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If x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then sd of y is?
Most Upvoted Answer
If x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then...
Given:
x and y are perfectly related by 2x + 3y + 4 = 0
Standard deviation of x is 6
To Find:
Standard deviation of y
Solution:
Step 1: Finding the correlation coefficient between x and y
From the given relation, 2x + 3y + 4 = 0, we can rewrite it as 2x = -3y - 4.
Dividing by -3, we get: x = (-3/2)y - 2(2/3)
This is the equation of a straight line in slope-intercept form, where the slope is -3/2 and the y-intercept is -2(2/3).
The correlation coefficient between x and y is given by the formula:
r = -1 * (slope of the line)
Therefore, r = -1 * (-3/2) = 3/2
Step 2: Using the formula to find the standard deviation of y
The formula for the standard deviation of y is:
SD(y) = SD(x) / |r|
Substituting the given values, we get:
SD(y) = 6 / (3/2) = 4
Therefore, the standard deviation of y is 4.
Conclusion:
The standard deviation of y is 4 when x and y are perfectly related by 2x + 3y + 4 = 0 and the standard deviation of x is 6.
x and y are perfectly related by 2x + 3y + 4 = 0
Standard deviation of x is 6
To Find:
Standard deviation of y
Solution:
Step 1: Finding the correlation coefficient between x and y
From the given relation, 2x + 3y + 4 = 0, we can rewrite it as 2x = -3y - 4.
Dividing by -3, we get: x = (-3/2)y - 2(2/3)
This is the equation of a straight line in slope-intercept form, where the slope is -3/2 and the y-intercept is -2(2/3).
The correlation coefficient between x and y is given by the formula:
r = -1 * (slope of the line)
Therefore, r = -1 * (-3/2) = 3/2
Step 2: Using the formula to find the standard deviation of y
The formula for the standard deviation of y is:
SD(y) = SD(x) / |r|
Substituting the given values, we get:
SD(y) = 6 / (3/2) = 4
Therefore, the standard deviation of y is 4.
Conclusion:
The standard deviation of y is 4 when x and y are perfectly related by 2x + 3y + 4 = 0 and the standard deviation of x is 6.
Community Answer
If x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then...
SD of X is 6
2x+3y+4=0
to find SD of y we eliminate constant term
therefore 2x=|3y|
2(6)=3y
12=3y
therefore SD of y is 4
2x+3y+4=0
to find SD of y we eliminate constant term
therefore 2x=|3y|
2(6)=3y
12=3y
therefore SD of y is 4
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If x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then sd of y is?
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If x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then sd of y is? 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 x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then sd of y is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then sd of y is?.
If x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then sd of y is? 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 x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then sd of y is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are perfectly related by 2x 3y 4= 0 and sd of x is 6 then sd of y is?.
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