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Question 1

The following table shows the values of two variables, $X$ and $Y$ :

\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline X & 10 & 12 & 12 & 14 & 16 & 16 & 18 & 20 \\ \hline Y & 32 & 30 & 34 & 32 & 38 & 36 & 36 & 40 \\ \hline \end{array}

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

[6]

Question 2

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

\begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Observation} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline R_X & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline R_Y & 2 & 1 & 4 & 3 & 6 & 5 & 8 & 7 \\ \hline \end{array}

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

[4]

Question 3

Given the following paired data:

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

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

[6]

Question 4

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

Student	1	2	3	4	5	6	7	8	9	10
$R_X$	1	2	3	4	5	6	7	8	9	10
$R_Y$	2	1	4	3	6	5	8	7	10	9

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

[3]

Question 5

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

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

[5]

Question 6

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

Observation	1	2	3	4	5	6	7
$R_X$	1	3	4	2	5	7	6
$R_Y$	2	4	5	1	3	6	7

Calculate the Spearman's rank correlation coefficient.

[4]

Question 7

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, $r_s$ .

[5]

Question 8

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

$X$	10	12	15	13	14	11
$Y$	8	9	11	10	12	7

[6]

Question 9

For the following data set:

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

Calculate the Spearman's rank correlation coefficient.

[4]

Question 10

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

[4]

Question 11

Spearman's rank correlation coefficient calculation with tied data ranks.

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.

[6]

Question 12

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.

[5]

Question Type 2: Finding the Spearman's Rank Coefficient using rank tables Exercises