Question

how to calculate the coefficient of rank correlation from the following data x 48 33 40 9 16 16 65 24 16 57 y 13 13 24 6 15 4 20 9 6 19​

Answer 1

Answer :

The coefficient of rank correlation, r, is -0.44.

Explanation :

The coefficient of rank correlation, also known as Spearman's rank correlation coefficient, measures the strength and direction of the relationship between two variables when they are measured on an ordinal or continuous scale. To calculate the coefficient of rank correlation, you need to rank the values of both variables, calculate the difference in ranks between each corresponding pair of values, and then find the correlation between these differences.

Here is the step-by-step process to calculate the coefficient of rank correlation for the data given above:

1.Rank the values of X and Y:

Rank X: 9 16 16 24 33 40 48 57 65

Rank Y: 4 6 6 9 13 13 19 20 24

2.Calculate the difference in ranks between each pair of values:

d = |Rank X - Rank Y|

d = |9 - 4| = 5

d = |16 - 6| = 10

d = |16 - 6| = 10

d = |24 - 9| = 15

d = |33 - 13| = 20

d = |40 - 13| = 27

d = |48 - 19| = 29

d = |57 - 20| = 37

d = |65 - 24| = 41

3.Square the differences:

d^2 = 25, 100, 100, 225, 400, 729, 841, 1369, 1681

4.Sum the squared differences:

d^2 = 5600

5.Divide the sum of the squared differences by the number of pairs of values (n - 1), where n is the number of values in each variable:

r = 1 - (6 * 5600) / (9 * (9 - 1))

r = 1 - 3200 / 72

r = 1 - 44.44

r = -0.44

The coefficient of rank correlation, r, is -0.44. This indicates that there is a weak negative relationship between the two variables, meaning that as the values of X increase, the values of Y tend to decrease. The negative sign indicates the direction of the relationship, while the absolute value of r (i.e., 0.44) indicates the strength of the relationship.

To know more about the concept please go through the links :

https://brainly.in/question/44949002

https://brainly.in/question/24050396

#SPJ3