Find the rank correlation coefficient from the following marks awarded by the examiners in statistics: R.Nos.: 1 2 3 4 5 6 7 8 9 10 11 Marks Awarded by Examiner A: 24 29 19 14 30 19 27 30 20 28 11 Marks Awarded by Examiner B: 37 35 16 26 23 27 19 20 16 11 21 Marks Awarded by Examiner C: 30 28 20 25 25 30 20 24 22 29 15?

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Rank Correlation Coefficient in Statistics

Introduction:
Rank correlation coefficient is a statistical measure that determines the degree of similarity or dissimilarity between two sets of rankings. It is used to establish the degree of association between two variables or factors. The rank correlation coefficient ranges from -1 to +1, and the closer the value is to +1 or -1, the stronger the association.

Given Data:
R.Nos.: 1 2 3 4 5 6 7 8 9 10 11
Marks Awarded by Examiner A: 24 29 19 14 30 19 27 30 20 28 11
Marks Awarded by Examiner B: 37 35 16 26 23 27 19 20 16 11 21
Marks Awarded by Examiner C: 30 28 20 25 25 30 20 24 22 29 15

Steps to Calculate Rank Correlation Coefficient:

Step 1: Assign ranks to the data in each set. For example:
Marks Awarded by Examiner A: 7 9 3 1 10 3 6 10 4 8 2
Marks Awarded by Examiner B: 11 10 2 6 4 6 1 3 2 1 5
Marks Awarded by Examiner C: 9 8 4 6 6 9 4 7 5 10 1

Step 2: Calculate the difference between the ranks in each set. For example:
Marks Awarded by Examiner A: 0 0 0 0 0 0 0 0 0 0 0
Marks Awarded by Examiner B: 0 0 -2 0 -6 0 10 7 14 10 0
Marks Awarded by Examiner C: 0 0 -1 0 0 0 -3 -1 -1 0 8

Step 3: Calculate the square of the differences in each set. For example:
Marks Awarded by Examiner A: 0 0 0 0 0 0 0 0 0 0 0
Marks Awarded by Examiner B: 0 0 4 0 36 0 100 49 196 100 0
Marks Awarded by Examiner C: 0 0 1 0 0 0 9 1 1 0 64

Step 4: Calculate the sum of the squares of the differences in each set. For example:
Marks Awarded by Examiner A: 0
Marks Awarded by Examiner B: 385
Marks Awarded by Examiner C: 76

Step 5: Calculate the rank correlation coefficient using the formula:
r = 1 - (6 * sum of squares of differences) / (n * (n^2 - 1))
where n is the number of rankings.

Applying the formula, we get:
r = 1 - (6 * 76) / (11 * (11^2 - 1))
r = 1 - (456 / 1210)
r = 0.623

Conclusion:
Therefore, the rank correlation coefficient between the marks awarded by Examiner A, B, and C is 0.623,

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