IB Mathematics Applications & Interpretation Question Type 2: Finding the Spearman's Rank Coefficient Using Rank Tables Exercises

Compute the Spearman's rank correlation coefficient for the data provided.

The ranks for eight observations of two variables, $X$ and $Y$, are given in the following table:

$$\begin{array}{lcccccccc}\text{Observation}& 1& 2& 3& 4& 5& 6& 7& 8\\ R_X& 1& 2& 3& 4& 5& 6& 7& 8\\ R_Y& 2& 1& 4& 3& 6& 5& 8& 7\end{array}$$

Calculate the Spearman's rank correlation coefficient, $r_s$.

Given the following paired data:

$$\begin{array}{ccccccccc}X& 23& 31& 27& 45& 29& 33& 41& 37\\ Y& 15& 20& 18& 25& 22& 19& 24& 21\end{array}$$

Calculate the Spearman's rank correlation coefficient, $r_s$.

The exam ranks ($R_X$) and project ranks ($R_Y$) for 10 students are shown in the following table.

Calculate the Spearman's rank correlation coefficient for this data.

Compute the Spearman's rank correlation coefficient for the following data:

$X=82,96,75,88,92,85$ $Y=33,38,30,36,35,34$

The following table shows the ranks for variables $X$ and $Y$ for 7 observations:

Calculate the Spearman's rank correlation coefficient.

Given the data for two variables $X$ and $Y$:

$X:5,7,3,9,1$ $Y:10,14,6,18,2$

Calculate the Spearman's rank correlation coefficient, $r_s$.

Calculate the Spearman's rank correlation coefficient for the following data:

For the following data set:

$X:15,18,21,24,27$ $Y:10,8,6,4,2$

Calculate the Spearman's rank correlation coefficient.

Given $X=\{11,22,33,44,55\}$ and $Y=\{5,15,25,35,45\}$, calculate the Spearman's rank correlation coefficient, $r_s$.

Calculate the Spearman's rank correlation coefficient for the following data, which contains ties:

$X=40,42,39,45,42,38$ $Y=205,195,200,175,205,215$

Assign tied ranks by taking their average.

A study records hours studied and test scores for 7 students as follows:

Hours ($X$): $2,4,1,5,3,6,7$ Scores ($Y$): $50,80,45,90,70,85,60$

Calculate the Spearman's rank correlation coefficient for this data.