Question Type 3: Using parameter or algebraic forms of data when calculating with rank tables Exercises

Compute Spearman's rank correlation coefficient $\rho$ for the data points $(a,a),(b,b),(c,c),(d,d)$ with distinct $a<b<c<d$.

Compute Spearman's rank correlation coefficient $\rho$ for the 5-point data $(1,5),(2,4),(3,3),(4,2),(5,1)$.

Compute Spearman's rank correlation coefficient $\rho$ for the data points $(a,c),\,(b,b),\,(c,a)$ under the assumption $a<b<c$.

Compute Spearman's rank correlation coefficient $\rho$ for the 5-point data $(1,4),(2,3),(3,5),(4,1),(5,2)$.

For distinct $a<b<c<d$, compute Spearman's rank correlation coefficient $\rho$ for the data points $(a,d),\,(b,c),\,(c,b),\,(d,a)$.

Compute Spearman's rank correlation coefficient $\rho$ for the data points $(a,c),\,(b,b),\,(c,a)$ under the assumption $b<c<a$.

Compute Spearman's rank correlation coefficient $\rho$ for the data points $(a,c),\,(b,b),\,(c,a)$ under the assumption $b<a<c$.

For distinct $a<b<c<d$, compute Spearman's rank correlation coefficient $\rho$ for the data points $(a,b),(b,a),(c,d),(d,c)$.

For distinct $a<b<c<d$, compute Spearman's rank correlation coefficient $\rho$ for the data points $(a,b),(b,c),(c,a),(d,d)$.

Find $k$ such that Spearman's rank correlation coefficient $\rho$ for the data $(1,k),(2,3),(3,2),(4,4),(5,1)$ equals zero.

Express Spearman's rank correlation coefficient $\rho$ for the data points $(1,\alpha),(2,\beta),(3,\gamma)$ in terms of $\alpha,\beta,\gamma$, assuming they are distinct.