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

Given $X = 11,22,33,44,55$ and $Y = 5,15,25,35,45$, 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.

For the data
$X = 15,18,21,24,27$
$Y = 10,8,6,4,2$
calculate the Spearman's rank correlation coefficient.

Compute the Spearman's rank correlation coefficient for the data: $X = 82,96,75,88,92,85$
$Y = 33,38,30,36,35,34$.

Compute the Spearman's rank correlation coefficient for
$X = 10,12,15,13,14,11$
$Y = 8,9,11,10,12,7$.

Given ranks directly:

Obs: $1, 2, 3, 4, 5, 6, 7, 8$
$R_X$: 1, 2, 3, 4, 5, 6, 7, 8
$R_Y$: 2, 1, 4, 3, 6, 5, 8, 7

Calculate the Spearman's rank correlation coefficient.

The ranks for variables $X$ and $Y$ for 7 observations are:

Obs: $1, 2, 3, 4, 5, 6, 7$
$R_X$: 1, 3, 4, 2, 5, 7, 6
$R_Y$: 2, 4, 5, 1, 3, 6, 7

Calculate the Spearman's rank correlation coefficient.

The exam ranks ($R_X$) and project ranks ($R_Y$) for 10 students are listed below. Calculate the Spearman's rank correlation coefficient.

Obs: 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

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

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

Calculate the Spearman's rank correlation coefficient.

Given the paired data
$X = 23,31,27,45,29,33,41,37$
$Y = 15,20,18,25,22,19,24,21$, calculate the Spearman's rank correlation coefficient.

Compute the Spearman's rank correlation coefficient for the data with ties:

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

Assign tied ranks by average.

For data with tied ranks:

$X = 10,12,12,14,16,16,18,20$ $Y = 32,30,34,32,38,36,36,40$

Compute the Spearman's rank correlation coefficient.