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.