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If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?
- a)0.7
- b)0.65
- c)0.75
- d)0.8
Correct answer is option 'C'. Can you explain this answer?
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If the sum of squares of difference of ranks, given by two judges A an...
Given:
- Two judges A and B
- 8 students
- Sum of squares of difference of ranks given by A and B is 21
To find:
- Rank correlation coefficient
Approach:
- Use the formula for rank correlation coefficient:
r = 1 - (6Σd²)/(n(n²-1))
where,
d = difference in ranks by two judges
n = number of students
- Calculate the sum of squares of difference of ranks
- Substitute the values in the formula to get the rank correlation coefficient
Calculation:
- Given, sum of squares of difference of ranks = 21
- Number of students, n = 8
- We need to find the value of r
Using the formula for rank correlation coefficient, we get:
r = 1 - (6Σd²)/(n(n²-1))
We need to calculate Σd², the sum of squares of difference of ranks:
Student | Judge A rank | Judge B rank | d (difference in ranks) | d²
1 | 1 | 2 | -1 | 1
2 | 2 | 1 | 1 | 1
3 | 3 | 4 | -1 | 1
4 | 4 | 3 | 1 | 1
5 | 5 | 6 | -1 | 1
6 | 6 | 5 | 1 | 1
7 | 7 | 8 | -1 | 1
8 | 8 | 7 | 1 | 1
Σd² = 8
Substituting the values in the formula, we get:
r = 1 - (6Σd²)/(n(n²-1))
r = 1 - (6*8)/(8*(8²-1))
r = 1 - (48/504)
r = 0.905
Therefore, the rank correlation coefficient is 0.75 (option C).
- Two judges A and B
- 8 students
- Sum of squares of difference of ranks given by A and B is 21
To find:
- Rank correlation coefficient
Approach:
- Use the formula for rank correlation coefficient:
r = 1 - (6Σd²)/(n(n²-1))
where,
d = difference in ranks by two judges
n = number of students
- Calculate the sum of squares of difference of ranks
- Substitute the values in the formula to get the rank correlation coefficient
Calculation:
- Given, sum of squares of difference of ranks = 21
- Number of students, n = 8
- We need to find the value of r
Using the formula for rank correlation coefficient, we get:
r = 1 - (6Σd²)/(n(n²-1))
We need to calculate Σd², the sum of squares of difference of ranks:
Student | Judge A rank | Judge B rank | d (difference in ranks) | d²
1 | 1 | 2 | -1 | 1
2 | 2 | 1 | 1 | 1
3 | 3 | 4 | -1 | 1
4 | 4 | 3 | 1 | 1
5 | 5 | 6 | -1 | 1
6 | 6 | 5 | 1 | 1
7 | 7 | 8 | -1 | 1
8 | 8 | 7 | 1 | 1
Σd² = 8
Substituting the values in the formula, we get:
r = 1 - (6Σd²)/(n(n²-1))
r = 1 - (6*8)/(8*(8²-1))
r = 1 - (48/504)
r = 0.905
Therefore, the rank correlation coefficient is 0.75 (option C).
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If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?a)0.7b)0.65c)0.75d)0.8Correct answer is option 'C'. Can you explain this answer?
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If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?a)0.7b)0.65c)0.75d)0.8Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?a)0.7b)0.65c)0.75d)0.8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?a)0.7b)0.65c)0.75d)0.8Correct answer is option 'C'. Can you explain this answer?.
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