IB Mathematics Applications & Interpretation Question Type 3: Using Parameter or Algebraic Forms of Data When Calculating with Rank Tables Exercises

Calculate 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 $r_s$ for the 5-point data $(1,5),(2,4),(3,3),(4,2),(5,1)$.

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

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

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

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

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

Calculate Spearman's rank correlation coefficient $r_s$ for the data points $(a,c)$, $(b,b)$, and $(c,a)$, given that $b<a<c$.

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

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.