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The rank correlation coefficients between two variables is 0.50, Sum of the squares of the difference in ranks is82.5. Find the number of pairs of observations.?
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The rank correlation coefficients between two variables is 0.50, Sum o...
Calculation of number of pairs of observations
Given:
- Rank correlation coefficient (ρ) = 0.50
- Sum of the squares of the difference in ranks = 82.5
Formula:
- \( \rho = 1 - \frac{6 \sum d^2}{n(n^2 - 1)} \)
Calculation:
- Given \( \rho = 0.50 \) and \( \sum d^2 = 82.5 \)
- Substituting the values in the formula, we get:
\( 0.50 = 1 - \frac{6 \times 82.5}{n(n^2 - 1)} \)
\( 0.50 = 1 - \frac{495}{n(n^2 - 1)} \)
\( 0.50 = \frac{n(n^2 - 1) - 495}{n(n^2 - 1)} \)
\( 0.50n(n^2 - 1) = n(n^2 - 1) - 495 \)
\( 0.50n^3 - 0.50n = n^3 - n - 495 \)
\( 0.50n^3 - n^3 = -0.50n - 495 \)
\( -0.50n^3 = -0.50n - 495 \)
\( n^3 = n + 990 \)
Solving for n:
- By trial and error method, we find that n = 10 satisfies the equation.
- Therefore, the number of pairs of observations is 10.
Conclusion:
- The number of pairs of observations is 10.
Given:
- Rank correlation coefficient (ρ) = 0.50
- Sum of the squares of the difference in ranks = 82.5
Formula:
- \( \rho = 1 - \frac{6 \sum d^2}{n(n^2 - 1)} \)
Calculation:
- Given \( \rho = 0.50 \) and \( \sum d^2 = 82.5 \)
- Substituting the values in the formula, we get:
\( 0.50 = 1 - \frac{6 \times 82.5}{n(n^2 - 1)} \)
\( 0.50 = 1 - \frac{495}{n(n^2 - 1)} \)
\( 0.50 = \frac{n(n^2 - 1) - 495}{n(n^2 - 1)} \)
\( 0.50n(n^2 - 1) = n(n^2 - 1) - 495 \)
\( 0.50n^3 - 0.50n = n^3 - n - 495 \)
\( 0.50n^3 - n^3 = -0.50n - 495 \)
\( -0.50n^3 = -0.50n - 495 \)
\( n^3 = n + 990 \)
Solving for n:
- By trial and error method, we find that n = 10 satisfies the equation.
- Therefore, the number of pairs of observations is 10.
Conclusion:
- The number of pairs of observations is 10.
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The rank correlation coefficients between two variables is 0.50, Sum of the squares of the difference in ranks is82.5. Find the number of pairs of observations.?
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The rank correlation coefficients between two variables is 0.50, Sum of the squares of the difference in ranks is82.5. Find the number of pairs of observations.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The rank correlation coefficients between two variables is 0.50, Sum of the squares of the difference in ranks is82.5. Find the number of pairs of observations.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rank correlation coefficients between two variables is 0.50, Sum of the squares of the difference in ranks is82.5. Find the number of pairs of observations.?.
The rank correlation coefficients between two variables is 0.50, Sum of the squares of the difference in ranks is82.5. Find the number of pairs of observations.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The rank correlation coefficients between two variables is 0.50, Sum of the squares of the difference in ranks is82.5. Find the number of pairs of observations.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rank correlation coefficients between two variables is 0.50, Sum of the squares of the difference in ranks is82.5. Find the number of pairs of observations.?.
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