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. For two variables x and y, it is known that cov (x, y) = 8, r = 0.4, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is?
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. For two variables x and y, it is known that cov (x, y) = 8, r = 0.4,...
Given:
- cov(x, y) = 8
- r = 0.4
- Variance of x = 16
- Sum of squares of deviation of y from its mean = 250
To Find:
- Number of observations for this bivariate data
Explanation:
To find the number of observations for this bivariate data, we can use the formula for the sample correlation coefficient (r):
r = cov(x, y) / (σx * σy)
Where cov(x, y) is the covariance of x and y, σx is the standard deviation of x, and σy is the standard deviation of y.
Step 1: Calculate the standard deviation of x (σx):
The variance of x is given as 16. The standard deviation (σx) is the square root of the variance.
σx = √(variance of x) = √16 = 4
Step 2: Calculate the standard deviation of y (σy):
To calculate the standard deviation of y, we need to find the variance of y. The variance of y can be calculated using the sum of squares of deviation of y from its mean.
variance of y = sum of squares of deviation of y from its mean / (n - 1)
where n is the number of observations.
Given, sum of squares of deviation of y from its mean = 250.
Using the above formula, we can find the variance of y:
variance of y = 250 / (n - 1)
Step 3: Calculate the covariance of x and y:
The covariance of x and y is given as 8.
cov(x, y) = 8
Step 4: Calculate the number of observations (n):
Now, we can substitute the values into the formula for the sample correlation coefficient and solve for n.
r = cov(x, y) / (σx * σy)
0.4 = 8 / (4 * σy)
0.4 = 2 / σy
σy = 2 / 0.4
σy = 5
Using the formula for the variance of y:
variance of y = 250 / (n - 1)
5^2 = 250 / (n - 1)
25 = 250 / (n - 1)
n - 1 = 250 / 25
n - 1 = 10
n = 10 + 1
n = 11
Therefore, the number of observations for this bivariate data is 11.
- cov(x, y) = 8
- r = 0.4
- Variance of x = 16
- Sum of squares of deviation of y from its mean = 250
To Find:
- Number of observations for this bivariate data
Explanation:
To find the number of observations for this bivariate data, we can use the formula for the sample correlation coefficient (r):
r = cov(x, y) / (σx * σy)
Where cov(x, y) is the covariance of x and y, σx is the standard deviation of x, and σy is the standard deviation of y.
Step 1: Calculate the standard deviation of x (σx):
The variance of x is given as 16. The standard deviation (σx) is the square root of the variance.
σx = √(variance of x) = √16 = 4
Step 2: Calculate the standard deviation of y (σy):
To calculate the standard deviation of y, we need to find the variance of y. The variance of y can be calculated using the sum of squares of deviation of y from its mean.
variance of y = sum of squares of deviation of y from its mean / (n - 1)
where n is the number of observations.
Given, sum of squares of deviation of y from its mean = 250.
Using the above formula, we can find the variance of y:
variance of y = 250 / (n - 1)
Step 3: Calculate the covariance of x and y:
The covariance of x and y is given as 8.
cov(x, y) = 8
Step 4: Calculate the number of observations (n):
Now, we can substitute the values into the formula for the sample correlation coefficient and solve for n.
r = cov(x, y) / (σx * σy)
0.4 = 8 / (4 * σy)
0.4 = 2 / σy
σy = 2 / 0.4
σy = 5
Using the formula for the variance of y:
variance of y = 250 / (n - 1)
5^2 = 250 / (n - 1)
25 = 250 / (n - 1)
n - 1 = 250 / 25
n - 1 = 10
n = 10 + 1
n = 11
Therefore, the number of observations for this bivariate data is 11.
Community Answer
. For two variables x and y, it is known that cov (x, y) = 8, r = 0.4,...
. For two variables x and y, it is known that cov (x, y) = 8, r = 0.4, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is
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. For two variables x and y, it is known that cov (x, y) = 8, r = 0.4, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data 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 . For two variables x and y, it is known that cov (x, y) = 8, r = 0.4, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . For two variables x and y, it is known that cov (x, y) = 8, r = 0.4, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is?.
. For two variables x and y, it is known that cov (x, y) = 8, r = 0.4, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data 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 . For two variables x and y, it is known that cov (x, y) = 8, r = 0.4, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . For two variables x and y, it is known that cov (x, y) = 8, r = 0.4, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is?.
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