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The coefficient of correlation between two variables X and Y is 0.48. The covariance is 36. The variance of X is 16. The standard deviation of Y is:
- a)10.15
- b)13.32
- c)16.5
- d)18.75
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The coefficient of correlation between two variables X and Y is 0.48. ...
Given:
- Coefficient of correlation (r) between X and Y = 0.48
- Covariance (cov) between X and Y = 36
- Variance (var) of X = 16
To find:
- Standard deviation (sd) of Y
Formula:
- Covariance (cov) = r * sd(X) * sd(Y)
Calculation:
Given that the covariance (cov) between X and Y is 36, we can use the formula for covariance to find the product of the standard deviations:
36 = 0.48 * sd(X) * sd(Y)
We also know that the variance (var) of X is 16, and the variance is equal to the square of the standard deviation:
var(X) = sd(X)^2
16 = sd(X)^2
Taking the square root of both sides, we can find the standard deviation of X:
sd(X) = √16 = 4
Now, substituting the value of sd(X) in the covariance formula:
36 = 0.48 * 4 * sd(Y)
Simplifying the equation:
36 = 1.92 * sd(Y)
Dividing both sides by 1.92:
sd(Y) = 36 / 1.92 = 18.75
Therefore, the standard deviation of Y is 18.75.
Answer:
The correct answer is option 'D' - 18.75.
- Coefficient of correlation (r) between X and Y = 0.48
- Covariance (cov) between X and Y = 36
- Variance (var) of X = 16
To find:
- Standard deviation (sd) of Y
Formula:
- Covariance (cov) = r * sd(X) * sd(Y)
Calculation:
Given that the covariance (cov) between X and Y is 36, we can use the formula for covariance to find the product of the standard deviations:
36 = 0.48 * sd(X) * sd(Y)
We also know that the variance (var) of X is 16, and the variance is equal to the square of the standard deviation:
var(X) = sd(X)^2
16 = sd(X)^2
Taking the square root of both sides, we can find the standard deviation of X:
sd(X) = √16 = 4
Now, substituting the value of sd(X) in the covariance formula:
36 = 0.48 * 4 * sd(Y)
Simplifying the equation:
36 = 1.92 * sd(Y)
Dividing both sides by 1.92:
sd(Y) = 36 / 1.92 = 18.75
Therefore, the standard deviation of Y is 18.75.
Answer:
The correct answer is option 'D' - 18.75.
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Community Answer
The coefficient of correlation between two variables X and Y is 0.48. ...
Given
σx = √16 = 4
r = 0.48
Covariance = ∑xy/N = 36
Fomula
Covariance = ∑xy/N
r = ∑xy/N.σx × σy
Calculation
According to question
⇒ 0.48 = 36/4 × σy
⇒ σy = 9/0.48
∴ The standard deviation of y(σy) is 18.75
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The coefficient of correlation between two variables X and Y is 0.48. The covariance is 36. The variance of X is 16. The standard deviation of Y is:a)10.15b)13.32c)16.5d)18.75Correct answer is option 'D'. Can you explain this answer?
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