ \text{Statistics}& 58& 76& 65& 58& 53& 49& 56\end{array}$

Answer 1

$\begin{array}{cccccc}\text{Marks in Eco. (X)}& R_1& \text{Marks in Stat. (Y)}& R_2& D=R_1-R_2& D^2\\ 66& 3& 58& 3.5& -.5& .25\\ 90& 1& 76& 1& 0& 0\\ 89& 2& 65& 2& 0& 0\\ 55& 5& 58& 3.5& +1.5& 2.25\\ 58& 4& 53& 6& -2& 4.0\\ 44& 6& 49& 7& -1& 1.0\\ 42& 7& 56& 5& +2& 4.0\\ N=7& & & & \sum D=0& \sum D^2=11.50\end{array}$

$R=1-\frac{6[\sum D^2+\frac{1}{12}(m^3-m\left)\right]}{N^3-N}R=1-\frac{6[11.5+\frac{1}{12}(2^3-2\left)\right]}{7^3-7}=1-\frac{6[11.5+.5]}{336}=-1-\frac{72}{336}=+\mathrm{0.786.}$