Ok so, 1, 5, 17, and 53. what's my rule?

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:

where, is mean of X

and  is mean of Y

Firstly calculating . We get,

= 9.5

= 12.375

Now, Putting all values in above formula. We get,

Sample Covariance = -8.64

b. Standard Deviation is the square root of sum of square of the distance of observation from the mean.  

where, is mean of the distribution.

Using formula we get,

Standard deviation = 4.81

c. Using above formula we get,

Standard deviation = 7.21

d. Correlation Coefficient is calculate by using formula:

where, = Covariance of X and Y

= Standard Deviation of X

= Standard Deviation of Y

Putting all values in above formula, we get,

Correlation Coefficient = -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.