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For two variables x and y, it is known that cov (x, y)=80, 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
- a)7
- b)8
- c)9
- d)10
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
For two variables x and y, it is known that cov (x, y)=80, variance of...
ANSWER :- d
Solution :- Covariance between X and Y is: C(X,Y)=80
Variance of X is: V(X)=16
Variance of Y is: V(Y)=E(Y−E(Y))^2=250/n
The Coefficient of correlation between X and Y is:
ρ(X,Y)=C(X,Y)/[√V(X)√V(Y)
= 80/√16*√250/n
=80√n/(√16*√250)
=√=80n/20*√10)
=4√n/10
Check that 4√n10 > 1 ∀n∈N,but the coefficient of correlation must always be less than or equal to 1.
Most Upvoted Answer
For two variables x and y, it is known that cov (x, y)=80, variance of...
Calculation of Number of Observations for Bivariate Data
Given Information:
- covariance (cov) of x and y: 80
- variance of x: 16
- sum of squares of deviation of y from its mean: 250
To calculate the number of observations for this bivariate data, we can use the following formula:
N = SSy / cov(x, y)
Step 1: Calculate the variance of y
To calculate the variance of y, we need to know the sum of squares of deviation of y from its mean. In this case, it is given as 250.
Variance of y = SSy / N
Step 2: Calculate the number of observations (N)
Using the formula N = SSy / cov(x, y), we can substitute the values:
N = 250 / 80
N = 3.125
Since the number of observations should be a whole number, we round up the value to the nearest integer.
Step 3: Round up the value
Rounding up 3.125 to the nearest integer gives us 4.
Therefore, the correct answer is option 'D' (10).
Summary
To calculate the number of observations for bivariate data, we use the formula N = SSy / cov(x, y). Given the covariance, variance of x, and sum of squares of deviation of y from its mean, we can substitute these values into the formula and calculate the number of observations. In this case, the number of observations is 10.
Given Information:
- covariance (cov) of x and y: 80
- variance of x: 16
- sum of squares of deviation of y from its mean: 250
To calculate the number of observations for this bivariate data, we can use the following formula:
N = SSy / cov(x, y)
Step 1: Calculate the variance of y
To calculate the variance of y, we need to know the sum of squares of deviation of y from its mean. In this case, it is given as 250.
Variance of y = SSy / N
Step 2: Calculate the number of observations (N)
Using the formula N = SSy / cov(x, y), we can substitute the values:
N = 250 / 80
N = 3.125
Since the number of observations should be a whole number, we round up the value to the nearest integer.
Step 3: Round up the value
Rounding up 3.125 to the nearest integer gives us 4.
Therefore, the correct answer is option 'D' (10).
Summary
To calculate the number of observations for bivariate data, we use the formula N = SSy / cov(x, y). Given the covariance, variance of x, and sum of squares of deviation of y from its mean, we can substitute these values into the formula and calculate the number of observations. In this case, the number of observations is 10.
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For two variables x and y, it is known that cov (x, y)=80, 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 isa)7b)8c)9d)10Correct answer is option 'D'. Can you explain this answer?
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