Answer :
Answer:
The given data is:
x = (2, 7, 6, 10, 9, 13, 11, 18)
y = (11, 21, 12, 25, 7, 12, 4, 7)
a. The formula used for Sample Covariance is:
[tex]S_{XY}=\frac{\sum_{i=1}^{n}(X_{i}-\bar{X})(Y_{i}-\bar{Y})}{n-1}[/tex]
where, [tex]\bar{X}[/tex] is mean of X
and [tex]\bar{Y}[/tex] is mean of Y
Firstly calculating [tex]\bar{X} and \bar{Y}[/tex]. We get,
[tex]\bar{X}[/tex] = 9.5
[tex]\bar{Y}[/tex] = 12.375
Now, Putting all values in above formula. We get,
Sample Covariance [tex]S_{XY}[/tex] = -8.64
b. Standard Deviation is the square root of sum of square of the distance of observation from the mean.
[tex] Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }[/tex]
where, [tex]\bar{x}[/tex] is mean of the distribution.
Using formula we get,
Standard deviation [tex](\sigma_{X})[/tex] = 4.81
c. Using above formula we get,
Standard deviation [tex](\sigma_{Y})[/tex] = 7.21
d. Correlation Coefficient is calculate by using formula:
[tex]r_{xy}=\frac{S_{XY}}{S_{X}S_{Y}}[/tex]
where, [tex]S_{XY}[/tex] = Covariance of X and Y
[tex]S_{X}[/tex] = Standard Deviation of X
[tex]S_{Y}[/tex] = Standard Deviation of Y
Putting all values in above formula, we get,
Correlation Coefficient [tex](r_{xy})[/tex] = -0.25
Correlation Coefficient tell us that X and Y has negative week relationship whereas Sample Covariance tell us that X and Y has negative relationship. It does not tell us strength of relationship.