Solution:

Given data:

X: 6, 2, 10, 4, 8
Y: 9, 11, ?, 8, 7, 6, 8

To find:

Coefficient of correlation between X and Y and arithmetic means of X and Y series.

Step 1: Calculate the mean of X and Y series

Mean of X series = (6+2+10+4+8)/5 = 6
Mean of Y series = (9+11+?+8+7+6+8)/7 = (49+?)/7

Step 2: Calculate the missing value of Y

We know that the mean of Y series is (49+?)/7.
Therefore, (49+?)/7 = 8.5 (as we assume that the mean of Y series is equal to 8.5)
49+? = 59.5
?= 10.5

Therefore, the missing value of Y is 10.5.

Step 3: Calculate the deviation of X and Y from their respective means

X series: 6, 2, 10, 4, 8
Y series: 9, 11, 10.5, 8, 7, 6, 8

Deviation of X series = (-4, -4, 4, -2, 2)
Deviation of Y series = (0, 1.5, 2, -0.5, -1.5, -2.5, -0.5)

Step 4: Calculate the product of deviations of X and Y

X deviation * Y deviation:
(-4*0), (-4*1.5), (4*2), (-2*-0.5), (2*-1.5), = [0, -6, 8, 1, -3]

Step 5: Calculate the sum of the product of deviations of X and Y

Sum of (X deviation * Y deviation) = 0+(-6)+8+1+(-3) = 0

Step 6: Calculate the sum of squares of deviations of X and Y

Sum of X deviation^2: 16+16+16+4+4 = 56
Sum of Y deviation^2: 0+2.25+4+0.25+2.25+6.25+0.25 = 15.5

Step 7: Calculate the coefficient of correlation

r = [n*(sum of X deviation * Y deviation) - (sum of X deviation)*(sum of Y deviation)] / [sqrt(n*sum of X deviation^2 - (sum of X deviation)^2) * sqrt(n*sum of Y deviation^2 - (sum of Y deviation)^2)]
r = [5*(0) - (0)*(0)] / [sqrt(5*56 - (0)^2) * sqrt(5*15.5 - (0)^2)]
r = 0 / (sqrt(280) * sqrt(77.5))
r = 0

Therefore, the coefficient of correlation between X and Y is 0, which indicates no linear relationship between the two variables.

Arithmetic means of X and Y series are 6 and 8.5 respectively.

Conclusion:

The coefficient of correlation between X