The given table shows the ranking of ten students in two subjects mathematics and statistics. Mathematics Statistics 3 6 5 4 8 9 4 8 7 1 10 2 2 3 1 10 6 5 9 7 The coefficient of rank correlation is:
-0.3
Using Spearman's formula with \(n=10\), compute \(d=R_1-R_2\) for each pair and sum the squares.
Differences: \(-3,1,1,-1,-4,6,-9,8,-1,2\); squares: \(9,1,1,1,16,36,81,64,1,4\).
\[\sum d^2=9+1+1+1+16+36+81+64+1+4=214\]
Apply the formula:
\[\rho=1-\dfrac{6\times 214}{10(10^2-1)}=1-\dfrac{1284}{990}=1-1.297\approx -0.297\]
Therefore the rank correlation coefficient is approximately -0.3.
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