Asked by Sudhir Sharma on Sep 24, 2024
Verified
If the standard deviation of x is 18,the covariance of x and y is 120,the coefficient r = 0.90,then the standard deviation of y is 54.87.
Standard Deviation
A measure that is used to quantify the amount of variation or dispersion of a set of data values.
Covariance
A measure indicating the extent to which two random variables change together.
Coefficient R
A measure used in statistics to represent the strength and direction of a linear relationship between two variables on a scatter plot.
- Compute the correlation coefficient using the provided data and comprehend its importance.
Verified Answer
JC
Jacob Carmona2 days ago
Final Answer :
False
Explanation :
Given that the coefficient of correlation r=0.90r = 0.90r=0.90 , the covariance of xxx and yyy is 120120120 , and the standard deviation of xxx is 181818 , we can find the standard deviation of yyy ( σy\sigma_yσy ) using the formula for the correlation coefficient r=cov(x,y)σxσyr = \frac{cov(x, y)}{\sigma_x \sigma_y}r=σxσycov(x,y) . Rearranging this formula to solve for σy\sigma_yσy gives σy=cov(x,y)r⋅σx\sigma_y = \frac{cov(x, y)}{r \cdot \sigma_x}σy=r⋅σxcov(x,y) . Plugging in the given values, σy=1200.90⋅18=12016.2=7.41\sigma_y = \frac{120}{0.90 \cdot 18} = \frac{120}{16.2} = 7.41σy=0.90⋅18120=16.2120=7.41 , not 54.8754.8754.87 .
Learning Objectives
- Compute the correlation coefficient using the provided data and comprehend its importance.