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The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation is
- a)0.48
- b)0.78
- c)0.87
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The value of covariance of two variables x and y is -(148/3) and the v...
Given,
Covariance of x and y, Cov(x,y) = -(148/3)
Variance of x, Var(x) = (272/3)
Variance of y, Var(y) = (131/3)
We need to find the coefficient of correlation between x and y.
Formula to calculate coefficient of correlation:
r = Cov(x,y) / (σx * σy)
where,
Cov(x,y) = covariance of x and y
σx = standard deviation of x
σy = standard deviation of y
Steps to solve the problem:
1. Calculate the standard deviation of x and y.
σx = √Var(x) = √(272/3) = 8.28
σy = √Var(y) = √(131/3) = 6.07
2. Substitute the given values in the formula of r
r = Cov(x,y) / (σx * σy)
r = -(148/3) / (8.28 * 6.07)
r = -0.31
3. Check the options given and choose the correct answer.
The calculated value of r is negative and its absolute value is less than 0.5. None of the options given match with the calculated value. Hence, the correct answer is option 'D' (none of these).
Note: The absolute value of the coefficient of correlation ranges from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation. A negative value of r indicates a negative correlation between x and y, while a positive value indicates a positive correlation.
Covariance of x and y, Cov(x,y) = -(148/3)
Variance of x, Var(x) = (272/3)
Variance of y, Var(y) = (131/3)
We need to find the coefficient of correlation between x and y.
Formula to calculate coefficient of correlation:
r = Cov(x,y) / (σx * σy)
where,
Cov(x,y) = covariance of x and y
σx = standard deviation of x
σy = standard deviation of y
Steps to solve the problem:
1. Calculate the standard deviation of x and y.
σx = √Var(x) = √(272/3) = 8.28
σy = √Var(y) = √(131/3) = 6.07
2. Substitute the given values in the formula of r
r = Cov(x,y) / (σx * σy)
r = -(148/3) / (8.28 * 6.07)
r = -0.31
3. Check the options given and choose the correct answer.
The calculated value of r is negative and its absolute value is less than 0.5. None of the options given match with the calculated value. Hence, the correct answer is option 'D' (none of these).
Note: The absolute value of the coefficient of correlation ranges from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation. A negative value of r indicates a negative correlation between x and y, while a positive value indicates a positive correlation.
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The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation isa)0.48b)0.78c)0.87d)none of theseCorrect answer is option 'D'. Can you explain this answer?
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The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation isa)0.48b)0.78c)0.87d)none of theseCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation isa)0.48b)0.78c)0.87d)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation isa)0.48b)0.78c)0.87d)none of theseCorrect answer is option 'D'. Can you explain this answer?.
The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation isa)0.48b)0.78c)0.87d)none of theseCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation isa)0.48b)0.78c)0.87d)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation isa)0.48b)0.78c)0.87d)none of theseCorrect answer is option 'D'. Can you explain this answer?.
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